JP2009017520A - Sampling frequency conversion apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a sampling frequency conversion method and apparatus capable of changing, in real-time, a sampling frequency conversion ratio from up-sampling to down-sampling seamlessly with realistic computational complexity and achieving sampling frequency conversion with high accuracy also in the aspect of Shannon's sampling theorem. <P>SOLUTION: Together with an amplitude value of a sample of a pre-conversion discrete signal, a sample time is recorded or determined by sequential calculation and a detection value at a time when the sample is captured as a continuous signal, is determined from a difference between a detection time and the sample time. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

The present invention relates to a sampling frequency converter that converts a sampling frequency of discrete-time signal processing.

Conventionally, various implementation methods and application methods are known for sampling frequency converters for discrete-time signal processing.
For example, Patent Document 1 describes a method of realizing sampling frequency conversion only by digital signal processing without using an analog circuit through oversampling, filtering, and decimation processing.
Further, in Patent Document 2, when obtaining the coefficients of the band limiting FIR filter in the pre-decimation process, a method of generating filter coefficients having a required frequency characteristic by time-stretching a filter coefficient template stored in a table in advance. Is stated.
Further, in Patent Document 3, the sample value stored in the circular buffer for each input-side sampling period is determined by calculating the time difference between the stored sample value storage time and the output-side sampling period time at the timing of the output-side sampling period. And performing the polynomial interpolation on several intervals before and after the output side sampling cycle time, and setting the weighted average value of the output values as the output value of the output side sampling cycle A method of performing sampling frequency conversion without oversampling is described.
Patent Document 4 is a musical application example of a sampling frequency converter, and describes a method of reproducing the texture of an old digital audio device by deliberately lowering the sampling frequency.

Patent 3044739 Japanese Patent No. 3707148 JP2003-324337 Japanese Patent No. 3743326

By the way, the above-described conventional sampling frequency converter is based on the premise that the conversion ratio of the sampling frequency is fixed during operation. For the purpose of exchanging signals between equipment with different sampling frequencies, there is no problem with being fixed.
However, assuming that sampling frequency conversion is used as an acoustic effect, the range of the effect is limited with a fixed conversion ratio.
Furthermore, Patent Document 1 and Patent Document 2 are based on the premise of oversampling to the sampling frequency that is the least common multiple of the sampling frequency before and after the conversion, and further involve a filtering process such as convolution, which increases the amount of calculation. Have
Patent Document 3 shows a method of avoiding oversampling by using phase difference information, but presupposes polynomial interpolation of sample values before conversion, and is not necessarily in view of the Shannon sampling theorem described later. It is not an optimal interpolation method.
The present invention realizes a highly accurate sampling frequency conversion from the viewpoint of Shannon's sampling theorem, which can be changed in real time without a seamless transition from upsampling to downsampling, with a realistic calculation amount. It is an object to provide a sampling frequency conversion method and a sampling frequency conversion device.

First, we will briefly explain Shannon's sampling theorem.
Shannon's sampling theorem means that when sampling a continuous-time signal at regular intervals, frequency component information (amplitude and phase) up to half the sampling frequency (hereinafter Nyquist frequency) can be stored correctly. A frequency component higher than the Nyquist frequency appears to be folded back as a component (alias component) lower than the Nyquist frequency.
Since components once mixed as aliases cannot be removed, in order to sample a continuous-time signal correctly, frequency components higher than the Nyquist frequency must be removed in advance. Conversely, a continuous-time signal from which a frequency component higher than the Nyquist frequency is removed is mathematically retained even after being converted into a discrete-time signal, and can be converted again into the same continuous-time signal.

In order to equivalently convert a continuous time signal from which a frequency component higher than the Nyquist frequency is removed and a discrete time signal obtained by sampling the continuous time signal at a constant interval, a component higher than the Nyquist frequency is 0 times and a component lower than the Nyquist frequency is A filter must be assumed that is 1x and does not change the phase of a particular frequency.
A filter having the above characteristics is also referred to as an ideal filter, and is represented by Sin (x) / x in the mathematical expression. This mathematical expression is also called a Sinc function. FIG. 1 shows a graph of the Sinc function.

Specifically, when the sampling frequency is f, each sample value of the sampled discrete time signal is expressed as a continuous time waveform in the form of “Sinc (π · f · (time−sample time)) · sample value”. Therefore, the waveform obtained by adding and synthesizing the continuous time waveform to all the sample values is the same as the waveform of the continuous time signal before the sampling process. ("・" Represents multiplication)
Since a discrete-time signal and a continuous-time signal can be regarded as equivalent, this principle can be applied not only to the conversion of continuous-time → discrete-time signals, but also to the conversion of discrete-time → discrete-time signals with different sampling frequencies. .
Now, the present invention is aimed at the conversion of the sampling frequency at an arbitrary conversion ratio. This is because the discrete time signal (D1s) before the conversion is converted to the original discrete time signal via the theoretical continuous time signal (Cs). This can be said to be a process of converting to a discrete time signal (D2s) different from the time signal.

In order to realize this, the following functions must be provided.
1. A function of adjusting the upper limit frequency of Cs so that it is equal to or less than half of the smaller frequency among the sampling frequencies of D1s and D2s.
2. A function of sampling a Cs value at an arbitrary time without depending on the sampling frequency of D1s.
3. A function of adjusting the amplitude of D2s according to the sampling frequency ratio.

1 is a function necessary for satisfying the sampling theorem in the conversion process between discrete time → continuous time signals. In order to satisfy the sampling theorem for both discrete time signals before and after conversion, the sampling frequency must be adjusted to a smaller sampling frequency.
2 is an indispensable function for converting a continuous-time signal into a converted discrete signal. In the conventional technique, there is a method of performing oversampling or performing interpolation processing that is not strict with respect to the sampling theorem. It was taken.
3 is to compensate for this because the energy of the signal (root mean square amplitude value) changes depending on the density of sample values per unit time and the energy change due to the time expansion and contraction of the Sinc function when re-sampling is performed. It is a function.
The present invention provides a technique for realizing these functions in accordance with Shannon's sampling theorem.

The invention according to claim 1 is a data processing device that converts the sampling frequency (f1) of the first discrete time signal (D1s) to generate the discrete time signal (D2s) of the second sampling frequency (f2). Thus, a means for obtaining a time value (D1t) for outputting one sample of D1s and a time value (t2) for sampling one sample of D2s, and a cycle for storing the amplitude value (D1v) of each sample of D1s one by one In a process for obtaining the amplitude value of one sample of D2s, including a buffer and means for obtaining a value of a low-pass filter function (LPF) having a finite parameter section that can return a value other than 0 on the assumption that it is used for convolutional interpolation. A constant (ψ) · MIN (f1, f2) · that scales at least the blocking frequency of κ = LPF to 1 Hz among all samples of the circular buffer Data for (D1t−t2 + positive delay time (ct)) included in the valid section of the LPF function, ρ = LPF (κ) · D1v is obtained, and ρ is added to obtain the amplitude value of D2s at t2. It is a processing device. (Here, MIN (x, y) represents a small value of x and y.)

The invention according to claim 2 is the data processing device according to claim 1, wherein ρ is summed and then multiplied by a value proportional to SQRT (when f1 ≦ f2: f1 / f2, when f1> f2: f2 / f1). This is a data processing device for obtaining the oscillation value of D2s at t2. (Here, SQRT (x) represents the square root of x.)

The invention according to claim 3 is the data processing apparatus according to claim 1, wherein a set of D1t and D1v is recorded in a circular buffer and used for calculating κ.

According to a fourth aspect of the present invention, in the data processing device of the first aspect, the value of the positive delay time (ct) is set to (valid interval on the positive value side of LPF + 1) / (ψ · MIN (f1, f2)) This is a data processing apparatus that updates the values one by one so that the above values are obtained.

According to a fifth aspect of the present invention, in the processing for obtaining the amplitude value of one sample of D2s in claim 1, an alias is generated for the component of D2s by expanding and contracting the time width of the LPF in proportion to the variable parameter δ. Data processing device to be made.

As described above, according to the present invention, the conversion ratio of the sampling frequency can be changed in real time from the up-sampling to the down-sampling with a realistic calculation amount, and the accuracy from the point of view of the Shannon sampling theorem. It is possible to provide a sampling frequency conversion method and a sampling frequency conversion device that realize high sampling frequency conversion.
Furthermore, according to the fifth aspect, it is possible to provide seasoning as an acoustic effect by intentionally generating an alias component.

Embodiments will be described below for easier understanding of the present invention. Such an embodiment shows one aspect of the present invention, and can be arbitrarily changed within the scope of the present invention.

FIG. 2 shows an example of a circuit that operates a part of the signal processing circuit at a different sampling frequency in terms of software, and the conversion means from fixed to variable sampling frequency circuit and from variable to fixed sampling frequency circuit will be described.
As shown in the figure, a circuit 1 that operates at a fixed sampling frequency, a circuit 2 that operates at a variable sampling frequency, a converter 3 that converts a discrete signal at a fixed sampling frequency into a discrete signal at a variable sampling frequency, and a variable The circuit 2 that is composed of a conversion device 4 that converts a discrete signal having a sampling frequency into a discrete signal having a fixed sampling frequency and that operates at a variable sampling frequency can change the sampling frequency at any time by a variable sampling frequency value 8. .

The fixed sampling frequency assumes the hardware sampling frequency of the entire circuit, and the variable sampling frequency assumes a sampling frequency that is generated in software (ie, computationally). (Although it is a software sampling frequency, if it can cope with unexpected fluctuations in hardware sampling frequency such as jitter by providing a secondary circular buffer, it can also be applied to sampling frequency conversion between hardware. is there.)

First, a configuration common to fixed to variable conversion and variable to fixed conversion will be described.
In the present invention, the sample time is recorded together with the amplitude value of the sample of the discrete signal before conversion, or is obtained by calculation one by one, and the detected value when the sample is regarded as a continuous signal is calculated as the difference between the detected time and the sample time. It is characterized by seeking from.
By the way, in order to understand this visually, it is easier to understand it as a position difference rather than a time difference.
FIG. 3A is a schematic diagram in which samples of a discrete time signal before conversion in the sampling frequency converter of the present invention are compared to particles moving at a constant speed.
The sample value (D1v) of the discrete time signal (D1s) before conversion is emitted from the nozzle 101 as particles 102 at the timing of the sampling period before conversion, and the sensor 103 determines the amplitude of each particle at the timing of the sampling period after conversion. Considering the Sinc function multiplied by the value (FIG. 3B), the total value for all particles is taken as the sample value (D2v) of the discrete time signal (D2s) before conversion.
According to this example, the time taken for the particles to move from the nozzle to the sensor is proportional to the distance between the nozzle and the sensor. That is, the difference between the sampling time of the particle and the sensor can be considered by replacing it with a difference in distance.

If the sampling frequency of the nozzle and the sensor is the same, the sensor detection process can be performed at the same time as the nozzle releases new particles, and the output value of the sensor can be obtained.
However, when the sampling frequency of the nozzle and the sensor is not the same, for example, that of the nozzle is 44.1 KHz and the sensor is 48 KHz, the particle emission timing of the nozzle in a form depending on the hardware sampling time, In order to synchronize with the detection timing of the sensor, oversampling to the sampling frequency of the least common multiple of 44100 and 48000 is required, and it cannot be obtained with a realistic calculation amount.
Therefore, for a circuit that operates at a fixed sampling frequency, a particle emission or detection process is performed for each process, and for a circuit that operates at a variable sampling frequency, the processing timing is adjusted to the fixed circuit. The difference between the time at the timing and the time that should have been processed is corrected by the coordinate operation of the sensor (in the case of fixed → variable) or the nozzle (in the case of variable → fixed).

FIG. 4 shows a processing image when the sampling frequency of D1s is fixed and the sampling frequency of D2s is variable. The balloon written under the particle in the figure represents the time recorded on the particle, and the unit is 1 sample time (in this case, 1/3000 second) on the fixed sampling frequency side (hereinafter, fixed sample time). Called). Although four processing frames are illustrated, one frame represents a snapshot of the state at one fixed sample time.
Since the sampling frequency of the sensor, that is, D2s is 2000 Hz in this case, the detection processing is originally performed at intervals of 1.5 fixed sample times.
Since the operation timings of the nozzle and the sensor coincide with each other at the “first time”, the sensor performs the detection process at the reference position (the position of the particle at t = 2 in the example in the figure).
In the “second time”, since only one fixed sample time has elapsed since the operation in the first time, the detection process is not performed.
In the “third time”, since two fixed sample times have elapsed after operating in the first process, a detection process is performed. However, since what is actually desired to be detected is a state when 1.5 fixed sample times have elapsed since the first processing, detection is performed at a position shifted by 0.5 fixed sample times. (In the example in the figure, the intermediate position of the particles of t = 3 and t = 4, that is, the position of t = 3.5)
In the “fourth”, three fixed sample times have elapsed after operating in the first process. Since the detection interval of the sensor is 1.5 fixed sample times, and the 3 fixed sample times are integer multiples thereof, here, the detection process is performed at the reference position.

Contrary to the example in FIG. 4, when the sampling frequency of D1s is variable and the sampling frequency of D2s is fixed, the fractional time is handled without oversampling by shifting the position of the nozzle instead of the sensor. Can do.

The Sinc function (Sin (x) / x) used in the present invention is known to have a value in an infinite domain in terms of mathematics. Considering that the Sinc function is used as it is, an infinite calculation is considered. A quantity is required and is not feasible.
Therefore, it is necessary to terminate the Sinc function in a finite interval. Several such methods are known. Here, a method of terminating the domain of the Sinc function by a window function is introduced.
pSinc (t) = Sinc (π · t)
Win (t) = (1−Cos (π · t / n)) / 2
(N is an arbitrary natural number)
wSinc (t) = (when | t | ≦ n: pSinc (t) · Win (t), when | t |> n: 0)
pSinc () is called a normalized Sinc function. The normalized Sinc function functions as an ideal filter waveform in which the Nyquist frequency becomes the stop frequency by associating the sampling period (the reciprocal of the sampling frequency) with the parameter of 1. (The Sinc function is a symmetrical graph with 0 as the starting point.)
Win () is a window function called a Hanning window.
wSinc functions as a normalized Sinc function having a value corresponding to the number of periods represented by −n to n by multiplying pSinc () and Win ().
wSinc does not necessarily have a frequency component equal to or higher than the stop frequency at 0, but it can be regarded as 0 in practical use.
In the above-described sensor, each particle is regarded as a Sinc function multiplied by its amplitude value. However, the above-described wSinc function is used instead of the Sinc function.

Now, in order to satisfy the sampling theorem when converting from D1s to D2s, the stop frequency of the wSinc function must be lower than half of the sampling frequency of either D1s or D2s.
In order to realize this, wSinc may be expanded and contracted as follows.
ρ = wSinc (MIN (D1s sampling frequency, D2s sampling frequency) · (particle time−sensor sampling time + positive delay time (ct)) · δ)
Here, the unit of time difference between the particle and the sensor is second.
In the equation, δ is a value for finely adjusting the expansion / contraction rate of wSinc. wSinc is not an ideal Sinc function, and its stop frequency is strictly different from that of the Sinc function. Therefore, by setting δ to a value less than 1, the blocking frequency is lowered to suppress the occurrence of alias components.

Further, since the signal energy of the signal detected by the sensor changes due to the time expansion / contraction of wSinc and the change of the sampling frequency, this must be corrected.
There is a proportional relationship between the time expansion rate of wSinc and the amplitude of each spectral component after the Fourier transform of wSinc itself. Since wSinc is a filter coefficient, the amplitude amplification factor of the waveform filtered by this is proportional to the time expansion rate of wSinc.
Further, the amplitude of the waveform obtained by adding together uncorrelated continuous signals is proportional to the square root of the number of signals to be added. The addition of particles at the sensor can be regarded as the addition of continuous signals that are generally uncorrelated. The number of particles added is proportional to the sampling frequency ratio between D2s and D1s.
From these conditions, a correction value can be obtained as follows: α = SQRT (when f1 ≦ f2: f1 / f2, when f1> f2: f2 / f1) · δ
* Here, SQRT (x) represents the square root of x.

In the detection process of the sensor, “ρ · amplitude value of particle · α” may be obtained for all particles and summed up.

In the present invention, a circular buffer is used to hold a set of D1s sample values and sample times, and in the above example, particle information. Since the memory cannot be increased without limitation in terms of hardware, and the calculation amount of detection (convolution) processing by the sensor depends on the size of the circular buffer, the estimation of the circular buffer size is important.

First, the following variables are defined based on the maximum value and minimum value of the variable side sampling frequency.
VRMin = minimum value of variable-side sampling frequency VRMax = maximum value of variable-side sampling frequency CR = fixed-side sampling frequency TRMin = MIN (CR, VRMin)
TRMax = MAX (CR, VRMax)

If the particle disappears while the sensor is capturing the particle as an effective interval of the wSinc function, the detection value of the sensor will be affected as discontinuous noise. It must continue to exist.
If the coordinate of the particle is 0, the maximum width of the effective section of the wSinc function is
SincWidth = n / TRMin / δ
(* Unit is seconds. N is the number of times the 0 point of the Sinc function is repeated in the window function.)
-SincWidth ≦ t ≦ SincWidth
It becomes.

Further, as described above, in order to process the fractional time from the difference in the sampling cycle, the process of releasing the particles or shifting the detection time value is performed.
The maximum value of time correction by this processing is obtained by the following calculation.
AdjustWidth = 1 / CR
The required buffer size in the fixed to variable sampling frequency converter is:
S1 = (SincWidth · 2 + AdjustWidth) · CR
= N / TRMin / δ · 2 · CR + 1
It is.
And the necessary buffer size in the variable → fixed sampling frequency converter is:
S2 = (SincWidth · 2 + AdjustWidth) · TRMax
= N / TRMin / δ · 2 · TRMax + 1 / CR · TRMax
It is.

By the way, in the above equation, SincWidth is obtained by TRMin regardless of the value of the variable sampling frequency.
For this reason, when the change range of the variable sampling frequency is wide (for example, from 1 KHz to 100 KHz), the buffer size, particularly the value of S2, becomes very large, and the amount of calculation also increases.
When the delay time of the signal accompanying the sampling frequency conversion is fixed (that is, when the distance between the nozzle and the sensor is fixed), the effective section of wSinc can be accommodated even when the variable side sampling frequency takes the minimum value. This problem cannot be avoided because a sufficient delay time is required.

However, if the delay time is variable based on the variable side sampling frequency, the buffer size and the calculation amount can be greatly reduced.
If the variable sampling frequency at that time is VRNow, the buffer size required at that time is obtained by the following equation.
Fixed to variable sampling frequency conversion:
S1Now = n / MIN (CR, VRNow) / δ · 2 · CR + 1
Variable to fixed sampling frequency conversion S2Now = n / MIN (CR, VRNow) / δ · 2 · VRNow + 1 / CR · VRNow
Since S1Now is inversely proportional to VRNow and S2Now is proportional to VRNow, the maximum buffer size is obtained by the following calculation.
S1VMax = n / MIN (CR, VRMin) / δ · 2 · CR + 1
S2VMax = n / MIN (CR, VRMax) / δ · 2 · VRMax + 1 / CR · VRMax

With respect to S2Now, since there is no great variation with respect to the variation of VRNow, the sensor detection process may be performed for all elements that are not buffered.
Since S1Now greatly depends on the change in VRNow, the amount of calculation can be further reduced by performing sensor detection processing only from the latest particle index to the past index of S1Now. The method for calculating the index of the circular buffer is omitted because it is obvious.

As described above, in the present invention, the sampling frequency conversion ratio is variable.
By changing the sampling frequency, there is a considerable nonlinear effect and noise is generated, and the effective section of wSinc may temporarily exceed the buffer size.
Therefore, it is possible to avoid these problems by securing a slightly larger buffer size and applying a low-pass filter to the variable sampling frequency value.

By the way, the value δ used for finely adjusting the expansion / contraction rate of the wSinc function can be generated by setting an alias component larger than 1 to this value.
Although it is not a meaningful operation in a measurement device or an audio device, it is meaningful when viewed as a kind of acoustic effect.

In addition, the interpolation function between samples described so far is mainly the Sinc function and wSinc derived therefrom, but the change in the stop frequency and the change in the amplitude value of the spectrum due to time expansion and contraction are based on the convolution process. Any interpolation function is applicable, and any interpolation function that has properties as a low-pass filter and has a sufficiently small amplitude above the stop frequency can be used in the sampling frequency conversion apparatus of the present invention.

It is the figure which showed the graph of the Sinc function. It is a block diagram which shows the structure of one Embodiment of this invention. It is a schematic diagram of the sampling frequency converter of this invention. It is the figure which showed the processing image of the sampling frequency converter of this invention.

Claims (5)

A data processing device for converting a sampling frequency (f1) of a first discrete time signal (D1s) to generate a discrete time signal (D2s) of a second sampling frequency (f2),
Means for obtaining a time value (D1t) for outputting one sample of D1s and a time value (t2) for sampling one sample of D2s, and a cyclic buffer for storing the amplitude value (D1v) of each sample of D1s one by one Means for obtaining a value of a low-pass filter function (LPF) having a finite parameter section that can return a value other than 0 on the assumption that it is used for convolution interpolation,
In the process of obtaining the amplitude value of one sample of D2s, a constant (ψ) · MIN (f1, f2) · (D1t−t2 + positive) that scales at least the blocking frequency of κ = LPF to 1 Hz among all samples of the circular buffer Is a data processing apparatus that obtains ρ = LPF (κ) · D1v for a sample sequence whose delay time (ct)) is included in the valid section of the LPF function, and sums ρ to obtain the amplitude value of D2s at t2. (Here, MIN (x, y) represents a small value of x and y.) 2. The data processing apparatus according to claim 1, wherein after summing ρ, the amplitude value of D2s at t2 is multiplied by a value proportional to SQRT (when f1 ≦ f2: f1 / f2, when f1> f2: f2 / f1). Data processing device. (Here, SQRT (x) represents the square root of x.) 2. The data processing apparatus according to claim 1, wherein a set of D1t and D1v is recorded in a circular buffer and used for calculating κ. 2. The data processing apparatus according to claim 1, wherein the value of the positive delay time (ct) is successively set to be equal to or greater than (LPF positive value side effective interval + 1) / (ψ · MIN (f1, f2)). Data processing device to be updated. 2. The data processing apparatus according to claim 1, wherein in the process of obtaining an amplitude value of one sample of D2s, an alias is generated for the component of D2s by expanding and contracting the time width of the LPF in proportion to the variable parameter δ.

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