JP2009188449A - Apparatus for reducing quantization distortion - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus for reducing harmonic distortion surely. <P>SOLUTION: Unnecessary harmonic distortion occurs when the analog conversion of quantized data of a minute amplitude signal is carried out, but the unnecessary harmonic distortion can be reduced because a white noise generator 13 in an apparatus 1 for reducing quantized distortion adds minute amplitude white noise to a quantized input signal and whitens harmonic distortion components, and whitened components of low autocorrelation are reduced by an adaptive filter 19. Switching can be performed naturally with no strange feeling because a cross fader 27 outputs an input signal as it is if it has a large level to some extent, and performs switching to the output signal of the adaptive filter only when it has a minute level. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to an apparatus for reducing unnecessary harmonic distortion that occurs when analog data of quantized data of a minute amplitude signal is converted.

  Recently, most of the music sold has been digitized. For example, music that is digitized by the PCM method is recorded on an optical disk such as a CD or DVD and sold, or music that is encoded in a file format such as MP3, AAC (registered trademark), or WMA is sold via the Internet. is doing.

  When a signal quantized by digital conversion is converted into an analog signal, it is distorted into a stepped waveform due to quantization. Therefore, a signal obtained by analog conversion of the quantized signal generates a harmonic that is not included in the original analog signal. This is generally called harmonic distortion. This harmonic distortion is not a problem with a signal having a certain level of level because the distortion is relatively small with respect to the original signal. However, when a minute analog signal is converted into an analog signal and then converted into an analog signal, the waveform becomes a stepped waveform as shown in FIG. 1A, and the distortion is relatively large with respect to the original signal. The relative level difference between the level of the original signal and the harmonic distortion component decreases, and the S / N ratio decreases.

  In the audio field, since digital audio was introduced on the market, it has been said that the harmonic distortion caused by this quantization causes the lingering music and the subtle nuance of hearing when it is attenuated.

In response to such a problem, an apparatus for reducing harmonic distortion has been proposed. For example, there has been proposed an apparatus that detects a change cycle of an input signal and switches a plurality of LPFs having different cutoff frequencies to reduce harmonic distortion in accordance with the result (see Patent Document 1).
JP-A-9-980924

  However, in the apparatus described in Patent Document 1, as shown in FIG. 1B, in the case of an input signal including a low frequency signal and a high frequency signal of the same level, the cutoff frequency of the LPF does not decrease. There is a problem that the harmonic distortion component generated by the low-frequency signal is not suppressed.

  Therefore, an object of the present invention is to provide an apparatus that can reliably reduce the harmonic distortion.

  The present invention has the following configuration as means for solving the above problems.

(1) A quantization distortion reducing apparatus for reducing harmonic distortion of a quantized input signal,
A white noise signal generating means for generating a white noise signal;
Adding means for adding the white noise signal to the quantized input signal and outputting an added signal;
Delay means for delaying the addition signal for a predetermined time and outputting a delayed addition signal;
Adaptive filter means for obtaining a difference between the sum signal and the delayed sum signal and removing and outputting a signal component having low autocorrelation from the sum signal;
With
The white noise signal generation unit generates a white noise signal having an amplitude level set in accordance with the data word length of the input signal, the input data word length of the adaptive filter unit, and the signal level of the harmonic distortion to be reduced. It is characterized by doing.

  In this configuration, the quantization distortion reducing device outputs a white noise signal having an amplitude level set in accordance with the data word length of the input signal, the input data word length of the adaptive filter means, and the signal level of the harmonic distortion to be reduced. The white noise signal is generated and added to the quantized input signal. Then, a signal component having low autocorrelation is removed and output from the addition signal obtained by adding the white noise signal to the quantized input signal and the delayed addition signal obtained by delaying the addition signal for a predetermined time. Therefore, unnecessary harmonic distortion occurs when the quantized data of the minute amplitude signal is converted to analog, but since the signal processing is performed as described above, the whitened component having low autocorrelation by the adaptive filter In addition, since the harmonic distortion component is reduced, this unnecessary harmonic distortion can be reduced. Thereby, if the quantized data of the minute amplitude signal is, for example, audio data, the audibility of the minute signal can be improved.

(2) envelope detecting means for detecting the level of the input signal;
A fade coefficient generation means for calculating and outputting a fade coefficient based on the level of the input signal detected by the envelope detection means and a predetermined threshold;
A crossfade unit that receives the signal output from the adaptive filter unit and the input signal and outputs the signal output from the adaptive filter unit or the input signal according to the magnitude of the fade coefficient;
It is provided with.

  In this configuration, the quantization distortion reducing device detects the level of the quantized input signal, calculates a fade coefficient based on the level of the input signal and a predetermined threshold value, and outputs the fade coefficient. An input signal or a distortion removal signal is output according to the magnitude of. When a signal with a relatively large input signal is passed through an adaptive filter that operates to suppress signals with low autocorrelation, components that are important in music and speech, such as non-integer harmonics generated by percussion instruments, In some cases, components having low autocorrelation included in plosives and frictional sounds in speech may be suppressed. However, the quantization distortion reducing apparatus outputs the input signal as it is when the fade coefficient is larger than the threshold value, and outputs the adaptive filter output signal when the fade coefficient is smaller than the threshold value. Accordingly, the output signal can be switched, and deterioration of sound quality can be prevented.

  According to the present invention, unnecessary harmonic distortion occurs when analog-converting quantized data of a minute amplitude signal. However, a minute amplitude white noise is added to the quantized input signal, and a harmonic distortion component is added. Since the whitened component having a low autocorrelation by the adaptive filter is reduced, this unnecessary harmonic distortion can be reduced. Further, if the quantized data of the minute amplitude signal is, for example, audio data, the audibility of the minute signal can be improved.

  FIG. 2 is a block diagram showing a schematic configuration of the quantization distortion reducing apparatus according to the embodiment of the present invention. Here, in the following description, it is assumed that the input signal of the quantization distortion reducing apparatus is quantized by the PCM method.

  A quantization distortion reduction device (hereinafter referred to as a reduction device) 1 includes an input terminal 11, a white noise generator 13, an adder 15, a delay device 17, an adaptive filter 19, a delay device 21, an envelope detector 23, and a fade coefficient. A generator 25, a crossfader 27, and an output terminal 29 are provided.

  The input terminal 11 is an input interface of the reduction device 1 and is connected to a reproduction device that outputs a quantized signal (digital signal) obtained by quantizing an analog signal by the PCM method.

  The white noise generator 13 generates a low-amplitude white noise signal. The white noise generator 13 may have any configuration as long as noise with low autocorrelation can be generated. The data word length of the white noise signal is adjusted to the input data word length of the subsequent adaptive filter. The amplitude of the white noise signal may be set in consideration of the data word length of the input signal, the input data word length of the adaptive filter, the signal level of the harmonic distortion to be suppressed, and the like. That is, the amplitude (average amplitude level) of the white noise signal may be set so that the harmonic distortion becomes white noise and becomes an inconspicuous amplitude according to the signal level (amplitude) of the harmonic distortion to be reduced. . For example, if the amplitude (average amplitude) of the white noise signal is set to be approximately the same level as the maximum amplitude level of the harmonic distortion, the harmonic distortion is converted into white noise, and the white noise signal is Wave distortion can be made inconspicuous. Further, the level of the white noise signal may be appropriately increased or decreased according to the harmonic distortion and the residual amount of the white noise signal among the output components of the adaptive filter.

  3A is a diagram illustrating an example of the white noise data output word length, and FIG. 3B is a block diagram illustrating a configuration example of the adaptive filter. As shown in FIG. 3A, for example, when the input signal (input data) is 16 bits, the input data word length of the adaptive filter is 24 bits, and it is desired to suppress the harmonic distortion of a minute signal of 1 LSB level, the data word White noise with a length of 24 bits and a maximum amplitude level of 9 bits is output.

  The input signal is not limited to 16 bits. For example, when the input signal is 24 bits, the input tone of the adaptive filter may be set to 36 bits.

  Returning to FIG. 2, the adder 15 adds the input signal and the output signal from the white noise generator. If the input signal word length is 16 bits and the white noise is 24 bits, an addition operation is performed by bit-extending 0 data for 8 bits on the LSB side of the input signal.

  The delay unit 17 gives a time sample delay to an input signal of an adaptive filter described later. This delay value is also called a correlation determination parameter. When the delay value is set to one sample, the adaptive filter operates so as to converge to a signal component having a high correlation with the signal one sample before. Therefore, a signal having a low correlation with the signal one sample before, that is, white noise can be reduced. This delay value is normally set in the range of about 1 to 10 samples, but may be arbitrarily determined depending on the characteristics of the input signal.

  The adaptive filter 19 may have any configuration as long as it is a general adaptive filter. When the adaptive filter 19 is configured by an FIR filter, the configuration is as follows. As shown in FIG. 3B, the adaptive filter 19 includes an FIR filter 36 including k + 1 delay elements 31-0 to 31-k, k + 1 multipliers 33-0 to 33-k, and an adder 35. And an adder 37 and a coefficient correction algorithm unit 38. The adaptive filter 19 obtains an error between the value obtained by filtering the input signal sent from the delay unit 17 by the FIR filter 36 and the desired signal sent from the adder 15 by the adder 37. The coefficient correction algorithm unit 38 operates while correcting the coefficients of the multipliers 33-0 to 33-k of the FIR filter 36 so that the error is minimized. As the coefficient correction algorithm applied to the coefficient correction algorithm unit 38, there are various methods including the LMS algorithm. However, any appropriate one may be adopted in consideration of the processing capability of the hardware and software to be mounted.

  In the LMS algorithm, the filter coefficient vector before adaptation is c (n), the filter coefficient vector after adaptation is c (n + 1), the step size parameter is μ, the error signal is e (n), and the tap input vector of the FIR filter is u. (N) is an algorithm for estimating the filter coefficient vector so that the mean square error between the input signal and the desired signal is minimized by repeatedly calculating the following equation sequentially.

c (n + 1) = c (n) + μe (n) u (n) (Formula 1)
Here, if the desired signal is d (n), the error signal e (n) is
e (n) = d (n) −u ^T (n) c (n) (Equation 2)
It is. As for the step size parameter, an appropriate value may be determined by considering the tradeoff between the convergence speed and the estimation accuracy within a range in which the step size parameter does not diverge. Further, in order to estimate the output signal as a smooth signal with high bit resolution, the operation word length of the adaptive filter is made longer than that of the input signal. For example, if the input signal is 16 bits, bit expansion is performed by adding white noise as shown in FIG. 3A, the operation word length of the adaptive filter is 24 bits or more, and the adaptive filter output signal is also a word of 24 bits or more. Make it long. As already described in the item of the delay unit 17, the adaptive filter 19 in which a delay is inserted into the input signal operates to remove a signal component having low autocorrelation from the input signal to which minute white noise is added. . Therefore, harmonic distortion components masked with white noise can be reduced.

  Hereinafter, a procedure for reducing harmonic distortion will be described using the waveform and frequency characteristics of simulation data. For example, when a 16-bit sine wave analog signal having a 1LSB amplitude is digitally converted, a waveform as shown in FIG. 4A is a graph showing a minute amplitude signal and a waveform example after digital conversion, and FIG. 4B is a graph showing a frequency characteristic example when the minute amplitude signal is digitally converted. The stepped waveform shown in FIG. 4A is obtained by digitally converting a sine wave analog signal, and the frequency characteristic of the waveform after this digital conversion is as shown in FIG.

  In FIG. 4B, the peak A of the frequency component on the leftmost side of the graph is the frequency component of the original sine wave signal. In the graph shown in FIG. 4B, many harmonic components exist in addition to the original sine wave signal component, and these are harmonic distortions. The frequency characteristics of a signal obtained by adding a small amplitude white noise to these harmonic distortion signals are as shown in the graph of FIG.

  5A is a graph showing an example of frequency characteristics when white noise is added to a signal obtained by digitally converting a minute amplitude signal, and FIG. 5B is a graph showing an example of frequency characteristics of an adaptive filter output signal. .

  As shown in FIG. 5A, since the frequency characteristic of white noise is wide, most of the harmonic distortion is masked by white noise and whitened. In general, sounds that are whitened are less audibly perceptible than those that have a harmonic structure. This is said to be a psychoacoustic action in which the human auditory sense unconsciously feels the pitch (pitch) when listening to a signal with a harmonic structure. Therefore, even in the state of the frequency characteristics as shown in FIG. 5A, since the harmonic distortion component is whitened, the harmonic distortion is less audible than the signal before the addition of white noise. It can be said.

  However, if this white noise can be reduced, the S / N ratio can be increased, and further improvement in hearing can be expected. For this purpose, an adaptive filter 19 is used to reduce the white noise component. The frequency characteristic of the output signal when the signal having the frequency characteristic shown in FIG. 5A is passed through the adaptive filter 19 is as shown in FIG. From FIG. 5B, it can be seen that, as a result of the reduction of the harmonic distortion component together with the white noise and the improvement of the S / N ratio, the input signal component is clear.

  As described in the explanation of the white noise generator 13, the amplitude of the white noise signal may be determined so as to be an amplitude corresponding to the signal level (amplitude) of the harmonic distortion, but how much harmonic distortion remains. And the level at which the white noise signal that cannot be removed by the adaptive filter is compromised.

  As a guideline, as described above, the amplitude of the white noise signal should be substantially the same as the maximum amplitude level of the harmonic distortion. For example, the amplitude of the white noise signal is set in the vicinity of −100 dB in the graph of FIG. In this case, the amplitude is almost the same as the maximum amplitude level of the harmonic distortion. At this time, since the amplitude level of the white noise signal is high, the white noise component may not be completely removed depending on the setting of the adaptive filter 19. In that case, the delay value of the adaptive filter 19 may be adjusted to a delay value that can remove the white noise component as much as possible. Further, as shown in FIG. 5A, when the amplitude of the white noise signal is set to around −110 dB, the masking effect is slightly lowered because the amplitude level of the white noise signal is low, and FIG. As shown in Fig. 5, some harmonics remain in the low frequency range. However, in this case, the amplitude levels of the harmonic and white noise signals are low, and the white noise component is almost removed by the adaptive filter, so that the harmonics and white noise are hardly bothered. Therefore, after adjusting the white noise generator 13 and the adaptive filter 19 as described above, the person who determines the final sound may check the actual sound and determine the balance of sound quality by hearing.

  The delay device 21 shown in FIG. 2 is for aligning the time difference between the input signal and the adaptive filter output signal at the input of a crossfader described later. The delay value is determined by the processing time delay of the adaptive filter.

  The envelope detector 23 is a block for detecting the level of the input signal. 6A is a block diagram illustrating a configuration example of an envelope detector, and FIG. 6B is a graph illustrating input / output signals for envelope detection.

  The envelope detection unit 23 includes an absolute value calculation unit 41, a logarithmic conversion unit 43, a constant storage unit 45, a delay element 47, an addition unit 49, a comparison determination unit 51, and a selector 53, as shown in FIG. ing.

  The absolute value calculation unit 41 calculates the absolute value of the input signal and outputs it to the logarithmic conversion unit 43.

The logarithmic conversion unit 43 outputs a value (a) obtained by logarithmically converting the input value to the comparison determination unit 51 and the selector 53. The logarithmic conversion unit 43 performs a general logarithmic conversion, and is obtained by the following equation, where u is an input and y is a value after conversion.
y = 20 log (u) (Expression 3)
The constant storage unit 45 stores a preset constant (time constant) and outputs the constant to the addition unit 49.

  The delay element 47 holds the value one sample before output from the selector 53, and outputs this value to the adder 49.

  The adding unit 49 outputs a value (b) obtained by subtracting the constant output from the constant storage unit 45 from the value one sample before output from the delay element 47 to the comparison determination unit 51 and the selector 53.

  The comparison determination unit 51 compares the value (a) output from the logarithmic conversion unit 43 with the value (b) output from the addition unit 49. If a> b, 0 is output to the selector 53, and if a ≦ b, 1 is output to the selector 53.

  The selector 53 selects and outputs the value (a) output from the logarithmic converter 43 or the value (b) output from the adder 49. That is, when the comparison determination unit 51 outputs 0, the value (a) output by the logarithmic conversion unit 43 is output. When the comparison determination unit 51 outputs 1, the value (b) output by the addition unit 49 is output.

  When a signal is input to the envelope detector 23, first, the absolute value calculation unit 41 takes the absolute value of the input signal, and the logarithmic conversion unit 43 performs decibel conversion. This is a general decibel transform and is calculated using the above equation 3. Further, the envelope detector 23 has a value obtained by calculating (subtracting) the constant stored in the constant storage unit 45 from the value one sample before the output value output from the delay element 47, and the logarithmic conversion unit 43. The comparison determination unit 51 compares the absolute value of the output input signal. If the absolute value of the input signal is larger, the selector 53 outputs the absolute value of the input signal. On the other hand, if the absolute value of the input signal is smaller, a value obtained by subtracting a constant from the value one sample before is output. The time constant for smoothing the envelope is determined by the size of this constant. By this processing, the level envelope is obtained and the value is set as the level value of the input signal. The input and output of the envelope detector 23 have waveforms as shown in FIG.

  Note that the slope of the envelope can be changed by the value of the constant (time constant) stored in the constant storage unit 45. In the present invention, if the detected envelope value fluctuates suddenly, it gives the listener a sense of incongruity (fluctuation), and if the detected envelope variation is too slow, accurate envelope detection is not performed and the input is tracked correctly. should not. Therefore, as shown in FIG. 6B, the output value of the envelope is gradually attenuated with a certain time constant, and when a value larger than that value is input, the large value is replaced with the output value. It is set.

  It should be noted that the value of the constant (time constant) stored in the constant storage unit 45 is preferably set by experiment.

  Further, as shown in FIG. 6A, the configuration of the envelope detector 23 may be other than that as long as the function can sequentially calculate and output the input level.

  7A is a block diagram illustrating a configuration example of a fade coefficient generator, and FIG. 7B is a graph illustrating a cross-fade coefficient calculation formula and a relationship between an input signal level and a fade coefficient.

  The fade coefficient generator 25 includes a coefficient calculation unit 55 that calculates a coefficient used by the crossfader 27 and an LPF (low-pass filter) 57. The LPF 57 is for smoothing a rapid change in coefficient.

  The user sets the saddle value TH as a parameter. This value serves as an input level threshold value for determining whether the input signal is output as it is or mixed with the adaptive filter output signal in the subsequent crossfader 27. If the input signal level is greater than the threshold value TH, a coefficient of 1.0 is output. When the input signal level is smaller than the threshold value TH, a value obtained by dividing the input signal level by the threshold value TH is output as a coefficient. Therefore, as the graph shown in FIG. 7B, the smaller the input signal level is, the closer this coefficient approaches 0.

  In addition, the slope of the fade coefficient when the input signal level is lower than the threshold TH does not need to be a straight line if it increases monotonically in proportion to the input signal level. It may be changed.

  FIG. 8 is a block diagram showing a schematic configuration of the crossfader. The crossfader 27 shown in FIG. 8 is a block for mixing and outputting an input signal and an adaptive filter output signal, and is configured as shown in FIG. That is, the crossfader 27 includes a coefficient storage unit 61, adders 63 and 69, and multipliers 65 and 67.

  The cross fader 27 multiplies the fade coefficient output from the fade coefficient generator 25 by the multiplier 65 to the input signal 1 output from the delay unit 21 as it is. This multiplication value is referred to as value 1. Further, the cross fader 27 multiplies the input signal 2 output from the adaptive filter 19 by a value obtained by subtracting the fade coefficient output from the fade coefficient generator 25 from the value 1.0 read from the coefficient storage unit 61. . This multiplication value is referred to as value 2. Then, the crossfader 27 adds the above value 1 and value 2 by the adder 69 and outputs the result.

  When the output of the delay device 21 is connected to the input 1 and the output of the adaptive filter 19 is connected to the input 2, the input signal is output as it is when the fade coefficient is 1.0, that is, the input signal is larger than the set threshold value TH. The On the other hand, when the fade coefficient is less than 1.0, that is, when the input signal is lower than the set threshold value TH, the adaptive filter output signal is mixed with the input signal and output. In the case of a sufficiently small signal, an adaptive filter output signal is almost output.

  However, if a relatively large signal is passed through an adaptive filter that operates to suppress signals with low autocorrelation, components that are important in music and speech, such as non-integer harmonics and speech generated by percussion instruments In some cases, components with low autocorrelation contained in plosives and frictional sounds are suppressed. In order to solve this problem, it is desirable to use the crossfader 27 to output the input signal as it is if the input signal is at a certain level, and to switch to the adaptive filter output signal only when the input signal is at a very low level. The reduction device 1 uses the crossfader 27 configured as described above in order to perform the switching naturally without a sense of incongruity.

  The output terminal 29 is an output interface for outputting a signal output from the crossfader 27 to another device or the like.

  The reduction device 1 performs the above-described processes with the above-described configuration, thereby generating unnecessary harmonic distortion when analog-converting quantized data of a minute amplitude signal. 1, the white noise generator 13 adds a small amplitude white noise to the quantized input signal to whiten the harmonic distortion component, and the adaptive filter 19 reduces the whitened component having low autocorrelation. This unnecessary harmonic distortion can be reduced. Further, the crossfader 27 outputs the input signal as it is if it is at a certain level, and switches to the adaptive filter output signal only when the input signal is at a very small level, so that the switching can be performed naturally without any sense of incongruity. Thereby, when the input signal is an audio signal, it is possible to reduce the adverse effect of harmonic distortion noise on the audibility.

  In the above description, the case where the quantizing distortion reducing apparatus is applied to the improvement of the audibility of the audio signal has been described. However, the present invention is not limited to the audio signal, and similar harmonic distortion generated in other digital signal processing applications. Applicable in general.

(A) is the wave form diagram which carried out the analog conversion after carrying out the digital conversion of the minute analog signal, (B) is a figure for demonstrating the process of a prior art. It is a block diagram which shows schematic structure of the quantization distortion reduction apparatus which concerns on embodiment of this invention. (A) is a figure which shows an example of a white noise data output word length, (B) is a block diagram which shows the structural example of an adaptive filter. (A) is a graph which shows the example of a waveform after a minute amplitude signal and its digital return, (B) is a graph which shows the example of a frequency characteristic at the time of carrying out digital conversion of the minute amplitude signal. (A) is a graph which shows the example of a frequency characteristic at the time of adding white noise to the signal which digitally converted the minute amplitude signal, and (B) is a graph which shows the example of the frequency characteristic of an adaptive filter output signal. (A) is a block diagram which shows the structural example of an envelope detector, (B) is a graph which shows the input-output signal of envelope detection. (A) is a block diagram showing a configuration example of a fade coefficient generator, and (B) is a graph showing a crossfade coefficient calculation formula and a relationship between an input signal level and a fade coefficient. It is a block diagram which shows schematic structure of a cross fader.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Quantization distortion reduction apparatus (reduction apparatus) 11 ... Input terminal 13 ... White noise generator 15 ... Adder 17 ... Delay device 19 ... Adaptive filter 21 ... Delay device 23 ... Envelope detector 25 ... Fade coefficient generator 27 ... Crossfader 29: Output terminal 31-0 to 31-k Delay element 33-0 to 33-k Multiplier 35 ... Adder 36 ... FIR filter 37 ... Adder 38 ... Coefficient correction algorithm unit 41 ... Absolute value calculation unit DESCRIPTION OF SYMBOLS 43 ... Logarithmic conversion part 45 ... Constant memory | storage part 47 ... Delay element 49 ... Adder part 51 ... Comparison determination part 53 ... Selector 55 ... Coefficient calculation part 61 ... Coefficient memory | storage part 63, 69 ... Adder 65, 67 ... Multiplier

Claims (2)

A quantization distortion reducing apparatus for reducing harmonic distortion of a quantized input signal,
A white noise signal generating means for generating a white noise signal;
Adding means for adding the white noise signal to the quantized input signal and outputting an added signal;
Delay means for delaying the addition signal for a predetermined time and outputting a delayed addition signal;
Adaptive filter means for obtaining a difference between the sum signal and the delayed sum signal and removing and outputting a signal component having low autocorrelation from the sum signal;
With
The white noise signal generation unit generates a white noise signal having an amplitude level set in accordance with the data word length of the input signal, the input data word length of the adaptive filter unit, and the signal level of the harmonic distortion to be reduced. A quantization distortion reducing device characterized by: Envelope detecting means for detecting the level of the input signal;
A fade coefficient generation means for calculating and outputting a fade coefficient based on the level of the input signal detected by the envelope detection means and a predetermined threshold;
A crossfade unit that receives the signal output from the adaptive filter unit and the input signal and outputs the signal output from the adaptive filter unit or the input signal according to the magnitude of the fade coefficient;
The quantization distortion reducing apparatus according to claim 1, comprising:

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