JP6307715B2 - Audio signal processing apparatus and audio signal processing method - Google Patents

Description

  The present invention relates to a technique for digital processing of an audio signal, such as quantization of an audio signal.

  When a digital audio signal is generated, a procedure for quantizing the signal is performed. Conventionally, in this quantization procedure, for example, delay means for delaying an output signal by one sampling time, addition means for adding the delay signal delayed by the delay means and the input signal, and obtaining an addition result; A noise shaping means comprising: a resonance means for amplifying only the frequency components before and after the inherent resonance frequency, and obtaining a resonance result; and a quantization means for quantizing the resonance result and obtaining a quantization result. A / A comprising a configuration in which an input signal is processed in the order of addition means, resonance means, and quantization means and output as an output signal, and a part of this input signal is fed back from the quantization means to the addition means again. A D converter is known (see, for example, Patent Document 1).

JP 2001-298365 A (see paragraphs [0022], [FIG. 1], etc.)

  However, the invention described in Patent Document 1 has a problem that the configuration and processing are complicated, for example, a configuration in which a part of the signal processed by the quantizing unit is fed back to the adding unit.

  The present invention has been made in view of the above problems, and provides an audio signal processing device and an audio signal processing method capable of realizing noise shaping with a simple configuration and processing to reduce the audible effect of quantization noise. The issue is to provide.

To solve such problems, the invention of claim 1 includes a quantization unit you quantizing audio signals, the noise shaping to reduce the influence of quantization noise generated in the process of the quantization A first filter provided at the subsequent stage of the quantization means having a first transfer function that can be realized, and a second filter provided at the front stage of the quantization means having a second transfer function that is an inverse function of the first transfer function . and 2 filters, and wherein the obtaining Bei a.

According to a second aspect of the present invention, in addition to the configuration according to the first aspect , the first transfer function has a configuration in which a feedback loop is removed from a configuration that realizes signal processing based on an initial transfer function including a feedback element. It is characterized by being obtained by the process of equivalent conversion to obtain By adding such a configuration of the invention described in claim 2, in the invention described in claim 3, in addition to the configuration described in claim 1, a gap between the first filter and the second filter is provided. The audio signal processing device can be configured such that no feedback means for feeding back the audio signal processed by the first filter to the second filter is provided.

As described above, the invention described in claim 3 has a novel configuration of the audio signal processing realized as a result of adding the configuration of the invention of claim 2 to the invention of claim 1. Stipulate .

The invention according to claim 4, in addition to the configuration of claim 3, prior Symbol first transfer function is characterized in that all the coefficients have been adapted Ru integer der.

Invention according to claim 5, in addition to the configuration according to any one of claims 1 to 4, in the audio signal processing device, by changing the frequency characteristics of the audio signal, the magnitude of the audio signal wherein a function to reduce the size of the quantization noise, further, a feature in that it comprises pretreatment means provided upstream of the second filter for of.

The invention according to claim 6 is an audio signal processing method executed by the audio signal processing device, and is capable of realizing noise shaping that reduces the influence of quantization noise generated in the process of quantizing the audio signal. Filtering an audio signal using a second transfer function that is an inverse function of the transfer function, quantizing the filtered audio signal, and filtering the quantized audio signal using the first transfer function And
According to a seventh aspect of the present invention, in addition to the configuration of the sixth aspect, the first transfer function excludes a feedback loop from a configuration that realizes signal processing based on an initial transfer function including a feedback element. It is obtained by the process of equivalent conversion to obtain the above configuration.

According to the first and sixth aspects of the invention, by performing the processing by the first filter having a characteristic capable of realizing noise shaping of the quantized audio signal in the subsequent stage of the processing of the quantization means, Noise shaping of quantization noise can be performed. Also,
By performing the processing by the second filter having the inverse characteristic of the first filter in the preceding stage of the processing of the quantization means, the processing of the second filter and the processing of the first filter are performed on the audio signal itself. Thus, quantization can be performed while maintaining the original state. Then, by processing the audio signal in the order of processing by the first filter, processing by the quantization means, and processing by the second filter, quantization and noise shaping can be realized as simple processing with a simple configuration. As a result, noise shaping that can reduce the influence of quantization noise by a simple configuration and processing that does not require a feedback loop to feed back the signal can be realized, and the alteration effect added to the original signal by noise shaping processing can be realized. It can be canceled by a filter having an inverse characteristic .

Further, according to the first and sixth aspects of the invention, the first filter and the second filter have a predetermined transfer function, so that noise shaping of an audio signal composed of a plurality of time-series signals is performed. Can be reliably performed using a transfer function. Further, since the transfer function of the second filter is configured to be an inverse function of the transfer function of the first filter, the signals processed by the second filter and the first filter are the original ones. State is maintained. As a result, quantization and noise shaping can be performed without altering the original signal.
According to the second and seventh aspects of the invention, the transfer function of the filter provided in the subsequent stage of the quantization processing unit is equivalently converted to a configuration that realizes signal processing based on an initial transfer function including a feedback element. Thus, the transfer function corresponds to a configuration in which the feedback loop is removed. In this way, according to the present invention, the noise shaping characteristics realized by the audio signal before the equivalent conversion realized including the feedback element are maintained as they are even in the configuration in which the feedback loop is removed after the equivalent conversion. can do.

According to the invention of claim 3, the audio signal processed by the first filter is converted to the second filter.
The feedback means is not provided, so that a complicated structure for returning the signal is formed and the signal processing including the returned signal is performed.
It is possible to suppress the instability of the system that can cause system damage due to infinite increase in system output due to the occurrence of complicated processing and feedback, and noise shaping with simple configuration and processing
The system can be realized concretely, and the system can be stabilized without special consideration.

According to the fourth aspect of the present invention, the first transfer function of the first filter is configured so that all the coefficients are integers, so that the value of the filter coefficient also includes a component after the decimal point. Unlike the case, it is not necessary to re-quantize the audio signal processed by the first filter, and quantization and noise shaping can be performed with a simple configuration and a simple procedure.

According to the fifth aspect of the present invention, the noise shaping means and the preprocessing means that can reduce the magnitude of the quantization noise with respect to the magnitude of the voice signal by changing the frequency characteristic of the voice signal before encoding. Used . Thus, according to the invention described in claim 5, noise shaping can be performed while reducing the size of the existing quantization noise with respect to the size of the audio signal, and the sound quality of the audio signal can be further improved. .

It is a functional block diagram which shows the whole structure of the audio | voice signal processing apparatus which concerns on embodiment of this invention. It is a functional block diagram which shows the principle of the process by the transfer function of an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the principle of the process by the transfer function of an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the principle of the process by the transfer function of an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the principle of the process by the transfer function of an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the principle of the process by the transfer function of an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the structure of the quantization part in an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the structure of the conventional pre-processing part (when not using the post filter and pre-filter of this embodiment) and a quantization part in an audio | voice signal processing apparatus same as the above. It is a functional block diagram which shows the structure of the pre-processing part based on this invention (when the post filter and pre-filter of this embodiment are used) and a quantization part in an audio | voice signal processing apparatus same as the above. It is a 1st figure which shows the result of having each reproduced | regenerated the audio | voice signal processed by the audio | voice signal processing apparatus same as the above, and the audio | voice signal which performed the process by the conventional audio | voice signal processing apparatus as a comparative example. It is a 2nd figure which shows the result of each reproducing | regenerating the audio | voice signal which processed with the audio | voice signal processing apparatus same as the above, and the audio | voice signal which performed the process by the conventional audio | voice signal processing apparatus as a comparative example.

[Basic configuration]
FIG. 1 shows an embodiment of the present invention.

  FIG. 1 is a functional block diagram showing the overall configuration of the audio signal processing apparatus according to this embodiment.

  The audio signal processing apparatus 1A according to this embodiment is used for, for example, a process of converting an input analog audio signal into a digital audio signal (A / D conversion) and outputting the digital audio signal. The audio signal processing apparatus 1A includes, for example, at least one control unit such as a CPU, and performs various processes for A / D conversion of an audio signal, various processes related to A / D conversion, and the like.

  As shown in FIG. 1, the audio signal processing device 1 </ b> A according to this embodiment includes an encoding unit 1, a preprocessing unit 2, and a quantization unit 3.

  The encoding unit 1 performs an encoding process at the time of A / D conversion. That is, the data obtained by sampling and quantizing the analog signal is input to the encoding unit 1, and this data is encoded to generate a digital signal. The encoding by the encoding unit 1 is, for example, a form in which a speech signal formed by a time-series signal is subjected to predictive encoding by linear prediction (for example, adaptive differential pulse code modulation (ADPCM), hereinafter “ It is described as “ADPCM”))). However, the present invention is not limited to this, and any encoding method may be used. Further, the encoding unit 1 may be configured to perform sampling or quantization at the time of A / D conversion.

The preprocessing unit 2 has a function of adjusting the signal component before the quantization processing in this embodiment is performed on the digital signal output from the encoding unit 1. Specifically, the preprocessing unit 2 has a function of amplifying a high frequency signal component of the audio signal before the quantization process is performed. For example, when the encoding unit 1 of this embodiment performs encoding by predictive encoding such as ADPCM, the pre-processing unit 2 performs high-pass filtering (not shown) on the encoded digital signal. It has a function of cutting frequency components other than a specific frequency band by a band frequency component cut or a band pass filter (not shown). This
It is possible to relatively reduce the magnitude of the quantization noise with respect to the voice data and the output voice.

  The quantization unit 3 quantizes the audio signal output from the encoding unit 1 and the preprocessing unit 2. The specific configuration and processing principle of the quantization unit 3 will be described later.

[Specific configuration of quantization unit]
As illustrated in FIG. 1, the quantization unit 3 includes a quantization processing unit 31 as a “quantization unit” that performs the “quantization procedure”, and a “noise shaping procedure” that is provided in the subsequent stage of the quantization processing unit 31. The “noise shaping means” for performing the “first filtering procedure”, the post filter 32 as the “first filter” for performing the “first filtering procedure”, and the “noise shaping procedure” provided before the quantization processing unit 31 are performed. A "noise shaping means" and a prefilter 33 as a "second filter" for performing a "second filtering procedure".

  Note that the quantization unit 3 has only a configuration in which processing is performed in the order of the pre-filter 33, the quantization processing unit 31, and the post filter 32, and corresponds to “feedback means” that feeds back a part of the processed signal. A configuration (for example, a configuration for returning a part of the audio signal processed by the post filter 32 to the pre-filter 33) is not provided. For this reason, it is possible to suppress instability of the system, such as generation of complicated processing and system output resulting from infinite increase due to feedback. The system can be stabilized with a simple configuration without special consideration.

  The quantization processing unit 31 performs specific processing for quantizing the sampled audio signal (in this embodiment, the audio signals output from the encoding unit 1 and the preprocessing unit 2).

  The post filter 32 has a characteristic capable of realizing noise shaping of the quantized audio signal, and performs noise shaping on the quantized audio signal. In other words, the post filter 32 is a high frequency band or audio signal that is a frequency band in which noise is conspicuous in various noises present in the audio signal output from the quantization processing unit 31, for example, quantization noise generated by quantization. The sound quality when a quantized audio signal is output by moving from a low frequency band to a low frequency band where noise is less noticeable or to a high frequency band where the audio signal is large. Has a function to improve. The post filter 32 has a predetermined transfer function as will be described later, and performs an audio signal calculation process using this transfer function. Further, the transfer function of the post filter 32 is configured such that all the coefficients are integers, as will be described later.

  The prefilter 33 has the reverse characteristics of the postfilter 32. Similar to the post filter 32, the pre-filter 33 also has a predetermined transfer function, and performs an audio signal calculation process using this transfer function. The transfer function included in the pre-filter 33 is configured to be an inverse function of the transfer function included in the post-filter 32, and an audio signal calculation process is performed using this transfer function. Thus, when the transfer function provided in the prefilter 33 and the transfer function provided in the postfilter 32 are multiplied, the filter is configured to be an all-pass filter. When the arithmetic processing is performed at, the signal value of the audio signal becomes the same as the signal value of the original signal.

  Note that the quantization unit 3 is provided with a buffer (not shown), and this buffer (not shown) is used when processing is performed using a transfer function by the post filter 32 or the prefilter 33. The signals (or signal values) for the last few signals are temporarily stored.

[Principles of post filter]
In the post filter 32, the transfer function shown in the following (formula 1) in the z region.

Process using. In addition,

Is a feedback element and includes a time delay of z- ¹ .

The transfer function of Equation 1 is

It can also be expressed as Note that the coefficient in a _n is limited to an integer. This can be achieved by limiting the coefficient a _n integer, when it is not necessary to further quantize the audio signal processed by the post-filter 32 (the value after the decimal point coefficient occurs, the signal further by quantizing There is a possibility that proper processing cannot be achieved unless it is subdivided into small units, but since further subdivision is not required by using only integer coefficients.) Simplification of configuration and simplification of processing It is because it can plan.

  The reason why the noise shaping can be performed without performing the feedback of the audio signal from the post filter 32 to the post filter 32 using the transfer functions of the above (Expression 1) and (Expression 2) will be described below.

  First, processing in a transfer function including a feedback element is generally realized by a configuration including feedback as shown in FIG. In the same figure, the signal is sent to the post-filter 32 from the previous stage and the subsequent stage of the quantization processing unit 31 and further fed back to the previous stage of the quantization processing unit 31 so that the transfer functions of (Equation 1) and (Equation 2) are used. Processing is realized.

In FIG. 2, if the quantization noise generated in the quantization processing unit 31 is Q, it is equivalent to adding the quantization noise Q to the original audio signal, and equivalent to that shown in FIG. Become. Here, since the difference signal before and after the quantization is the quantization noise Q, if the feedback loop is removed, the difference signal becomes equivalent to that shown in FIG. When the quantization noise Q is summarized from the one shown in FIG. 4, it has the same value as that shown in FIG. A parallel element of the one shown in FIG. 5 (in FIG.

(The element indicated by the solid line immediately above it) is an addition (generally known equivalent exchange rule), and a line without an element can be treated as having one element. 5 is equivalent to that shown in FIG. FIG. 6 does not include feedback as an element, and is equivalent to that shown in the above (Expression 1) and (Expression 2). Therefore, the noise shaping of this embodiment can be realized in (Expression 1) and (Expression 2). In FIGS. 2 to 5, the post filter 32 is described for convenience for the sake of simplicity. However, these are in the process of equivalent conversion, and as shown in FIGS. 2 to 5, The contents are different from those shown in FIG. In that regard, the post filter 32 shown in FIGS. 2 to 5 is not exactly the same as the post filter 32 of FIG. 6 (even if equivalent).

[Configuration using post-filter and pre-filter]
As described above, the predetermined transfer function used for noise shaping by the post filter 32 is represented by H (z) (Equation 3).
In this case, in the pre-filter 33, as a predetermined transfer function, a function reverse to the transfer function of the post-filter 32, that is,

Will be used.
Thus, the quantization unit 3 of this embodiment is configured as shown in FIG. Thereby, noise shaping can be realized by a simple process with a simpler configuration than a general noise shaping system.

[Configuration by combining pre-processing and quantization units (mounting optimization)]
In this embodiment, the transfer function Gn ^* (z) of the filter used in the preprocessing unit 2 has a zero at z = −1.

If the transfer function of the filter used in the preprocessing unit 2 is Gn ^* (z) and the quantization noise is removed only by the preprocessing unit 2, the preprocessing unit 2 and the quantization unit of the audio signal processing device 1 are used. 8 is as shown in FIG. 8 (in FIG. 8, the quantization unit 3 is not provided with the pre-filter 33 and the post filter 32, and only the quantization processing unit 31 is provided). ). If the prefilter 33 and the postfilter 32 are provided in this configuration, the configuration shown in FIG. 9 is obtained. As shown in FIGS. 8 and 9, the configuration of both system configurations is not greatly different. That is, even if the pre-filter 33 and the post-filter 32 of this embodiment are used together with the configuration of the preprocessing unit 2, the configuration does not have to be so complicated.

Note that the transfer function Gn (z) shown in FIG. 9 is the transfer function Gn ^* (z) of the filter used in the preprocessing unit 2 shown in FIG.
Divided by the transfer function H (z) of the post filter 32 shown in (Equation 3) above, that is,

It is.

As described above, since the transfer function Gn ^* (z) shown in (Equation 5) has a zero at z = −1, the inverse characteristic filter of the post filter 32 used for the prefilter 33 is used.

Characteristics in series with

Can remove z from the denominator by reduction, and can be implemented with an FIR filter.

Here, the transfer function Gn ^* (z) is a filter having a zero point at z = −1 and whose amplitude gradually decreases monotonously toward the high frequency band. Here, assuming that the quantization noise Q generated by filtering by the transfer function Gn ^* (z) is a constant level regardless of the frequency, the quantization noise Q exceeds the energy after filtering in the band near the Nyquist frequency, The effect of deterioration becomes stronger. In particular, when the high frequency energy of the original signal is small, the band affected by the deterioration due to the quantization noise Q becomes wide. Therefore, a characteristic that satisfies the following condition (that is, a characteristic of the transfer function H (z)) is considered to be effective for the quantization noise Q.
・ Set the amplitude to zero at the Nyquist frequency.
・ The order is set to 1 for simple implementation.
The post filter 32 of the transfer function H (z) is a causal filter.

  Furthermore, as the above (Formula 1) shows, the zero-order term of the transfer function H (z) needs to be 1.

The transfer function H (z) of the post filter 32 satisfying these conditions is expressed as H (z) = 1 + z ⁻¹ (Equation 9).
Then, the transfer function Gn (z) is calculated as in the following (Expression 10) to (Expression 13) when n = 3, 5, 7, 9 for example.

  The output of the audio signal processing apparatus 1A using the filter of the transfer function Gn (z) shown in the above (Equation 10) to (Equation 13) is the same as the system using the post filter 32 shown in FIG.

The noise shaping shown in this embodiment described above can be applied to any post filter 32 that satisfies the following conditions (condition 1) (condition 2).
(Condition 1): All the coefficients of the transfer function H (z) are integers.
(Condition 2): z in the denominator can be removed by dividing the composite characteristic {Gn ^* (z) / H (z)} with the transfer function Gn ^* (z) of the preprocessing unit 2.

  As described above, in the audio signal processing apparatus 1A according to this embodiment, the post-filter 32 having a characteristic capable of realizing noise shaping of the quantized audio signal is performed in the subsequent stage of the process of the quantization processing unit 31. Thus, noise shaping of quantization noise can be performed. Further, by performing the processing by the prefilter 33 having the inverse characteristics of the postfilter 32 in the previous stage of the processing of the quantization processing unit 31, the processing of the prefilter 33 and the processing of the postfilter 32 are performed on the audio signal itself. Thus, quantization can be performed while maintaining the original state. Then, by processing the audio signal in the order of processing by the post filter 32, processing by the quantization means, and processing by the prefilter 33, quantization and noise shaping can be realized as simple processing with a simple configuration. As a result, noise shaping can be realized with a simple configuration and processing, and the audible effect of quantization noise can be reduced.

  The audio signal processing apparatus 1A according to this embodiment is configured so that no feedback means for returning the audio signal processed by the post filter 32 to the prefilter 33 is provided, so that the signal is fed back. Instability of the system such as the formation of a complicated configuration and the generation of complicated processing such as signal processing including the feedback signal, and system output infinitely increasing the system output due to feedback Therefore, noise shaping can be specifically realized with a simple configuration and processing, and the system can be stabilized without special consideration.

  In the audio signal processing apparatus 1A of this embodiment, the post filter 32 includes a transfer function H (z), and the prefilter 33 includes a transfer function 1 / H (z), and thus includes a plurality of time series signals. It is possible to reliably perform noise shaping of an audio signal using a transfer function. Further, since the transfer function 1 / Hz of the pre-filter 33 is configured to be an inverse function of the transfer function H (z) of the post-filter 32, the pre-filter 33 and the post-filter 32 are respectively processed. The signal remains in its original state. As a result, quantization and noise shaping can be performed without altering the original signal.

  In the audio signal processing apparatus 1A according to this embodiment, the transfer function H (z) included in the post filter 32 is configured so that all the coefficients are integers, so that the audio signal processed by the post filter 32 is processed. There is no need to quantize again, and quantization and noise shaping can be performed with a simple configuration and simple procedure.

  In the audio signal processing apparatus 1A of this embodiment, the magnitude of the quantization noise with respect to the size of the audio signal can be reduced by changing the frequency characteristics of the audio signal before encoding. By using the post filter 32 and the pre-filter 33, it is possible to perform noise shaping while reducing the size of the existing quantization noise with respect to the size of the audio signal, thereby further improving the sound quality of the audio signal.

  In the above embodiment, the time series signal is an audio signal. However, the present invention is not limited to this, and any video signal such as a moving image signal that shows a dynamic change in time series and has high correlation can be used. It may be a thing. Also, the audio signal forming the time series signal of this embodiment is an audio sample or the like recorded in advance in a database or the like, and a plurality of sequences are formed by extracting highly correlated ones from them. It may be realized.

  The above embodiment is an exemplification of the present invention, and it is needless to say that the present invention is not limited to the above embodiment.

  10 and 11, the audio signal reproduction result based on the signal subjected to the process according to the present invention in the audio signal processing apparatus 1A according to this embodiment and the process according to the conventional method are performed as a comparative example. The reproduction | regeneration result of the audio | voice data based on a signal is shown. 10 and 11, reference numeral 101 denotes a reproduction result of audio data based on the present invention. Specifically, the quantization processing unit 31 uses the post filter 32 and the pre-filter 33 to quantize the speech signal encoded by performing the predictive coding by the linear prediction in the coding unit 1 shown in FIG. The sound quality of the sound reproduced by decoding the reproduced audio signal is shown (in this embodiment, the preprocessing unit 2 performs the process on the audio data (shown in the reproduction result 101) based on the present invention. Not.) On the other hand, reference numeral 102 denotes a reproduction result of audio data as a comparative example. Specifically, the quantization processing unit 31 (without using the post-filter 32 and the pre-filter 33) is added to the speech signal encoded by performing the predictive coding by linear prediction in the coding unit 1 shown in FIG. Shows the sound quality of the sound reproduced by decoding the quantized sound signal (in the present embodiment, the pre-processing unit 2 also represents sound data (shown in the reproduction result 102) as a comparative example). Is not performed).

  As shown in the figure, the ODG score is higher (that is, the sound quality is better) in the reproduction result 101 of the audio data processed according to the present invention than in the reproduction result 102 of the audio data of the comparative example. ing. As a result, it was shown that the sound processed according to the present invention can be reproduced with better sound quality than the sound processed by the conventional method.

DESCRIPTION OF SYMBOLS 1A ... Audio | voice signal processing apparatus 2 ... Pre-processing part (Pre-processing means)
31 ... Quantization processing unit (quantization means)
32 ... Post filter (noise shaping means, first filter)
33 ... Pre-filter (noise shaping means, second filter)

Claims (7)

And quantization means you quantizing audio signal,
A first filter provided at a subsequent stage of the quantization means, having a first transfer function capable of realizing noise shaping that reduces the influence of quantization noise generated in the quantization process ;
A second filter provided in front of the quantization means, having a second transfer function that is an inverse function of the first transfer function ;
The audio signal processing apparatus characterized by obtaining Bei a. 2. The audio signal processing device according to claim 1, wherein the first transfer function is obtained by an equivalent conversion process for obtaining a configuration in which a feedback loop is removed from a configuration that realizes signal processing based on an initial transfer function including a feedback element. . The audio signal processing apparatus according to claim 1 from the previous SL first filter, characterized in that no feedback means for feeding back an audio signal to the second filter. Before Symbol first transfer function, Ru all coefficients integer der
The audio signal processing apparatus according to claim 1 or 2, characterized and this. The audio signal processing device further includes:
By changing the frequency characteristics of the audio signal, the has a function to reduce the size of the quantization noise to the magnitude of the speech signal, preprocessing means provided upstream of the second filter
The audio signal processing apparatus according to any one of claims 1 to 3, feature in that it comprises. An audio signal processing method executed by an audio signal processing device,
Filtering the audio signal using the second transfer function, which is an inverse function of the first transfer function that can realize noise shaping that reduces the influence of quantization noise generated in the process of quantizing the audio signal;
Quantizing the filtered audio signal;
An audio signal processing method, wherein the quantized audio signal is filtered using the first transfer function . 7. The audio signal processing method according to claim 6, wherein the first transfer function is obtained by an equivalent conversion process for obtaining a configuration in which a feedback loop is removed from a configuration for realizing signal processing based on an initial transfer function including a feedback element. .

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