TW201713039A - Serial finite impulse response filter and signal processing method thereof - Google Patents

Abstract

The invention provides a signal processing method for a series-connected finite impulse response filter, comprising first and second filtering steps. The first filtering step transmits the input signal to the integer filter, and the integer filter is used to multiply the input signal by the integer conversion function to generate an integer output signal. The second filtering step transmits the integer output signal to the prototype filter, and uses the prototype filter to multiply the integer output signal by the prototype conversion function to generate an output signal. The prototype transfer function can be converted to a prototype frequency response, and the prototype frequency response increases exponentially with increasing frequency before the cutoff frequency. In this way, a special prototype filter combined with an integer filter can produce a flatter passband response and a filtering effect after increasing the cutoff frequency, and can be applied to low pass, band pass or high pass filtering.

Description

Serial finite impulse response filter and its signal Approach

The present invention relates to a finite impulse response filter and a signal processing method thereof, and more particularly to a series finite impulse response filter capable of generating a flat passband response and capable of increasing a filtering effect, and a signal processing method thereof.

The form of a general digital filter can be divided into a finite impulse response (FIR) filter and an Infinite Impulse Response (IIR) filter. Since the FIR filter has the advantages of circuit stability, and the FIR filter coefficient can be symmetrical, and the completely correct linear phase characteristics can be realized, many FIR filter architectures have been successively proposed to improve the filtering characteristics. A conventional FIR filter is an impulse response expressed by a finite time length as a filter coefficient. Therefore, in the process of studying the FIR filter, it is important to determine the filter coefficients in order to obtain the desired frequency response characteristics.

The conventional FIR filter calculates the filter coefficients according to the frequency response characteristics of the target, and performs a window design method (WDM; The Window Design Method) obtains a finite number of coefficient groups, and the Fourier transform performs a Fourier transform to know its frequency characteristics, and can further confirm whether it satisfies the target characteristics for planning and creation. In order to calculate the filter coefficients of the target frequency characteristics, the general method is to perform a convolution operation of the approximation method based on the ratio of the sampling frequency to the cutoff frequency to obtain the filter coefficients. However, the number of coefficients thus obtained is usually too large, and if all coefficients are used, the circuit of the filter can become quite complicated and impractical.

In addition, some filter creations reduce the number of filter coefficients to a practically tolerable level by conventional WDM. However, if the FIR filter created by such conventional WDM is not skillfully set, good frequency characteristics cannot be obtained.

Moreover, conventional WDMs can be combined with multiple sets of circuit series to achieve linear product characteristics. However, when the number of filter coefficients is large enough, the complexity of the overall filter is too high to be used, and the balance between the two is often difficult for the technician to overcome. It can be seen that there is currently a lack of a FIR filter with low hardware complexity and good filtering effect and its signal processing method in this field, so the relevant technology seeks its solution.

Therefore, the present invention provides a series-connected finite impulse response filter and a signal processing method thereof, which utilize a special prototype filter combined with an integer filter to not only generate a flat passband response but also greatly increase the cutoff. The filtering effect after the frequency can also reduce the chopping of the passband edge by the compensation effect of the integer filter. In addition, the parameters of the integer filter and the specially selected exponential response of the prototype filter form a series of finite impulse response filters, which require only a low complexity hardware cost to achieve a filter of more than 20dB amplitude. Improve the effect.

According to an aspect of the present invention, a signal processing method for a series-connected finite impulse response filter for converting an input signal into an output signal is provided. The signal processing method of the serial finite impulse response filter includes a first filtering step and a second filtering step. The first filtering step is to transmit the input signal to the integer filter, and the integer filter is used to multiply the input signal by the integer conversion function to generate an integer output signal. Furthermore, the second filtering step transmits the integer output signal to the prototype filter, and uses the prototype filter to multiply the integer output signal by the prototype conversion function to generate an output signal. The prototype conversion function contains the prototype frequency response, and the prototype frequency response increases exponentially with increasing frequency before the cutoff frequency.

Therefore, the signal processing method of the series finite impulse response filter of the present invention utilizes a special exponential response prototype filter combined with an integer filter, which not only produces a relatively flat passband response, but also greatly increases the cutoff. The filtering effect after the frequency exceeds 20 dB.

According to an embodiment of the invention, the signal processing method of the serial finite impulse response filter may include a first serial connection step, a second serial connection step, and a third serial connection step. The first series of steps is connected in series with a plurality of complementary comb filters to form an integer filter. The second series of steps is a series of prototype filter sub-units to form a prototype filter. The third series connection step connects the prototype filter to the integer filter. Furthermore, the aforementioned complementary comb filter has a complementary comb-type transfer function, and the complementary comb-type transfer function includes a complementary comb-type frequency response, a complex parameter, and a filter order. The complementary comb type frequency response is expressed as H _ccb (ω), the complex parameter is expressed as z , the filter order is expressed as K , where ω is the angular frequency, and the complementary comb type frequency response H _ccb (ω) is the complementary comb filter. Frequency response. The complementary comb type conversion function can conform to the following formula: among them , k =0,1,..., K -1, and K is a positive integer.

According to an embodiment of the invention, the aforementioned prototype conversion function may include frequency sampling, shape parameters, and frequency domain sampling numbers. The prototype frequency response is denoted as H _pro (ω); the frequency sample is denoted as m ; the shape parameter is denoted as γ; the frequency domain sample number is denoted as M . The prototype conversion function can conform to the following formula: H _pro ( m )= e ^{γ | m |} ; where 0<γ, and -( M -1)/2 m ( M -1)/2.

According to an embodiment of the invention, the integer conversion function may include a plurality of complementary comb-type conversion functions and a plurality of integer filter orders. The order of each integer filter is expressed as i , the number of orders of each integer filter is expressed as k _i , and the maximum value of the order of the integer filter is expressed as L , and the transfer function of the cascaded finite impulse response filter Expressed as H _cmp ( z ). The conversion function of the series finite impulse response filter can meet the following formula: as well as among them The size of the integer conversion function, and k ₁ ~ k _L are integers; For the indicator function, when k _i ≠ 0, Is 1; when k _i =0, Is 0.

According to an embodiment of the invention, wherein the positive integer is expressed as And the number of the above-mentioned integer filter orders can be consistent with the following formula:

According to an embodiment of the invention, the attenuation amount corresponding to the cutoff frequency of each of the complementary comb-type filters is represented as δ _i , and the prototype frequency has a prototype cutoff frequency amplitude in response to the cutoff frequency, and the prototype cutoff frequency amplitude is expressed as Δ _γ . The total attenuation of the integer filter can be as follows: Where Δ _γ >0 and Δ ₀ <0.

According to an embodiment of the invention, wherein the total number of the integer filters is expressed as η, and the total number of integer filters conforms to the following formula:

According to another aspect of the present invention, a series finite impulse response filter is provided for converting an input signal into an output signal. The series finite impulse response filter includes an integer filter and a prototype filter. The integer filter is formed by connecting a plurality of complementary comb filters in series with each other. This integer filter multiplies the input signal by the integer conversion function to produce an integer output signal. In addition, the prototype filter is formed by a plurality of prototype filter subunits connected in series with each other. The prototype filter multiplies the integer output signal by the prototype conversion function to produce an output signal. The prototype conversion function contains a prototype frequency response that is exponentially functioned with increasing frequency before the cutoff frequency. increase. Furthermore, the integer filter is connected to the prototype filter to form a series finite impulse response filter.

Thereby, the series-connected finite impulse response filter of the present invention utilizes a special exponential response prototype filter combined with an integer filter, which not only produces a relatively flat passband response, but also greatly increases the filtering after the cutoff frequency. effect. Furthermore, the series-connected finite impulse response filter consisting of various parameters of the integer filter and the specially selected exponential response prototype filter requires only a low complexity hardware cost to achieve a filter of more than 20 dB amplitude. Improve the effect.

According to an embodiment of the invention, the complementary comb filter may have a complementary comb-type transfer function, and the complementary comb-type transfer function includes a complementary comb-type frequency response, a complex parameter, and a filter order. The complementary comb type frequency response is expressed as H _ccb (ω), the complex parameter is expressed as z , the filter order is expressed as K , where ω is the angular frequency, and the complementary comb type frequency response H _ccb (ω) is the complementary comb filter. The frequency response of the device. The complementary comb type conversion function can conform to the following formula: among them , k =0,1,..., K -1, and K is a positive integer.

According to an embodiment of the invention, the aforementioned prototype conversion function may include frequency sampling, shape parameters, and frequency domain sampling numbers. The prototype frequency response is expressed as H _pro (ω), the frequency sample is represented as m , the shape parameter is represented as γ, and the frequency domain sample number is represented as M. The prototype conversion function can conform to the following formula: H _pro ( m )= e ^{γ | m |} ; where 0<γ, and -( M -1)/2 m ( M -1)/2.

According to an embodiment of the invention, the integer conversion function may include a complementary comb conversion function and an integer filter order. The order of each integer filter is expressed as i , the number of orders of each integer filter is expressed as k _i , and the maximum value of the order of the integer filter is expressed as L , and the transfer function of the cascaded finite impulse response filter Expressed as H _cmp (ω). The conversion function of the series finite impulse response filter can meet the following formula: as well as among them The size of the integer conversion function, and k ₁ ~ k _L are integers; For the indicator function, when k _i ≠ 0, Is 1; when k _i =0, Is 0.

According to an embodiment of the invention, wherein the positive integer is expressed as The number of integer filter stages can be as follows:

According to an embodiment of the invention, the attenuation amount corresponding to the cutoff frequency of each of the complementary comb filters is expressed as δ _i , the prototype frequency has a prototype cutoff frequency amplitude in response to the cutoff frequency, and the prototype cutoff frequency amplitude is represented as Δ _γ . The total attenuation of the integer filter can be as follows: Where Δ _γ >0 and Δ ₀ <0.

According to an embodiment of the invention, the total number of the integer filter orders is expressed as η, and the total number of integer filter orders is in accordance with the following formula:

100‧‧‧Sequential finite impulse response filter

ω _C ‧‧‧ cutoff frequency

m ‧‧‧frequency sampling

200‧‧‧ integer filter

210‧‧‧Complementary comb filter

300‧‧‧ prototype filter

310‧‧‧Prototype filter subunit

X ( z ), x ( k )‧‧‧ input signal

H _sha ( z ) X ( z )‧‧‧ integer output signal

Y ( z ), y ( k )‧‧‧ output signals

b ₀ ~ b ₃₂ ‧‧‧ parameters

H _sha ( z )‧‧‧ integer conversion function

h _sha ( k )‧‧‧ integer impulse response

z ‧‧‧ plural parameters

H _pro ( z )‧‧‧ prototype conversion function

h _pro ( k )‧‧‧ prototype impulse response

γ‧‧‧Shape parameters

M , N ‧‧ ‧ frequency domain sampling

f _s ‧‧‧Sampling frequency

Δ _γ ‧‧‧ prototype cutoff frequency amplitude

s _shift ( k ) ‧ ‧ sequence of displacement frequencies

S1‧‧‧ first cascade step

S2‧‧‧Second cascade step

S3‧‧‧ third cascade step

S4‧‧‧First filtering step

S41~S43‧‧‧Decision substeps

S5‧‧‧Second filter step

S51~S53‧‧‧Decision substeps

FIG. 1A is a block diagram showing a series-connected finite impulse response filter according to an embodiment of the present invention.

FIG. 1B is a schematic diagram showing the circuit architecture of the series finite impulse response filter of FIG. 1A.

Figure 2A is a schematic diagram showing the integer frequency response of the integer filter of Figure 1B.

Figure 2B shows the zero point distribution of Figure 2A.

Figure 3A is a schematic diagram showing the continuous prototype frequency response of the prototype filter of Figure 1B.

Figure 3B is a schematic diagram showing the discrete prototype frequency response of the prototype filter of Figure 1B.

Fig. 4 is a comparison diagram showing different shape parameters of the prototype filter of Fig. 1B.

Fig. 5 is a graph showing the relationship between the amplitude of the prototype cutoff frequency and the shape parameter of Fig. 4.

Figure 6A is a graph showing a comparison of the frequency response of the conventional window design method and the modified window design method of the present invention.

Figure 6B is a phase comparison diagram of a conventional window design method and a modified window design method of the present invention.

FIG. 7 is a schematic diagram showing the circuit structure of a band pass/high pass filter according to another embodiment of an embodiment of the present invention.

FIG. 8 is a flow chart showing a signal processing method of a series-connected finite impulse response filter according to an embodiment of another embodiment of the present invention.

Hereinafter, a plurality of embodiments of the present invention will be described with reference to the drawings. For the sake of clarity, many practical details will be explained in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not necessary. In addition, some of the conventional structures and elements are illustrated in the drawings in a simplified schematic manner, and the repeated elements may be represented by the same reference numerals.

Please refer to Figure 1A and Figure 1B together. FIG. 1A is a block diagram showing a series-connected finite impulse response filter 100 according to an embodiment of the present invention. FIG. 1B is a schematic diagram showing the circuit architecture of the tandem finite impulse response filter 100 of FIG. 1A. As shown, the series finite impulse response filter 100 is configured to convert the input signal X ( z ) into an output signal Y ( z ). The series finite impulse response filter 100 includes an integer filter 200 and a prototype. Filter 300.

The integer filter 200 is formed by serially connecting a plurality of complementary comb filters 210 to each other. The integer filter 200 can multiply the input signal X ( z ) by the integer conversion function H _sha ( z ) to generate an integer output signal H _sha ( z ) X ( z ). The complementary comb filter 210 having H _ccb (ω), the complex parameter z and the order of the complementary comb filter transfer function H _ccb (z), complementary comb this transfer function H _ccb (z) comprising a complementary comb-shaped frequency response K , where ω is the angular frequency and the complementary comb type frequency response H _ccb (ω) is the frequency response of the complementary comb filter 210. This complementary comb-type conversion function H _ccb ( z ) can be expressed by the formula (1): among them , k =0,1,..., K -1, and K is a positive integer. Furthermore, since the integer filter 200 is formed by a plurality of complementary comb filters 210, the integer conversion function H _sha ( z ) also includes the complementary comb conversion function H _ccb of the complementary comb filters 210. ( z ), and the integer conversion function H _sha ( z ) further comprises a plurality of integer filter orders i and an integer frequency response H _sha (ω), wherein the integer filter order has a maximum value L , and The integer conversion function H _sha ( z ) can be expressed by the formula (2): Where k _i is the number of stages of each integer filter, which corresponds to the number of i- th order complementary comb filters. As can be seen from equation (2), when k _i =0, the integer filter 200 will not use the complementary comb filter 210 of the i th order. Furthermore, comparing the equation (1) with the equation (2), it can be known that when a plurality of complementary comb filters 210 are connected in series, the corresponding plurality of complementary comb-type conversion functions H _ccb ( z ) are related to each other. Multiply the integer conversion function H _sha ( z ). In addition, the integer filter 200 does not need to use a hardware complicated multiplier, and only an adder and a memory unit are needed. Therefore, the finite filter 200 can be used to implement the tandem finite impulse response filter 100. The body greatly improves the filtering effect.

The prototype filter 300 is formed by serially connecting a plurality of prototype filter subunits 310 to each other. The prototype filter 300 multiplies the integer output signal H _sha ( z ) X ( z ) by the prototype conversion function H _pro ( z ) to generate an output signal Y ( z ). The prototype conversion function H _pro ( z ) is a complex number The parameter b _i is composed of, and the prototype conversion function H _pro ( z ) of the embodiment is composed of b ₀ ~ b ₃₂ . Prototype transfer function H _pro (z) comprises a prototype frequency response H _pro (ω), the prototype frequency response H _pro (ω) prior to the cutoff frequency ω _C exponentially increases with increasing frequency. The prototype conversion function H _pro ( z ) further includes a frequency sample m , a shape parameter γ, a frequency domain sample number M, and a prototype frequency response H _pro (ω), and the prototype conversion function H _pro (z) can utilize the formula (3) ) means: H _pro ( m )= e ^{γ | m |} (3); where 0<γ, and -( M -1)/2 m ( M -1)/2. As can be seen from equation (3), the prototype filter 300 is a special exponential response. When the shape parameter γ is greater than zero, the prototype frequency response H _pro (ω) will appear as an upward arc, and at the cutoff frequency ω After _C , the prototype frequency response H _pro (ω) will show a downward trend, so adjusting the size of the shape parameter γ can effectively control the prototype transfer function H _pro ( z ).

The above-described integer filter 200 is connected to the prototype filter 300 to form a series-connected finite impulse response filter 100. This tandem type finite impulse response filter 100 having a transfer function H _cmp (z), this finite impulse response series amplitude filter 100 transfer function H _cmp (z) may utilize equation (4): Where k ₁ ~ k _L are integers. It can be seen from equation (4) that the amplitude of the transfer function H _cmp ( z ) of the tandem finite impulse response filter 100 is also the amplitude of the integer transfer function H _sha ( z ) and the prototype transfer function H _pro ( z ). The product of the amplitude. In addition, the series-connected finite impulse response filter 100 of the present invention can generate a relatively flat passband response by controlling the number k _{i of} the i- th order complementary comb filter and the shape parameter γ, and can greatly increase the cutoff frequency ω. Filter effect after _C.

Fig. 2A is a schematic diagram showing the integer frequency response H _sha (ω) of the integer filter 200 of Fig. 1B. Figure 2B shows the zero point distribution of Figure 2A. As shown, this integer transfer function H _sha ( z ) can be represented by the formula (5): H _sha ( z )=(1+ z ^-1 ) ² (1+ z ^-2 ) ² (1+ z ^-3 ) ³ (1+ z ^-4 )(1+ z ^-5 )(5); comparing equation (5) and equation (1), this integer filtering is known when the filter order K is equal to The number of stages is 2, that is, the number of first order complementary comb filters is 2. Similarly, when K is equal to 2, the number of second-order complementary comb filters is 2; when K is equal to 3, the number of third-order complementary comb filters is 3; when K is equal to 4, the fourth order The number of complementary comb filters is one; when K is equal to five, the number of fifth-order complementary comb filters is one. At this time, the hardware complexity used by the integer filter 200 requires only 9 adders and 24 memory cells. Furthermore, by comparing the equation (1) with z = e ^jω =cos( ω )+ j sin( ω ), the zero value of the complementary comb-type conversion function H _ccb ( z ) can be obtained to satisfy the expression (6): The numerical value corresponding to this equation (6) is shown in Fig. 2B. Although the above-described integer filter 200 can be implemented with a simple hardware, its integer frequency response H _sha (ω) combined with the prototype filter 300 can produce a very ideal and flat low-pass amplitude, and can achieve an amplitude of more than 20 dB. Cut-off band filtering improves the effect.

Figure 3A shows a continuous line Prototype Prototype frequency of the filter 300 of FIG. 1B H _pro (ω) in response to a schematic diagram. FIG. 3B is a schematic diagram showing the discrete prototype frequency response H _pro ( m ) of the prototype filter 300 of FIG. 1B. Fig. 4 is a comparison diagram showing different shape parameters γ of the prototype filter 300 of Fig. 1B. FIG. 5 shows a prototype of the system of FIG. 4 cutoff frequency-amplitude graph _γ Δ γ of the shape parameters. , The prototype frequency response of the prototype filter 300 shown in FIG H _pro (z) to the cutoff frequency ω _C prototype having a cutoff frequency amplitude Δ _γ. When the shape parameter γ is equal to zero, the prototype cutoff frequency amplitude Δ _γ is equal to Δ ₀ and Δ _{0 is} less than zero. This condition is the conventional Window Design Method. The continuous prototype frequency response H _pro ( z ) generated by this window design method is the dashed line in Figure 3A, which corresponds to the discrete prototype frequency response H _pro ( m ) is the square point in Figure 3B. In addition, when the shape parameter γ is greater than zero, the prototype cutoff frequency amplitude Δ _γ will increase. This condition is called the Modified Window Design Method, and the continuous prototype generated by the modified window design method is used. The frequency response H _pro ( z ) is the solid line in Fig. 3A, and the corresponding discrete prototype frequency response H _pro ( m ) is the circular point in Fig. 3B. 3A and 3B show that the prototype filter 300 has a sampling frequency f _s and a frequency domain sampling number M , N . It can be clearly seen from Fig. 3B and Fig. 4 that the difference between the modified window design method and the window design method is that the modified window design method is before the cutoff frequency ( M -1)/2, and the discrete prototype frequency response H _pro ( m ) As the frequency increases, it increases exponentially, and its exponential function conforms to the equation (3). It is worth mentioning that the exponential function is just balanced and balanced with the amplitude attenuation caused by the series connection of the plurality of complementary comb filters 210 of the integer filter 200, thereby generating a flat and stable filtering effect before the cutoff frequency. Furthermore, the limitation of the prototype filter 300 of FIG. 5 is that 33 prototype filter sub-units 310 are connected in series with each other, and the cutoff frequency ω _C is 0.1 π (diameter/sampling). Wherein the prototype cutoff frequency amplitude Δ ₀ is equal to -5.29 dB when the shape parameter γ is equal to zero. Further, apparent from the drawing, when the shape parameter gamma] is larger, the cutoff frequency of the amplitude Δ _γ prototype increased rate will slow down. In this embodiment, γ is selected to be 0.1, the prototype cutoff frequency amplitude Δ _γ is equal to +3.5 dB, and Δ _γ minus Δ ₀ is equal to 8.79 dB.

Fig. 6A is a graph showing the frequency response of the tandem finite impulse response filter 100 of the conventional window design method and the modified window design method of the present invention. Fig. 6B is a phase comparison diagram of the tandem finite impulse response filter 100 of the conventional window design method and the modified window design method of the present invention. As shown, the difference between the modified window design method and the conventional window design method is that the tandem finite impulse response filter 100 utilizes a special exponential response prototype filter 300 in combination with a low complexity integer filter 200. Produces a flatter passband response and greatly increases the filtering effect after the cutoff frequency. In other words, the series-connected finite impulse response filter 100 of the present invention has a very sharp transition band and a suppression band of high suppression capability.

FIG. 7 is a schematic diagram showing the circuit structure of a band pass/high pass filter according to another embodiment of an embodiment of the present invention. As shown, the tandem finite impulse response filter 100 includes an integer impulse response h _sha ( k ) and a prototype impulse response h _pro ( k ), wherein the integer impulse response h _sha ( k ) corresponds to an integer conversion function. H _sha ( z ), the prototype impulse response h _pro ( k ) corresponds to the prototype conversion function H _pro ( z ). The series finite impulse response filter 100 can be applied not only to a low pass filter but also to a band pass or high pass filter. To be applied to a bandpass or highpass filter, the frequency can be adjusted prior to the series finite impulse response filter 100 by the input signal x ( k ) product-sequence frequency sequence s _shift ( k ) The output signal y ( k ) can achieve a very sharp transition band and a high suppression band of suppression for low pass, band pass or high pass applications.

FIG. 8 is a flow chart showing a signal processing method of the series-connected finite impulse response filter 100 according to an embodiment of another embodiment of the present invention. As shown, the signal processing method of the series finite impulse response filter 100 includes a first serial connection step S1, a second serial connection step S2, a third serial connection step S3, a first filtering step S4, and a second filtering. Step S5.

Referring to FIG. 1B together, the first series connection step S1 of FIG. 8 is a series connection of a plurality of complementary comb filters 210 to form an integer filter 200. The second series connection step S2 is a series connection of a plurality of prototype filter sub-units 310 to form a prototype filter 300. The third series connection step S3 connects the prototype filter 300 and the integer filter 200 to form a series-connected finite impulse response filter 100. The first filtering step S4 transmits the input signal X ( z ) to the integer filter 200, and multiplies the input signal X ( z ) by the integer conversion function H _sha ( z ) by the integer filter 200 to generate an integer output. Signal H _sha ( z ) X ( z ). The second filtering step S5 transmits the integer output signal H _sha ( z ) X ( z ) to the prototype filter 300, and multiplies the integer output signal H _sha ( z ) X ( z ) by the prototype filter 300 by the prototype conversion. The function H _pro ( z ) produces an output signal Y ( z ). The prototype conversion function H _pro ( z ) contains the prototype frequency response H _pro (ω), and the prototype frequency response H _pro (ω) increases exponentially with increasing frequency before the cutoff frequency ω _C , and the exponential function conforms to the expression ( 3). Furthermore, the first filtering step S4 includes a maximum order determining sub-step S41, an order total number determining sub-step S42, and an optimization parameter determining sub-step S43. The second filtering step S5 includes a parameter relationship determining sub-step S51, a shape parameter determining sub-step S52, and a prototype conversion function determining sub-step S53.

In detail, the maximum order determining sub-step S41 determines the maximum value L of the integer filter order, that is, determines the maximum order of the complementary comb filter 210, which can be calculated by the equation (6). For example, when the cutoff frequency ω _C is equal to 0.1 π (radius/sampling), L is equal to 9. At the same time, the attenuation amount δ _i corresponding to the order of each integer filter and the corresponding integer filter order i are also determined in the first filtering step S4, as shown in Table 1.

The total number of orders determines that sub-step S42 determines the total number η of integer filter orders. The total number η of the integer filter orders determines the complexity of the integer filter 200. If the value of the total number η is set to be smaller, the complexity of the integer filter 200 is lower. The total number η of this embodiment is set to 10.

The optimization parameter determination sub-step S43 determines the optimum values of the parameters k ₁ to k _L of the series-connected finite impulse response filter 100 using a plurality of constraint conditions. These restrictions are listed as equation (7) ~ equation (10): Where k ₁ ~ k _L is zero or a positive integer; For the indicator function, when k _i ≠ 0, Is 1; when k _i =0, Is 0; Expressed as a positive integer. The parameters k ₁ to k _L selected by the above-described constraints of the equations (7) to (10) allow the series-connected finite impulse response filter 100 to achieve a filter improvement effect of more than 20 dB amplitude. In addition, each constraint has a corresponding number of solutions, and the more restrictions there are, the fewer the number of solutions that meet the constraints. For example, there are 9,369 solutions that meet the constraints of equation (8). If you add the restrictions of equation (9), there are only 418 solutions, as shown in Table 2. The optimization parameter determination sub-step S43 of the present embodiment is proposed before the constraint conditions are the equations (7) to (10), and four final solutions satisfying the restriction conditions are found, as shown in Table 3.

The parameter relationship determining sub-step S51 determines the relationship between the shape parameter γ and the prototype cutoff frequency amplitude Δ _γ . In other words, this parameter relationship decision sub-step S51 will produce a corresponding fifth picture.

The shape parameter determining sub-step S52 determines the relationship between the shape parameter γ determined by the sub-step S51 and the prototype cutoff frequency amplitude Δ _γ according to the parameter relationship, and selects a suitable shape parameter γ. This suitable shape parameter γ must conform to its corresponding value of Δ _γ minus Δ ₀ sufficient to provide a combined amount of attenuation δ _i in several Tables 1 to compensate each other to produce a flat passband response.

The prototype conversion function determining sub-step S53 is carried out by the shape parameter γ determined by the shape parameter determining sub-step S52 into the equation (3) to obtain the prototype conversion function H _pro ( z ) of the prototype filter 300.

The corresponding parameters of the integer filter 200 may be determined by the maximum order determining sub-step S41, the order total number determining sub-step S42, and the optimizing parameter determining sub-step S43 of the first filtering step S4. The parameter relationship determining sub-step S51, the shape parameter determining sub-step S52, and the prototype conversion function determining sub-step S53 of the second filtering step S5 can determine the corresponding parameters of the prototype filter 300. It is worth mentioning that the series finite impulse response filter 100 of the present invention first performs the second filtering step S5 by using the modified window design method to implement the prototype filter 300, and then selects the best by the first filtering step S4. Corresponding parameters of the integer filter 200. Solutions 1 to 4 in Table 3 can achieve filter improvement effects of more than 20 dB amplitude, and can be widely applied to low-pass, band-pass or high-pass requirements.

It can be seen from the above embodiments that the present invention has the following advantages: First, the prototype filter obtained by modifying the window design method combined with the integer filter can not only generate a flat passband response but also greatly increase the filtering effect after the cutoff frequency. . Second, the parameters of the integer filter are matched with the specially selected exponential response of the prototype filter to form a series of finite impulse response filters, which require only a low complexity hardware cost to achieve an amplitude of more than 20 dB. Filtering improves the effect. Third, the series-connected finite impulse response filter can be implemented in low-pass, band-pass or high-pass applications through a simple frequency shifting mechanism. In these different applications, a very sharp transition band and high suppression can be achieved. The ability to suppress the band effect.

Although the present invention has been disclosed in the above embodiments, it is not intended to limit the present invention, and the present invention can be modified and modified without departing from the spirit and scope of the present invention. The scope is subject to the definition of the scope of the patent application attached.

100‧‧‧Sequential finite impulse response filter

200‧‧‧ integer filter

210‧‧‧Complementary comb filter

300‧‧‧ prototype filter

310‧‧‧Prototype filter subunit

X ( z )‧‧‧ input signal

H _sha ( z ) X ( z )‧‧‧ integer output signal

Y ( z )‧‧‧ output signal

b ₀ ~ b ₃₂ ‧‧‧ parameters

z ‧‧‧ plural parameters

Claims (15)

A signal processing method for a series finite impulse response filter for converting an input signal into an output signal, wherein the signal processing method of the series finite impulse response filter comprises the following steps: a first filtering step Transmitting the input signal to an integer filter, and using the integer filter to multiply the input signal by an integer conversion function to generate an integer output signal; and a second filtering step of transmitting the integer output Signaling to a prototype filter, and using the prototype filter to multiply the integer output signal by a prototype conversion function to generate the output signal, the prototype conversion function includes a prototype frequency response, and the prototype frequency response is at a cutoff frequency It has been incremented by an exponential function as a frequency increases. The signal processing method of the tandem finite impulse response filter according to the first aspect of the patent application, further comprising: a first serial connection step of serially connecting a plurality of complementary comb filters to form the integer filter; a second concatenation step of serially connecting the plurality of prototype filter sub-units to form the prototype filter; and a third concatenation step connecting the prototype filter and the integer filter to form the series connection limited Impulse response filter. The signal processing method of the tandem finite impulse response filter according to claim 2, wherein the complementary comb filter has a complementary comb type conversion function, and the complementary comb type conversion function includes a complementary comb type frequency The complementary comb type frequency response is represented as H _ccb (ω), the complex parameter is represented as z , and the filter order is expressed as K , where ω is an angular frequency, the complement, the response, a complex parameter, and a filter order The comb conversion function conforms to the following formula: among them , k =0,1,..., K -1, and K is a positive integer. The signal processing method of the tandem finite impulse response filter according to claim 3, wherein the prototype conversion function further comprises a frequency sampling, a shape parameter and a frequency domain sampling number, wherein the prototype frequency response is expressed as H _pro (ω), the frequency sample is denoted as m , the shape parameter is represented as γ, the frequency domain sample number is represented as M , and the prototype conversion function conforms to the following formula: H _pro ( m )= e ^{γ | m |} 0<γ, and -( M -1)/2 m ( M -1)/2. The signal processing method of the tandem finite impulse response filter according to claim 4, wherein the integer conversion function includes the complementary comb conversion function and a plurality of integer filter orders, each of which is The order of the type of filter is expressed as i , the number of the order of each integer filter is expressed as k _i , and the maximum value of the order of the integer filter is expressed as L , the finite impulse response filter of the series The conversion function is expressed as H _cmp ( z ), and the conversion function of the cascaded finite impulse response filter conforms to the following equation: as well as among them The size of the integer conversion function, and k ₁ ~ k _L are integers; Is an index function, when k _i ≠ 0, Is 1, when k _i =0, Is 0. A signal processing method for a series finite impulse response filter according to claim 5, wherein a positive integer is expressed as The number of each integer filter order is in accordance with the following formula: The signal processing method of the tandem finite impulse response filter according to claim 6, wherein the attenuation of the complementary comb filter corresponding to the cutoff frequency is expressed as δ _i , and the prototype frequency is responsive to the cutoff The frequency has a prototype cutoff frequency amplitude, and the prototype cutoff frequency amplitude is expressed as Δ _γ , and the total attenuation of the integer filter conforms to the following formula: Where Δ _γ >0 and Δ ₀ <0. The signal processing method of the tandem finite impulse response filter according to claim 7, wherein the total number of the integer filter orders is represented as η, and the total number of the integer filter orders The quantity meets the following formula: A series-connected finite impulse response filter for converting an input signal into an output signal, the series-connected finite impulse response filter comprising: an integer filter connected in series by a plurality of complementary comb filters The integer filter multiplies the input signal by an integer conversion function to generate an integer output signal; and a prototype filter is formed by serially connecting a plurality of prototype filter subunits to each other. The integer output signal is multiplied by a prototype conversion function to generate the output signal. The prototype conversion function includes a prototype frequency response, and the prototype frequency response is increased by an exponential function as a frequency increases before a cutoff frequency. An integer filter is coupled to the prototype filter to form the series finite impulse response filter. The tandem finite impulse response filter of claim 9, wherein the complementary comb filter has a complementary comb-type conversion function, the complementary comb-type conversion function comprising a complementary comb-type frequency response, a complex number a parameter and a filter order, the complementary comb type frequency response is represented as H _ccb (ω), the complex parameter is represented as z , the filter order is expressed as K , where ω is an angular frequency, and the complementary comb-type conversion function Meet the following formula: among them , k =0,1,..., K -1, and K is a positive integer. The tandem finite impulse response filter according to claim 10, wherein the prototype conversion function further comprises a frequency sampling, a shape parameter and a frequency domain sampling number, and the prototype frequency response is represented as H _pro (ω The frequency sample is represented as m , the shape parameter is represented as γ, the frequency domain sample number is represented as M , and the prototype conversion function conforms to the following formula: H _pro ( m )= e ^{γ | m |} ; where 0<γ, And -( M -1)/2 m ( M -1)/2. The tandem finite impulse response filter according to claim 11, wherein the integer conversion function includes the complementary comb type conversion function and the complex integer filter order, and the integer filter order Expressed as i , the number of stages of each integer filter is expressed as k _i , and the maximum value of the order of the integer filter is expressed as L , and the conversion function of the series-connected finite impulse response filter is represented as H _Cmp ( z ), the conversion function of the cascaded finite impulse response filter conforms to the following formula: as well as among them The size of the integer conversion function, and k ₁ ~ k _L are integers; Is an index function, when k _i ≠ 0, Is 1, when k _i =0, Is 0. A tandem finite impulse response filter as described in claim 12, wherein a positive integer is expressed as The number of each integer filter order is in accordance with the following formula: The tandem finite impulse response filter according to claim 13, wherein the complementary comb filter has a corresponding attenuation amount at the cutoff frequency expressed as δ _i , and the prototype frequency has a response in response to the cutoff frequency. Prototype cutoff frequency amplitude, the prototype cutoff frequency amplitude is expressed as Δ _γ , and the total attenuation of the integer filter conforms to the following formula: Where Δ _γ >0 and Δ ₀ <0. The tandem finite impulse response filter according to claim 14, wherein the total number of the integer filter orders is expressed as η, and the total number of the integer filter orders is in accordance with the following formula :