DE102014203369B4 - Method and system for compensating system errors between multiple analog-to-digital converters - Google Patents

Abstract

Method for compensating for mismatches in the transfer function and / or in the sampling time offsets between a plurality of analog-to-digital converters (200, 200, ..., 200) which are sampled with a time offset from one another, by using in each first time-variant compensation filter (100, 100 ,. .., 100; 100), each of which is connected downstream of an analog-to-digital converter, each time a cyclically time-variant convolution of a certain number (L) of the associated analog-to-digital converter (200, 200, ..., 200) generated Sample values with a certain number (B) of filter coefficients, characterized in that each first time-variant compensation filter (100,100, ..., 100; 100) each with a plurality of second time-invariant compensation filters (2,2,2, ..., 2) each have a minimized number (B) of filter coefficients, which in each case in the same cycle a time-invariant partial filtering of the cyclic time-variant convolution of the first time-variant compensation filter (100,100, ..., 100; 100) corresponding filtering.

Description

The invention relates to a method and a system for compensating for system errors between a plurality of analog-to-digital transducers scanning at different times with respect to one another.

In today's communication technology increasingly signals with a higher sampling rate - typically a few gigahertz - used. To measure these high-frequency signals in a measuring device - for example in a digital oscilloscope - in real time, the signal processing in the measuring device is parallelized. The parallelization of the analog-to-digital conversion of the measurement signal leads to parallel-connected analog-to-digital converters, each time offset from each other (so-called time-interleaved analog-to-digital converter). In this way, analog-to-digital converters can be used with a realizable sampling rate, which is reduced by the number of parallel-connected analog-to-digital converters compared to the sampling rate of the signal to be measured.

In order for the analog-to-digital conversion of the analog signal to be measured in the parallel-connected analogue-to-digital converters, which each time offset with respect to each other, leads to a correctly corresponding digital signal, the transfer functions of the individual analog-to-digital converters must be identical, ie the DC voltage Superimpositions (DC components) in the individual analog-to-digital converter channels be identical and have the sampling times of the individual analog-to-digital converters to each other a correct equidistant time offset.

Since this is typically not the case in reality, a respective compensation filter is connected downstream of each individual analog-to-digital converter, which compensates for the mismatches in the transfer functions and in the sampling instantaneous offsets between the individual analog-to-digital converters. In 1 is one of the DE 10 2011 011 711 A1 known system for the compensation of such mismatches in real parallel connected A / D converters shown. By contrast, the mismatching in the DC superimposition is typically compensated for by a subtractor respectively connected downstream of the individual compensation filters, which connects the respective negative DC voltage superposition to the output signal of the individual compensation filter.

The analog signal x (t) is used in the total of M analog-to-digital converter channels 1 each with the respective analog-to-digital converter 100 ₀ . 100 ₁ , ..., 100 _m-1 appropriate impulse response h ₀ (t) . h ₁ (t) , ..., h _M-1 (t) folded and then with a to the respective analog-to-digital converter 200 ₀ . 200 ₁ , ..., 200 _M-1 associated DC voltage superposition o ₀ . o ₁ , ..., o _M-1 superimposed additively and finally in a symbolically shown as a switch sample and hold element of the respective analog-to-digital converter 200 ₀ . 200 ₁ , ..., 200 _M-1 to the respective analog-to-digital converter 200 ₀ . 200 ₁ , ..., 200 _M-1 corresponding sampling times t / T _A = M · ν + ε ₀ , t / T _A = M · ν + 1 + ε ₁ , ..., t / T _A = M · ν + M-1 + ε _M-1 with the respective analog-to-digital converter 200 ₀ . 200 ₁ , ..., 200 _M-1 associated sample timing offsets ε ₀ , ε ₁ , ..., ε _M-1 sampled. The individual analog-to-digital converters 200 ₀ . 200 ₁ , ..., 200 _M-1 is in each case a compensation filter 100 ₀ . 100 ₁ ... 100 _M-1 Each of the distorted samples at the output of the respective analog-to-digital converter 200 ₀ . 200 ₁ , ..., 200 _M-1 with the associated filter impulse response hc _{, 0} (t) . h _{c, 1} (t) , ..., hc _{, M-1} (t) equalized. Finally, the equalized samples of the output signals of the individual compensation filters 100 ₀ . 100 ₁ , ..., 100 _M-1 in an adder 300 to a single stream of samples x (ν) the originally analog signal x (t) together.

In each of the compensation filters, a certain number of samples of the digital measurement signal generated by the preceding analog-to-digital converter are cyclically convolved with a certain number of filter coefficients. The convolution is composed of additions and multiplications. In order to be able to perform the compensation necessary for the parallelization of the analog-to-digital conversion in real time, the number of additions and multiplications must advantageously be minimized.

In the US Pat. No. 7,049,992 B1 a method according to the preamble of claim 1 for the compensation of mismatches in the transfer function and / or in the sampling times between a plurality of temporally staggered to each other scanning analog-to-digital converters are described with corresponding commentary filters.

Corresponding filters, each with a minimized number of filter coefficients are as such from the document LIN, K. et. al.: "Digital filters for high performance audio delta-sigma analog-to-signal and digital-to-analog conversions", Proceedings of ICSP'96, pages 59-63 basically known. However, this document does not suggest that these filters be used in conjunction with time-shifted analog-to-digital converters.

From the WO 2008/156400 A1 is a method for compensating for fitting error of the transfer function or the impulse response with respect to multi-channel time-shifted analog-to-digital converter known. The compensation is done here with periodic time-varying filters.

The object of the invention is therefore to provide a method and a system for compensating for mismatches in the transfer function and / or in the Abtastzeitpunktversätzen between a plurality of temporally staggered to each other scanning analog-to-digital converters in real time.

The object is achieved by a method according to the invention for compensating for mismatches in the transfer function and / or in the sampling time offsets between a plurality of analog-to-digital converters scanned with a time offset from one another with the features of patent claim 1 and by a corresponding system according to the invention having the features of patent claim 9 , Advantageous technical extensions are listed in the respective dependent claims.

According to the invention, each compensation filter-referred to below as the first compensation filter-is decomposed into a plurality of compensation filters-referred to below as second compensation filters-which each have a minimized number of filter coefficients. By minimizing the filter coefficients within a second compensation filter, the number of additions and multiplications for realizing the convolutions performed in all the second compensation filters is reduced and thus advantageously reduced over the number of additions and multiplications required in the convolution of a corresponding compensation filter according to the prior art real-time implementation of system error compensation realized.

Preferably, the second compensation filters, which belong in each case to a first compensation filter, operate in parallel in order in this way to obtain an additional time gain in the compensation.

The individual second compensation filters are preferably supplied via a supply unit arranged upstream of the individual second compensation filters with the sequences of sample values of the input signal of the first compensation filter which are respectively required for the convolution in the respective second compensation filter.

Correspondingly, the sample values respectively generated by the individual second compensation filters of the first compensation filter are combined in a mating unit connected downstream of the individual second compensation filters to form a single sequence of samples of the output signal of the first compensation filter.

Since a plurality of second compensation filters belonging to a first compensation filter each convolute an identical sequence of samples, or at least an identical subsequence of samples of the input signal of the first compensation filter with their respective filter coefficients, a preferred feed unit is configured to provide them generates identical sequences or partial sequences of samples of the input signal of the first compensation filter only once and supplies the associated second compensation filters in parallel.

The number of second compensation filters and the convolutions respectively performed in the individual second compensation filters, preferably consisting of the sequence of samples of the input signal of the first compensation filter convoluted with the associated filter coefficients of the second compensation filter, which is supplied to the respective second compensation filter, become from the filter equations of FIG pre-structurally determined first compensation filter determined in a two-stage process according to the invention.

In a first stage, in each case a third compensation filter is preferably provided for each phase p of a cycle of sampled values respectively generated in the respective first compensation filter. In the respective third compensation filter, in each case those filterings of the sequence of samples supplied to the first compensation filter in a cycle are used, which are used to determine each polyphase component of the respective phase of the sequence of samples respectively generated by the first compensation filter in a cycle.

In a second stage, the filters of the individual third compensation filters of the first compensation filter are preferably each decomposed into a plurality of sub-filters, each of which realizes a complete convolution and is carried out by a respective second compensation filter. These Second compensation filters are time-invariant in themselves and each have a minimized number of filter coefficients.

Such filters with a minimized number of filter coefficients are preferably referred to as short-length (SL) filters (German: filter with the shortest filter length) and are off Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332 , to further reduce the number of additions and multiplications to be made in terms of minimizing numerical complexity.

The filter coefficients for the individual third compensation filters, which finally yield the filter coefficients for the individual second compensation filters, are preferably determined separately in each case. Thus, the third and second compensation filters each have mutually different filter coefficients. The first compensation filter, which consists of a plurality of second compensation filters connected in parallel in a possible embodiment according to the invention, thus switches between the second compensation filters with respectively different filter coefficients during the successive determination of the polyphase components of the output signal belonging to the individual polyphases and thus represents a time-variant compensation filter The second and third compensation filters each represent time-invariant compensation filters.

The division of the individual polyphase components of the output signal for each polyphase on each of a third compensation filter in the first stage allows a uniform distribution of the individual sections of the folding to be performed in the first compensation filter on every third compensation filter of the first compensation filter. This ensures that in every third compensation filter of the first compensation filter, an equal portion of the transient process, the steady state and the decay process of the entire convolution process is implemented.

The use of only polyphase component of a single polyphase of the entire convolution process in a third compensation filter of the first compensation filter causes the filtering realized in the third compensation filter of the first compensation filter to include an incomplete and thus incomplete convolution. To realize a complete convolution, the filters of every third compensation filter are decomposed into a plurality of sub-filters, which are each realized in a second compensation filter and include a complete convolution for themselves.

• 1 ein Blockdiagramm mit mehreren zeitlich versetzt abtastenden Analog-Digital-Wandlern und zugehörigen Kompensationsfiltern nach dem Stand der Technik,
• 2A ein Blockdiagramm eines Ausführungsbeispiels eines aus mehreren parallelen dritten Kompensationsfiltern bestehenden ersten Kompensationsfilters und eines zugehörigen aus mehreren parallelen zweiten Kompensationsfiltern bestehenden ersten Kompensationsfilters,
• 2B ein detaillierteres Blockschaltbild, welches 2A entspricht,
• 3 ein Blockdiagramm eines Ausführungsbeispiels des erfindungsgemäßen Systems zur Kompensation von Fehlanpassungen von mehreren zeitlich versetzt zueinander abtastenden Analog-Digital-Wandlern, und
• 4 ein Flussdiagramm eines Ausführungsbeispiels des erfindungsgemäßen Verfahrens zur Kompensation von Fehlanpassungen von mehreren zeitlich versetzt zueinander abtastenden Analog-Digital-Wandlern.

The method according to the invention and the system according to the invention for compensating for mismatches in the transfer function and in the sampling time offsets of a plurality of analog-to-digital converters sampled with a time offset from one another are explained in detail below with reference to the drawing. The figures of the drawing show:

• 1 a block diagram with a plurality of time-shifted sampling analog-to-digital converters and associated compensation filters according to the prior art,
• 2A 3 shows a block diagram of an embodiment of a first compensation filter consisting of a plurality of parallel third compensation filters and an associated first compensation filter consisting of a plurality of parallel second compensation filters,
• 2 B a more detailed block diagram, which 2A corresponds,
• 3 a block diagram of an embodiment of the system according to the invention for the compensation of mismatches of a plurality of temporally offset from one another sampling analog-to-digital converters, and
• 4 a flowchart of an embodiment of the method according to the invention for the compensation of mismatches of several temporally offset from one another scanning analog-to-digital converters.

Before the inventive system and the inventive method for the compensation of mismatches in the transfer function and in the sampling time offsets of a plurality of temporally offset from each other sampling analog-to-digital converters based on the block diagram in 3 and based on the flowchart in 4 will be explained in detail, the mathematical relationships are based on a first example with analog-to-digital converters with four filter coefficients and four samples per convolution and a second example with analog-to-digital converters with eight filter coefficients and eight samples per folding explained.

$$\left[\begin{array}{l}{y}_0\hfill \\ y_1\hfill \\ y_2\hfill \\ y_3\hfill \\ y_4\hfill \\ y_5\hfill \\ y_6\hfill \end{array}\right]=\left[\begin{array}{llll}{x}_0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_1\hfill & x_0\hfill & 0\hfill & 0\hfill \\ x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill \\ x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill \\ 0\hfill & x_3\hfill & x_2\hfill & x_1\hfill \\ 0\hfill & 0\hfill & x_3\hfill & x_2\hfill \\ 0\hfill & 0\hfill & 0\hfill & x_3\hfill \end{array}\right]\cdot \left[\begin{array}{c}{h}_0\\ h_1\\ h_2\\ h_3\end{array}\right]$$

The cyclic convolution of blocks each with a number B of four samples x ₀ . x ₁ . x ₂ . x ₃ in a first compensation filter with a number L of four filter coefficients h ₀ . h ₁ . h ₂ , h ₃ according to equation (1A) results in a number M of seven polyphase components of the output signal y ₀ . y ₁ . y ₂ . y ₃ . y ₄ . y ₅ . y ₆ , The convolution of the samples x ₀ . x ₁ . x ₂ . x ₃ in a first compensation filter with the filter coefficients h ₀ . h ₁ . h ₂ . h ₃ for determining the samples y ₀ . y ₁ . y ₂ . y ₃ . y ₄ . y ₅ . y ₆ of the output signal can be described according to equation (1B). $$M=L+B-1$$

$$\left[\begin{array}{l}{y}_0\hfill \\ y_1\hfill \\ y_2\hfill \\ y_3\hfill \\ y_4\hfill \\ y_5\hfill \\ y_6\hfill \end{array}\right]=\left[\begin{array}{llll}{x}_0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_1\hfill & x_0\hfill & 0\hfill & 0\hfill \\ x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill \\ x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill \\ 0\hfill & x_3\hfill & x_2\hfill & x_1\hfill \\ 0\hfill & 0\hfill & x_3\hfill & x_2\hfill \\ 0\hfill & 0\hfill & 0\hfill & x_3\hfill \end{array}\right]\cdot \left[\begin{array}{c}{H}_0\\ H_1\\ H_2\\ H_3\end{array}\right]$$

$$y\left(2k+1\right)={\displaystyle \sum _{\xi =0}^{L-1}{h}_1\left(\xi \right)}\cdot x\left(2k+1-\xi \right)$$

The first compensation filter, which performs a convolution according to equation (1B), is realized in a first step of the method according to the invention by a plurality of third compensation filters connected in parallel. For this purpose, the even polyphase components of the output signal are determined in a third compensation filter according to equation (2A) and the odd polyphase components of the output signal in a third compensation filter according to equation (2B). $$y\left(2k\right)={\displaystyle \underset{\xi =0}{\overset{L-1}{\Sigma }}{H}_0\left(\xi \right)}\cdot x\left(2k-\xi \right)$$

$$y\left(2k+1\right)={\displaystyle \underset{\xi =0}{\overset{L-1}{\Sigma }}{H}_1\left(\xi \right)}\cdot x\left(2k+1-\xi \right)$$

$$\left[\begin{array}{c}{y}_1\\ y_3\\ y_5\end{array}\right]=\left[\begin{array}{cccc}{x}_1& x_0& 0& 0\\ x_3& x_2& x_1& x_0\\ 0& 0& x_3& x_2\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,0}}\\ h_{\mathrm{1,1}}\\ h_{\mathrm{1,2}}\\ h_{\mathrm{1,3}}\end{array}\right]$$

The third compensation filter according to equation (2A) performs filtering with the filter coefficients h ₀ (ξ) = [h _0.0 h _0.1 h _0.2 h _0.3 ] ^T , while the third compensation filter according to equation (2B) with the filter coefficients h ₁ (ξ) = [h _1.0 h _1.1 h _1.2 h _1.3 ] ^T filters. Thus, there is a time-varying compensation filter, which switches with its two third compensation filters in the determination of respectively successive polyphase components of the output signal in each case between the two filter coefficients h ₀ (ξ) and h ₁ (ξ). Starting from equation (1B), the filtering results in the two third compensation filters of the time-variant first compensation filter according to equation (3A) and (3B): $$\left[\begin{array}{c}{y}_0\\ y_2\\ y_4\\ y_6\end{array}\right]=\left[\begin{array}{cccc}{x}_0& 0& 0& 0\\ x_2& x_1& x_0& 0\\ 0& x_3& x_2& x_1\\ 0& 0& 0& x_3\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.0}\\ H_{0.1}\\ H_{0.2}\\ H_{0.3}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_1\\ y_3\\ y_5\end{array}\right]=\left[\begin{array}{cccc}{x}_1& x_0& 0& 0\\ x_3& x_2& x_1& x_0\\ 0& 0& x_3& x_2\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.0}\\ H_{1.1}\\ H_{1.2}\\ H_{1.3}\end{array}\right]$$

From the 2A goes a first compensation filter 100 consisting of two parallel third filters 7 ₀ and 7 ₁ with the associated filter transfer functions F ₀ respectively. F ₁ out. The two third filters 7 ₀ and 7 ₁ be via a feed unit 2 the individual polyphase components x ₀ . x ₁ . x ₂ . x ₃ of the input signal x fed. The two filters 7 ₀ and 7 ₁ Generate the respective polyphase components according to equations (3A) and (3B) y ₀ . y ₂ . y ₄ . y ₆ respectively. y ₁ . y ₃ . y ₅ the filter output signal y from the convolution of respective samples x ₀ . x ₁ . x ₂ . x ₃ with the respective filter coefficients h _0.0 . h _0.1 h _0.2 . h _0.3 respectively. h _1.0 . h _1,1 , h _1,2 . h _1,3 , In an assembly unit 4 become the of the two parallel second filters 7 ₀ and 7 ₁ generated polyphase components of the output signal y to one complete block of polyphase components of the output signal y together.

In the second step of the method according to the invention, the filters in the individual second compensation filters of the time-variant first compensation filter are each decomposed into a plurality of sub-filters. The partial filters in the individual third compensation filters of the time-variant first compensation filter are each realized in a second compensation filter with a minimized filter length of a time-variant first compensation filter.

$$\left[\begin{array}{c}{y}_1\\ y_3\\ y_5\end{array}\right]=\left[\begin{array}{cc}{x}_1& 0\\ x_3& x_1\\ 0& x_3\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,0}}\\ h_{\mathrm{1,2}}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_2& x_0\\ 0& x_2\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,1}}\\ h_{\mathrm{1,3}}\end{array}\right]$$

Thus, starting from the equations (3A) and (3B), the four second compensation filters each having a minimized filter length of the time-variant first compensation filter are produced according to Equations (4A) and (4B). $$\left[\begin{array}{c}{y}_0\\ y_2\\ y_4\\ y_6\end{array}\right]=\left[\begin{array}{cc}{x}_0& 0\\ x_2& x_0\\ 0& x_2\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.0}\\ H_{0.2}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_1& 0\\ x_3& x_1\\ 0& x_3\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.1}\\ H_{0.3}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_1\\ y_3\\ y_5\end{array}\right]=\left[\begin{array}{cc}{x}_1& 0\\ x_3& x_1\\ 0& x_3\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.0}\\ H_{1.2}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_2& x_0\\ 0& x_2\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.1}\\ H_{1.3}\end{array}\right]$$

The four second compensation filters in equations (4A) and (4B) each have a minimized filter length L _Min of two.

From the 2 B goes a first compensation filter 100 consisting of four parallel second filters 2 ₀ . 2 ₁ . 2 ₂ and 2 ₃ with the associated filter transfer functions F ₀ . F ₁ . F ₂ and F ₃ show the same filter characteristics as in 2A illustrated first compensation filter 100 having. The four parallel second filters 2 ₀ . 2 ₁ . 2 ₂ and 2 ₃ be via the feed unit 2 at the respective sampling times the respective samples x ₀ . x ₂ respectively. x ₁ . x ₃ the individual blocks x of the input signal supplied. The four parallel second filters 2 ₀ . 2 ₁ . 2 ₂ and 2 ₃ According to equations (4A) and (4B), they produce the respective polyphase components y ₀ . y ₂ . y ₄ . y ₆ respectively. y ₁ . y ₃ . y ₅ in the individual blocks y _B the filter output signal y from the convolution of the respective samples x ₀ . x ₂ respectively. x ₁ . x ₃ with the respective filter coefficients h _0.0 . h _0.2 respectively. h _0.1 . h _0.3 respectively. h _1.0 . h _1,2 respectively. h _1,1 . h _1,3 , In an assembly unit 4 become the of the four parallel second filters 2 ₀ . 2 ₁ . 2 ₂ and 2 ₃ generated polyphase components of the output signal y to one complete block of polyphase components of the output signal y together.

In this way, the filterings of the four second compensation filters of a time-variant first compensation filter shown in equations (4A) and (4B) are produced.

The second filters 2 ₀ . 2 ₁ . 2 ₂ and 2 ₃ are preferably implemented as short-length (SL) filters (German: filter with the shortest filter length), which Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332, to additionally reduce the number of additions and multiplications to be performed.

Thus, for the example of filtering a sequence of four samples each with a first compensation filter having a filter length of four, each twelve multiplies according to equation (6) are required. $$N_{MultiplikatiOnen}=4\cdot 3=12$$

In each of the four second compensation filters, each with a minimized filter length of two, three multiplies are required in each case, as from line 4 in equation (a1) in Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332 , shows.

The number of additions to be made for the example of filtering a sequence of four samples each with a compensation filter having a minimized filter length of two is given by equation (7) of FIG. $$N_{AdditiOnen}=2\cdot 1+4\cdot 2+\left(2+3\right)+3=18$$

The first summand in equation (7) results from the superposition of the polyphase components of the input signal in the two second compensation filters. In the second compensation filters of equations (4A) and (4B), either the polyphase components are used x ₀ and x ₂ of the input signal or the polyphase components x ₁ and x ₃ of the input signal taking into account line 2 in equation (a1) in Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332 , added together.

The second summand in equation (7) contains the additions in the four second compensation filters, in which according to the rows 5 and 6 in equation (a1) in Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332 , two additions are performed.

The third term in equation (7) contains the additions of the results of the second compensation filters to determine the polyphase components of the output signal, i. the two additions in the second and third rows of equation (4A) and the three additions in the first, second and third rows of equation (4B).

The fourth summand contains the additions of the last three polyphase components of the samples produced by the first compensation filter in the respective cycle to the first three polyphase components of the samples produced by the first compensation filter in the respective subsequent cycle as part of the "overlap-add" algorithm -Algorithm). The overlap of three polyphase components results from the difference between the number M of seven polyphase components of the output signal generated in one cycle and the number B of four polyphase components of the input signal supplied in one cycle.

The cyclic convolution of blocks of eight samples each x ₀ . x ₁ . x ₂ . x ₃ . x ₄ . x ₅ . x ₆ . x ₇ in a first compensation filter with eight filter coefficients h ₀ . h ₁ . h ₂ . h ₃ . h ₄ . h ₅ . h ₆ . h ₇ leads according to equation (8) to a total of seven polyphase components of the output signal y ₀ . y ₁ . y ₂ . y ₃ . y ₄ . y ₅ . y ₆ . y ₇ . y ₈ . y ₉ . y ₁₀ . y ₁₁ . y ₁₂ , y ₁₃ . y ₁₄ : $$\left[\begin{array}{c}{y}_0\\ y_1\\ :\\ y_6\\ y_7\\ y_{\mathrm{8th}}\\ :\\ y_{13}\\ y_{14}\end{array}\right]=\left[\begin{array}{cccccccc}{x}_0& 0& 0& 0& 0& 0& 0& 0\\ x_1& x_0& 0& 0& 0& 0& 0& 0\\ :& :& :& :& :& :& :& :\\ x_6& x_5& x_4& x_3& x_2& x_1& x_0& 0\\ x_7& x_6& x_5& x_4& x_3& x_2& x_1& x_0\\ 0& x_7& x_6& x_5& x_4& x_3& x_2& x_1\\ :& :& :& :& :& :& :& :\\ 0& 0& 0& 0& 0& 0& x_7& x_6\\ 0& 0& 0& 0& 0& 0& 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{H}_0\\ H_1\\ H_2\\ H_3\\ H_4\\ H_5\\ H_6\\ H_7\end{array}\right]$$

The first compensation filter, which performs a convolution according to equation (8), is realized in a first step of the method according to the invention by four parallel-connected third compensation filters. For this purpose, the polyphase components of the output signal of the first compensation filter are determined according to the respective polyphase p according to equation (9). $$y\left(4k+p\right)={\displaystyle \underset{\xi =0}{\overset{L-1}{\Sigma }}{H}_p\left(\xi \right)}\cdot x\left(4k+p-\xi \right)\text{For}p=\mathrm{0,1,2,3}$$

durch.The four third compensation filters each carry a filtering with the respective filter coefficients $$\begin{array}{ll}{H}_0\left(\xi \right)={\left[\begin{array}{cccc}{H}_{0.0}& H_{0.1}& H_{0.2}& H_{0.3}\end{array}\right]}^T.\hfill & H_1\left(\xi \right)={\left[\begin{array}{cccc}{H}_{1.0}& H_{1.1}& H_{1.2}& H_{1.3}\end{array}\right]}^T.\hfill \\ H_2\left(\xi \right)={\left[\begin{array}{cccc}{H}_{2.0}& H_{2.1}& H_{2.2}& H_{2.3}\end{array}\right]}^T\text{and}\hfill & H_3\left(\xi \right)={\left[\begin{array}{cccc}{H}_{3.0}& H_{3.1}& H_{3.2}& H_{3.3}\end{array}\right]}^T\hfill \end{array}$$

by.

Thus, in this example there is also a time-variant first compensation filter which, when determining respectively successive polyphase components of the output signal, has its four third compensation filters with the respective filter coefficients h ₀ (ξ), h ₁ (ξ), h ₂ (ξ) and h ₃ (ξ) used successively.

$$\left[\begin{array}{c}{y}_1\\ y_5\\ y_9\\ y_{13}\end{array}\right]=\left[\begin{array}{llllllll}{x}_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill \end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,0}}\\ h_{\mathrm{1,1}}\\ :\\ h_{\mathrm{1,7}}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_2\\ y_6\\ y_{10}\\ y_{14}\end{array}\right]=\left[\begin{array}{llllllll}{x}_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill \end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{2,0}}\\ h_{\mathrm{2,1}}\\ :\\ h_{\mathrm{2,7}}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_3\\ y_7\\ y_{11}\end{array}\right]=\left[\begin{array}{llllllll}{x}_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill \end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{3,0}}\\ h_{\mathrm{3,1}}\\ :\\ h_{\mathrm{3,7}}\end{array}\right]$$

The filterings in the four third compensation filters of the time-variant first compensation filter are obtained according to Equations (10A) to (10D): $$\left[\begin{array}{c}{y}_0\\ y_4\\ y_{\mathrm{8th}}\\ y_{12}\end{array}\right]=\left[\begin{array}{llllllll}{x}_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill \end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.0}\\ H_{0.1}\\ :\\ H_{0.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_1\\ y_5\\ y_9\\ y_{13}\end{array}\right]=\left[\begin{array}{llllllll}{x}_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill \end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.0}\\ H_{1.1}\\ :\\ H_{1.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_2\\ y_6\\ y_{10}\\ y_{14}\end{array}\right]=\left[\begin{array}{llllllll}{x}_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill \end{array}\right]\cdot \left[\begin{array}{c}{H}_{2.0}\\ H_{2.1}\\ :\\ H_{2.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_3\\ y_7\\ y_{11}\end{array}\right]=\left[\begin{array}{llllllll}{x}_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill & x_3\hfill & x_2\hfill & x_1\hfill & x_0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & x_7\hfill & x_6\hfill & x_5\hfill & x_4\hfill \end{array}\right]\cdot \left[\begin{array}{c}{H}_{3.0}\\ H_{3.1}\\ :\\ H_{3.7}\end{array}\right]$$

In the second step of the method according to the invention, the filters in the individual third compensation filters of the time-variant first compensation filter are each decomposed into a plurality of sub-filters. Each individual partial filtering of a third compensation filter of the time-variant first compensation filter is implemented in each case in a second compensation filter with a minimized filter length of a time-variant first compensation filter.

$$\left[\begin{array}{c}{y}_1\\ y_5\\ y_9\\ y_{13}\end{array}\right]=\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,0}}\\ h_{\mathrm{1,4}}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_4& x_0\\ 0& x_4\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,1}}\\ h_{\mathrm{1,5}}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,2}}\\ h_{\mathrm{1,6}}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_2& 0\\ x_6& x_2\\ 0& x_6\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{1,3}}\\ h_{\mathrm{1,7}}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_2\\ y_6\\ y_{10}\\ y_{14}\end{array}\right]=\left[\begin{array}{cc}{x}_2& 0\\ x_6& x_2\\ 0& x_6\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{2,0}}\\ h_{\mathrm{2,4}}\end{array}\right]+\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{2,1}}\\ h_{\mathrm{2,5}}\end{array}\right]+\left[\begin{array}{cc}{x}_0{}_{\text{}}& 0\\ x_4& x_0\\ 0& x_4\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{2,2}}\\ h_{\mathrm{2,6}}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{2,3}}\\ h_{\mathrm{2,7}}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_3\\ y_7\\ y_{11}\end{array}\right]=\left[\begin{array}{cc}{x}_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{3,0}}\\ h_{\mathrm{3,4}}\end{array}\right]+\left[\begin{array}{cc}{x}_2& 0\\ x_6& x_2\\ 0& x_6\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{3,1}}\\ h_{\mathrm{3,5}}\end{array}\right]+\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{3,2}}\\ h_{\mathrm{3,6}}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_4& x_0\\ 0& x_4\end{array}\right]\cdot \left[\begin{array}{c}{h}_{\mathrm{3,3}}\\ h_{\mathrm{3,7}}\end{array}\right]$$

Thus, for the example of a first compensation filter with eight filter coefficients, which filters one block of eight samples in a cycle, starting from equations (10A) to (10D), the four second compensation filters each with minimized filter length of the time-invariant first compensation filter according to equation ( 11A) to (11D). $$\left[\begin{array}{c}{y}_0\\ y_4\\ y_{\mathrm{8th}}\\ y_{12}\end{array}\right]=\left[\begin{array}{cc}{x}_0& 0\\ x_4& x_0\\ 0& x_4\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.0}\\ H_{0.4}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.1}\\ H_{0.5}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_2& 0\\ x_6& x_2\\ 0& x_6\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.2}\\ H_{0.6}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_1& 0\\ x_5& x_1\\ 0& x_5\end{array}\right]\cdot \left[\begin{array}{c}{H}_{0.3}\\ H_{0.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_1\\ y_5\\ y_9\\ y_{13}\end{array}\right]=\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.0}\\ H_{1.4}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_4& x_0\\ 0& x_4\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.1}\\ H_{1.5}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.2}\\ H_{1.6}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_2& 0\\ x_6& x_2\\ 0& x_6\end{array}\right]\cdot \left[\begin{array}{c}{H}_{1.3}\\ H_{1.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_2\\ y_6\\ y_{10}\\ y_{14}\end{array}\right]=\left[\begin{array}{cc}{x}_2& 0\\ x_6& x_2\\ 0& x_6\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{2.0}\\ H_{2.4}\end{array}\right]+\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{2.1}\\ H_{2.5}\end{array}\right]+\left[\begin{array}{cc}{x}_0{}_{}& 0\\ x_4& x_0\\ 0& x_4\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{c}{H}_{2.2}\\ H_{2.6}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ x_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{H}_{2.3}\\ H_{2.7}\end{array}\right]$$

$$\left[\begin{array}{c}{y}_3\\ y_7\\ y_{11}\end{array}\right]=\left[\begin{array}{cc}{x}_3& 0\\ x_7& x_3\\ 0& x_7\end{array}\right]\cdot \left[\begin{array}{c}{H}_{3.0}\\ H_{3.4}\end{array}\right]+\left[\begin{array}{cc}{x}_2& 0\\ x_6& x_2\\ 0& x_6\end{array}\right]\cdot \left[\begin{array}{c}{H}_{3.1}\\ H_{3.5}\end{array}\right]+\left[\begin{array}{cc}{x}_1& 0\\ x_5& x_1\\ 0& x_5\end{array}\right]\cdot \left[\begin{array}{c}{H}_{3.2}\\ H_{3.6}\end{array}\right]+\left[\begin{array}{cc}{x}_0& 0\\ x_4& x_0\\ 0& x_4\end{array}\right]\cdot \left[\begin{array}{c}{H}_{3.3}\\ H_{3.7}\end{array}\right]$$

The total 16 Second compensation filters in equations (11A) to (11D) each have a minimized filter length L _Min of two and are each preferably realized as a short-length (SL) filter (German: filter with the shortest filter length), the Mou Z. et al. "Short-Length FIR Filters and Their Use in Fast Nonrecursive Filtering", IEEE Transactions on Signal Processing, Vol. 6, June 1991, pages 1322-1332 , are known to additionally reduce the number of additions and multiplications to be performed.

Thus, for the example of filtering a sequence of eight samples each with a first compensation filter having a filter length of eight, 48 multiplies each are required according to equation (13). $$N_{MultiplikatiOnen}=16\cdot 3=48$$

The number of additions to be made for the example of filtering a sequence of eight samples each with a first compensation filter having a filter length of eight is 60 according to equation (14). $$N_{AdditiOnen}=4\cdot 1+16\cdot 2+\left(\mathrm{8th}+\mathrm{8th}+\mathrm{8th}+9\right)+7=76$$

On the basis of these mathematical principles, the exemplary embodiment of the method according to the invention will be described below with reference to the flowchart in FIG 4 and the system according to the invention with reference to the block diagram in FIG 3 explained in detail.

While the first three method steps of the method according to the invention relate to the determination and the configuration of the structure of the individual second compensation filters, the feed unit and the assembly unit and the determination of the parameters and the parameterization of the individual second compensation filters and are performed only once, become the subsequent process steps S40 to S70 the process of the invention continuously and cyclically carried out during operation of the system according to the invention.

In the first process step S10 of the method according to the invention 4 will be in one unit 1 for determining the structure and parameters based on the selected filter length of the first compensation filter and the selected number of samples of the input signal, which are processed by a first compensation filter in a cycle in a block, the structure of the time-variant first compensation filter consisting of a plurality of time-invariant second compensation filters.

The selected filter length of the first compensation filter and the selected number of samples of the input signal processed by the first compensation filter in one cycle corresponding to the number of polyphases of the input signal gives the number of output signals generated in one cycle of samples of the output signal produced by the first compensation filter corresponds to polyphases of the output signal.

For each polyphase p, in each case a third compensation filter of such a time-variant first compensation filter is generated. For this purpose, in order to determine the structure of such a third compensation filter belonging to the polyphase p, those filters which are required in each case for the generation of all p-th polyphase components of the output signal respectively generated by the first compensation filter are based on the equations (3A) and (3B). or to equations (10A) to (10D).

Based on the filter structure of every third compensation filter, the filter coefficients for each third compensation filter are determined separately using conventional filter optimization methods.

In the next process step S20 is any filtering that in process step S10 is performed in each case in a third compensation filter belonging to the time-variant first compensation filter, in each case broken down into a plurality of sub-filters, which are each carried out in a second compensation filter, each with a minimized filter length L _Min . Each second compensation filter is time invariant in itself and has a filter structure based on equations (5A) and (5B) and equations (11A) to (11D), respectively.

The filter coefficients of the individual second compensation filters result from those in the previous method step S20 respectively determined filter coefficients for the associated third compensation filter.

In the next process step S30 the first compensation filter is configured consisting of several second compensation filters processed in parallel. This is done by the unit 1 for structure and parameter determination from the total number N of existing second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 , which are present, for example, as programmable functional units in a programmable hardware, which are for the realization of the first compensation filter 100 required number i of compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 , for example, an in 1 unillustrated activation signal activated. Other technical implementations for activation or consideration of existing second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 for implementation of the respective first compensation filter 100 are covered by the invention.

The internal structure of the single second compensation filter to be considered 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 ie with the filter coefficients of the respective second compensation filter 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 to be weighted in the individual sampling times and the respective second compensation filter 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 each to be supplied samples of the input signal, the individual to be considered second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 also in process step S30 from the unit 1 assigned for structure and parameter determination and each second compensation filter to be considered 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 is configured accordingly.

Finally, the individual to be considered second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 also in process step S30 from the unit 1 for structural and parameter determination, the associated filter coefficients are supplied and the second compensation filters to be considered 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 are parameterized accordingly.

Also, in this process step S30 the preferred realization of the second compensation filter 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 configured as short-length (SL) filter (German: filter with the shortest filter length).

All existing second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 is a feeder unit 3 upstream, with the continuous sequence x is provided by samples of the input signal of the associated analog-to-digital converter, the respective first compensation filter 100 upstream.

This feeder unit 3 is in process step S30 from the unit 1 for determining the structure and parameters with the information which sequence of samples of the continuous sequence supplied by the respective upstream analog-to-digital converter x of samples of the input signal in the individual cycles, the individual in the respective first compensation filter 3 respectively used second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N - ₁ from the feeder unit 3 be supplied. Then the feeder unit becomes 3 configured accordingly.

It should be noted that every single second compensation filter used 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 in one cycle each time a number of samples from the continuous sequence corresponding to the minimized filter length L _min x of samples of the input signal is supplied in parallel.

All used second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 , the first compensation filter 100 downstream assembly unit 4 is also in process step S30 from the unit 1 for the structure and parameter determination supplied with the information which polyphase components of the first compensation filter 100 generated output signal in each case the second compensation filter used 2 ₀ , 2 ₁ . 2 ₂ , ..., 2 _i-1 of the first compensation filter 100 deliver. Then the assembly unit becomes 4 configured accordingly.

After configuration and parameterization of all to the first compensation filter 100 respectively associated and used compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 and the configuration of the feeder unit 3 and the assembly unit 4 , becomes in the following process step S40 with the ongoing operation of the equalization of the delivered from the respective upstream analog-to-digital converter continuous sequence x of samples of the input signal by means of the associated compensation filter 100 began.

In addition to the automatic determination of the structure and parameters and / or the automatic configuration or parameterization of the individual second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 , the feeder unit 3 and the assembly unit 4 by means of the unit 1 For structure and parameter determination is also a manual structure and parameter determination and a manual structure of the individual to the first compensation filter 100 associated compensation filter 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 , the feeder unit 3 and the assembly unit 4 possible and covered by the invention.

In the subsequent process step S40 receives the feeder unit 3 from the upstream analog-to-digital converter, the continuous sequence x of samples of the input signal and stores on the basis of that of the unit 1 information obtained for structure and parameter determination, if required, intercepts received samples of the input signal for one or more sampling periods and carries the individual second compensation filters used 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 , for the filtering in the respective sampling time respectively required samples of the input signal to the respective sampling time.

In the case that several used second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 each having an identical internal structure, which is in each case one cycle for the filtering in several second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 required sequence of samples only once in the feed unit 3 joined together and the respective second compensation filters 2 ₀ . 2 ₁ . 2 ₂ , ..., 2 _i-1 fed in parallel.

The next process step S50 included in the individual second compensation filters used 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 in each case the convolution of the individual compensation filters used in each case 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 Sequences of sample values supplied in each case with those of the unit in the individual sampling instants 1 for the structure and parameter determination respectively obtained filter coefficients on the basis of the equations (4A) and (4B) or to the equations (11A) to (11D).

The compensation filters used by each one 2 ₀ . 2 ₁ . 2 ₂ , ..., _2N-1 each generated polyphase components of the output signal of the compensation filter 100 will be in the next step S60 the assembly unit 4 fed and based on that of the unit 1 for structural and parameter determination information obtained in each cycle to a sequence y _B of samples of the output signal of the compensation filter 100 together.

In the final process step S70 become the sequences of samples of the output signal of the compensation filter 100 in one to the assembly unit 4 subsequent unit 6 for generating a continuous sequence to a continuous sequence of samples of the output signal of the compensation filter 100 composed.

For this purpose, the overlap-add algorithm (German: overlap-add algorithm) is typically used, which is a number of in each case last generated samples of the output signal of the compensation filter 100 , the number of samples of a sequence received in one cycle x of samples of the input signal of the compensation filter 100 exceeds, in each case, the first sample of the sequence generated in the subsequent cycle y _B of samples of the output signal of the compensation filter 100 added.

This creates a continuous sequence y of samples of the output signal of the compensation filter 100 ,

Finally, the method according to the invention is implemented with a first compensation filter which is divided into a plurality of second compensation filters, each with a minimized filter length 100 (Variant 1) on the one hand with a method of the prior art, in which the complete linear equation system of a compensation filter is calculated (Variant 2) and on the other hand with a method of the prior art, in which the discrete convolution of the compensation filter is calculated directly (Variant 3 ) are compared in terms of the required number of additions and multiplications.

Table 1 shows the case of a compensation filter with a filter length of four and a sequence length of four samples, and Table 2 shows the case of a compensation filter with a filter length of eight and a sequence length of eight samples. Table 1 Algorithm version: Number of multiplications Number of additions relative number of multiplications relative number of additions version 1 12 18 133.3% 70% Variant 2 9 20 100% 100% Variant 3 16 12 177.8% 60% Table 2 Algorithm version: Number of multiplications Number of additions relative number of multiplications relative number of additions version 1 48 76 177.8% 92.1% Variant 2 27 76 100% 100% Variant 3 64 56 237.0% 74.7%

It can be seen that in both cases the number of additions of the method according to the invention compared to the method for determining the linear equation system of the complete compensation filter according to the prior art is reduced, while the number of multiplications of the inventive method over the method for the determination of the linear equation system of the prior art discrete convolution compensation filter is reduced. However, the main advantage of the procedure according to the invention lies in the parallelization.

The invention is not limited to the illustrated embodiment. Of the invention, in particular the combinations of each claim claimed in the claims, all in the description respectively disclosed features and all in the figures of the drawing features are covered.

Claims (15)

Method for compensating for mismatches in the transfer function and / or in the sampling instantaneous offsets between a plurality of analog-to-digital converters (200 ₀ , 200 ₁ , ..., 200 _M-1 ) which are sampled with a time offset from one another, by using in each first time-variant compensation filter ( 100 ₀ , 100 ₁ , ..., 100 _M-1 , 100), which is each followed by an analog-digital converter, each a cyclically time-variant convolution of a certain number (L) of the associated analog-to-digital converter (200 ₀ , 200 ₁ , ..., 200 _M-1 ) with a certain number (B) of filter coefficients, characterized in that each first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 100) each having a plurality of second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ), each having a minimized number (B _min ) of filter coefficients, each in the same cycle a time-invariant partial filtering the cyclic time variant Convolution of the first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 ; 100) corresponding filtering. Method according to Claim 1 , characterized in that the second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) operate in parallel. Method according to Claim 1 or 2 , characterized in that in each cycle in each case a sequence of samples of samples which are generated in the respective cycle in that analog-to-digital converter to which the associated first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _{M). 1} , 100) is connected, and in each case a plurality of second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) of the respective first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 ; 100) is fed in parallel. Method according to one of Claims 1 to 3 , characterized in that each first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 , 100) consists of several time-invariant third compensation filters (7 ₀ , 7 ₁ ) each having different filter coefficients. Method according to Claim 4 , characterized in that a respective third time-invariant compensation filter (7 ₀ , 7 ₁ ) is provided for each polyphase p of a cycle of respectively generated sample values in the respective first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 ; is provided which performs the filtering of those samples which are generated in the analog-to-digital converter (200 ₀ , 200 ₁ , ..., 200 _M-1 ) to which the respective first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _{M -1} ; 100), and which are required to determine all the polyphase components of the respective first time-variant compensation filters (100 ₀ , 100 ₁ , ..., 100 _{M -1} , 100). Method according to Claim 4 or 5 , characterized in that the filter coefficients for each third time-invariant compensation filter (7 ₀ , 7 ₁ ) are determined separately. Method according to one of Claims 4 to 6 , characterized in that in each third time-invariant compensation filter (7 ₀ , 7 ₁ ) each summarized filters are each decomposed into a plurality of sub-filters each having a minimized number (B _Min ) of filter coefficients, wherein the individual sub-filters in each case one the second time-invariant compensation filter (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) can be realized. Method according to one of Claims 1 to 7 , characterized in that a plurality of second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) in each case an identical sequence of samples is supplied in parallel. System for compensating for mismatches in the transfer function and / or in the sampling time offsets between a plurality of analog-to-digital converters (200 ₀ , 200 ₁ , ..., 200 _M-1 ) which are sampled at a time offset from one another Digital converter (200 ₀ , 200 ₁ , ..., 200 _M-1 ) and in each case a downstream first time-varying compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 , 100) for the cyclic time-variant convolution of a specific Number (L) of samples produced in the associated analog-to-digital converter (200 ₀ , 200 ₁ , ..., 200 _M-1 ) with a certain number (B) of filter coefficients, characterized in that each first time-variant compensation filter ( 100 ₀ , 100 ₁ , ..., 100 _M-1 , 100) a plurality of second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) each having a minimized number (B _min ) of Having filter coefficients. System after Claim 9 , characterized in that the second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i ) corresponding to a first time-variant compensation filter (100 ₀ , 100 ₁ , ..., 100 _M-1 ; _-1 ) are connected in parallel. System after Claim 9 or 10 , Characterized in that between a respective analog-to-digital converter (200 _0, 200 _1, ..., 200 _M -1) and the (to the corresponding first time-varying compensation filter 100 _0, 100 _1, ..., 100 _{M- 1} , 100) respectively associated second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) in each case a feed unit (3) is connected, which is designed such that they time invariant to the individual second Compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) which supplies required sequences of samples. System after Claim 11 , characterized in that the feed unit (3) is configured such that it feeds an identical sequence of samples in parallel to a plurality of second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) in parallel. System according to one of Claims 9 to 12 , characterized in that the first time-variant compensation filter (100) respectively associated second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) is followed by an assembly unit (4), such it is designed to be that of The individual second time-invariant compensation filters (2 ₀ , 2 ₁ , 2 ₂ , ..., 2 _i-1 ) each assembled sequences of samples into a single sequence ( y _B ) of samples zusammenfügt. Computer program with program code means for performing all the steps according to one of Claims 1 to 8th when the program is run on a computer or digital signal processor. Computer program product having program code means stored on a machine-readable medium for carrying out all the steps according to one of Claims 1 to 8th when the program is run on a computer or digital signal processor.

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