JP2007228349A - Sampling frequency converting method, its program, and its recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To realize reduced power consumption and high speed by reducing amount of calculation in a sampling frequency converting method using a complex index modulation filter bank. <P>SOLUTION: An apparatus comprises a first intermediate signal producing unit 101 for outputting a first intermediate signal after calculating from an input signal, a second intermediate signal producing unit 102 for outputting a second intermediate signal after calculating from the first intermediate signal, an FFT unit 103 for outputting a third intermediate signal after calculating from the second intermediate signal by a fast fourier transform, a fourth intermediate signal producing unit 104 for outputting a fourth intermediate signal after calculating from the third intermediate signal, an FFT unit 105 for outputting a fifth intermediate signal after calculating from the fourth intermediate signal by the fast fourier transform, a sixth intermediate signal producing unit 106 for outputting a sixth intermediate signal after calculating from the fifth intermediate signal, and an output signal producing unit 107 for outputting an output signal after calculating from the sixth intermediate signal. Consequently, a necessary amount of calculation can be reduced for realizing sampling frequency conversion which uses a complex index modulation filter bank. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a sampling frequency conversion method using a complex exponential modulation filter bank with reduced calculation amount and low power consumption or high speed.

  In recent years, a signal analysis filter bank that divides a signal into a plurality of band division signals and a signal synthesis filter bank that synthesizes the band division signals and reproduces the original signals have achieved high efficiency by subband coding of audio signals and image signals. It is attracting attention as a signal analysis and signal synthesis means for realizing encoding. In particular, a complex exponential modulation filter bank that does not cause aliasing even when the gain is changed for each band is attracting attention. The complex exponential modulation filter bank is used in a spectrum band replication (hereinafter referred to as SBR) technique that improves the sound quality of an encoded audio signal at a low bit rate by band expansion. As an audio codec using band extension technology based on SBR, HEAAC (High Efficiency AAC), which combines MPEG (Moving Picture Experts Group) AAC (Advanced Audio Coding) and SBR described in Non-Patent Document 1 and Non-Patent Document 2. In addition, mp3PRO that combines mp3 (MPEG Audio Layer 3) described in Non-Patent Document 3 and SBR is known.

  A sampling frequency conversion method using a conventional complex exponential modulation filter bank will be described below. FIG. 8 is a block diagram showing the configuration of a conventional sampling frequency conversion method using a signal analysis filter bank and a signal synthesis filter bank.

  The signal analysis filter bank 801 includes a sampling frequency K-times interpolator 803, M analysis band-pass filters 804, and M decimation units 805. The signal synthesis filter bank 802 includes M interpolators 806 and M It comprises a synthesis band pass filter 807, an adder 808, and a sampling frequency 1 / L decimation unit 809. The analysis band pass filter 804 and the synthesis band pass filter 807 are paired with each other. Here, K and L are positive divisors including 1 of the band division number M and take different values.

  First, the operation of the signal analysis filter bank 801 will be described. The sampling frequency K-times interpolator 803 inserts (K−1) zero data for each data into the input signal sampled at the input sampling frequency fs, thereby multiplying the input sampling frequency fs by K times. Ascend to Kfs. Next, a bandpass signal is generated by an analysis bandpass filter 804 that divides the entire band into M equal bandwidth bands, and (M−1) pieces of data are thinned out for every M pieces of data by a thinning device 805. By outputting one piece of data, it is converted into a band division signal having a sampling frequency (fsK / M) and output. Since the input sampling frequency fs of the input signal is multiplied by K times, the band division signal equal to or higher than the M / K band is zero.

  Next, the operation of the signal synthesis filter bank 802 will be described. The sampling frequency (fsK / M) output from the signal analysis filter bank 801 is input, and the sampling frequency is inserted by interpolator 806 by inserting (M−1) zero data for each data. Is increased to M times Kfs, and a bandpass signal is generated by the M bandpass filters for equal bandwidth 807, and then synthesized by an adder 808 to reproduce a signal having a sampling frequency Kfs. Next, the sampling frequency 1 / L times decimation unit 809 decimates (L−1) data for every L data, and outputs a signal sampled at the output sampling frequency (fsK / L).

  Therefore, the signal analysis filter bank and the signal synthesis filter bank in FIG. 8 operate as a sampling frequency converter that converts an input signal sampled at the input sampling frequency fs into an output signal sampled at the output sampling frequency (fsK / L).

  As described in Patent Document 1, the complex exponential modulation filter bank is configured by performing complex exponential modulation on a prototype filter. From Patent Document 1, when the filter coefficient of the linear phase acyclic prototype filter is h (n) (where 0 ≦ n ≦ N, N is the filter order), the complex exponential modulation signal analysis filter bank of the kth band The filter coefficient ha (k, n) at the sampling time n is given by (Equation 1) (where j is an imaginary unit and A is the phase of signal analysis).

  Therefore, when the values of the filter coefficients of the first and last prototype filters are zero (h (0) = h (N) = 0), the input signal at the sampling time n of the signal analysis filter bank is set to x (n). For example, the complex band division output signal X (k, mM / K) at the sampling time mM / K in the k-th band (where 0 ≦ k ≦ (M / K−1)) is given by (Equation 2).

  Since the amount of calculation increases when (Equation 2) is directly calculated, a complex exponential modulation signal analysis filter bank with a reduced amount of calculation has been conventionally used. FIG. 9 is a flowchart showing processing steps of a conventional complex exponential modulation signal analysis filter bank analysis method. In step 901, the intermediate signal w (n) is calculated from the input signal x (n) at the sampling time n by (Equation 3).

  Next, in step 902, the complex band division output signal X (k, mM / K) from the intermediate signal w (n) to the kth band (where 0 ≦ k ≦ (M / K−1)) at the sampling time mM / K. ) Is calculated by (Equation 4) (where A is the phase of signal analysis).

  For example, Non-Patent Document 1 discloses a complex exponential modulation signal analysis filter bank when the band division number M is 64, the filter order N of the prototype filter is 640, the upsampling factor K is 2, and the signal phase A is -1. Examples are described. However, in Non-Patent Document 1, c (n) calculated from (Expression 5) from h (n) is used instead of the filter coefficient h (n) of the prototype filter.

  Here, INT (x) is a function that rounds off the decimal part of x to make it an integer.

  In the conventional example of FIG. 9, the amount of calculation can be reduced by introducing an intermediate signal as compared with the case of directly calculating (Equation 2).

  Here, the number of operations necessary to realize the complex exponential modulation signal analysis filter bank of FIG.

  In step 901, if c (n) calculated in advance in (Equation 5) instead of h (n) is stored in a table and used, the real number addition count is (N / 2M-1) (2M / K). = (N / K-2M / K) times, the number of real multiplications is (N / 2M) (2M / K) = N / K times.

In step 902, if Kexp (jπ (k + 0.5) (2Kn + A) / (2M)) is calculated in advance and stored in a table, the number of real additions is 2 (2M / K−1) (M / K) = (4 (M / K) ² −2 (M / K)) times, and the number of real multiplications is 2 (2M / K) (M / K) = 4 (M / K) ² times.

  If the order N of the prototype filter is 640, the band division number M is 64, and the upsampling factor K is 1, the real number addition number is 512, the real number multiplication number is 640 times, and the real number addition is step 902. The total number of times is 16256, the number of real multiplications is 16384, and the total of Step 901 and Step 902 is 16768 times for real number addition and 17024 times for real number multiplication.

  Next, a conventional complex exponential modulation signal synthesis filter bank will be described. From Patent Document 1, the filter coefficient hs (k, n) at the sampling time n of the k-th band of the complex exponential modulation signal synthesis filter bank is given by (Equation 6) (where B is the phase of signal synthesis).

  Here, the phase B of the signal synthesis satisfies the relational expression of the phase A of the signal analysis and (Expression 7) (where P is an arbitrary integer).

  The real part of the sum in the effective band (band from the 0th band to the (M / L-1) band) of the signal obtained by convolving the input complex band division signal with the filter coefficient of (Equation 6) is the signal synthesis filter This is the output of bank 802. When the values of the filter coefficients of the first and last prototype filters are zero, the complex band division input signal at the sampling time (mM / K) of the kth band of the complex exponential modulation signal synthesis filter bank is represented by X (k, mM / K). ), The output signal x (mM / K + nL / K) at the sampling time (mM / K + nL / K) is given by (Equation 8) (where Re (x) is the real part of the complex number x).

  Since the amount of calculation increases when (Equation 8) is directly calculated, a complex exponential modulation signal synthesis bank with a reduced amount of calculation has been conventionally used as in the case of the complex exponential modulation signal analysis filter bank. . FIG. 10 is a flowchart showing processing steps of a conventional method for synthesizing a complex exponential modulation signal synthesis filter bank. In step 1001, the intermediate signal w (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w (n + 2M / L), and the complex band at the sampling time mM / K of the kth band. An intermediate signal w (n) for 0 ≦ n ≦ (2M / L−1) is calculated from the divided input signal X (k, mM / K) by (Equation 9).

  Next, in step 1002, the output signal x (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is determined from the intermediate signal w (n) ( It is calculated by the equation (10).

  For example, in Non-Patent Document 1, the band division number M is 64, the filter order N of the prototype filter is 640, the upsampling factor K is 2, the downsampling factor 1 / L is 1, and the signal synthesis phase B is − An example of a complex exponential modulation signal synthesis filter bank in the case of 255 is described.

  The number of operations required to realize the complex exponential modulation signal synthesis filter bank of FIG. 10 is evaluated as the real number addition number and the real number multiplication number.

In step 1001, if (1 / M) exp (jπ (k + 0.5) (2Ln + B) / (2M)) is calculated in advance and stored in a table, the number of real additions is (M / L−1). ) (2M / L) + (M / L) (2M / L) = (4 (M / L) ² −2 (M / L)) times, and the number of real multiplications is 2 (M / L) (2M / L) = 4 (M / L) ² times.

  If c (n) calculated in (Equation 5) is stored in a table instead of h (n) in step 1002, the number of real additions is (N / M-1) (M / L) = ( N / L-M / L) times, the number of real multiplications is (N / 2M) 2 (M / L) = N / L times.

  If the order N of the prototype filter is 640, the band division number M is 64, and the downsampling factor 1 / L is 1/2, in step 1001, the number of real additions is 4032, the number of real multiplications is 4096, and step 1002 Thus, the real number addition number is 288 times, the real number multiplication number is 320 times, and the total of Step 1001 and Step 1002 is 4320 times, and the real number multiplication number is 4416 times.

Therefore, by adding up the amount of calculation required to realize the complex exponential modulation signal analysis filter bank (upsampling factor 1) and the complex exponential modulation signal synthesis filter bank (downsampling factor 1/2), The calculation amount of the sampling frequency conversion method using the complex exponential modulation filter bank (converting the sampling frequency to ½) is 16768 + 4320 = 201088 real number additions and 17024 + 4416 = 2440 real number multiplications.
International Publication No. 02/080362 Pamphlet ISO / IEC 14496-3: 2001 (ISO / IEC 14496-3: 2001), Information Technology Coding of Audio-Visual Object Part 3 Audio (Information technology-Coding of audio-visual objects, Part 3 Audio), March 2003 , (FDAM1 text, Bandwidth Extension) Walter, three others, "A closer look into MPEG-4 High Efficiency AAC" 115th AES conference, paper number 5871, 10 October 2003 Moon Ziegler, 3 others, “Enhancement of mp3 with SBR: Features and capabilities of the new mp3PRO algorithm” 5560, May 2002

  However, the sampling frequency conversion method using the conventional complex exponential modulation filter bank has a problem that the amount of calculation is large. Therefore, there is a problem that the operating clock frequency becomes high and the power consumption is large when the sampling frequency conversion is implemented by using a limited number of multipliers and adders in a time division manner like a digital signal processor. It was. In addition, there is a problem that the processing time when executing sampling frequency conversion by software using a computer is long.

  SUMMARY OF THE INVENTION The present invention solves the above-described conventional problems, and an object thereof is to provide a sampling frequency conversion method that reduces the amount of calculation when executing sampling frequency conversion and reduces power consumption. Another object of the present invention is to provide a sampling frequency conversion method that shortens the processing time when executing the sampling frequency conversion and increases the processing speed.

  In order to solve this problem, the sampling frequency conversion method of the present invention uses an input signal sampled at an input sampling frequency fs as an output sampling frequency (fsK / L) (where M is an input signal divided by an equal bandwidth). A sampling frequency conversion method for converting to an output signal sampled with a division number of K, and L is a positive divisor including 1 of M and different values), and calculating a first intermediate signal from the input signal; Calculating a second intermediate signal from the first intermediate signal, calculating a third intermediate signal from the second intermediate signal by fast Fourier transform or inverse fast Fourier transform at the M / K point, Calculating a fourth intermediate signal from the three intermediate signals, and a fifth intermediate signal from the fourth intermediate signal by fast Fourier transform or inverse fast Fourier transform at the M / L point. Calculating a signal, shifting the sixth intermediate signal, then calculating a sixth intermediate signal from the fifth intermediate signal, and calculating an output signal from the sixth intermediate signal. It is characterized by that.

  Thereby, since the fast Fourier transform or the inverse fast Fourier transform can be efficiently applied using the periodicity of the complex exponential function, the amount of calculation of the complex exponential modulation filter bank can be reduced. The sampling frequency conversion method can reduce the amount of calculation by adopting a configuration that does not depend on the phase of signal analysis and the phase of signal synthesis.

  According to the present invention, it is possible to reduce the amount of calculation when performing sampling frequency conversion. Therefore, it is possible to reduce the operation clock frequency when the sampling frequency conversion is implemented by a digital signal processor or LSI, and to realize the sampling frequency conversion with low power consumption. In addition, the processing time when the sampling frequency conversion is executed by software using a computer can be shortened, and the processing speed can be increased.

  In the sampling frequency conversion method using the complex exponential modulation filter bank of the present invention, the input signal x (n) (n is the sampling time) sampled at the input sampling frequency fs is output to the output sampling frequency (fsK / L) (where M is The input signal is converted into an output signal y (n) sampled by dividing the input signal into equal bandwidths, where K and L are positive divisors including 1 of M and different values. The complex exponential modulation filter bank is constructed by performing complex exponential modulation on a prototype filter. In the following embodiment, the filter order of the linear phase acyclic prototype filter is N (where N = 2MQ, Q is a positive integer), and the filter coefficient is h (n) (0 ≦ n ≦ N, first and last). The value of the filter coefficient is set to zero (h (0) = h (N) = 0)).

  Embodiments of the present invention will be described below with reference to the drawings.

(Embodiment 1)
FIG. 1 is a block diagram illustrating a configuration of an apparatus that executes the sampling frequency conversion method according to the first embodiment.

  The first intermediate signal generator 101 outputs the first intermediate signal w1 (n) from the input signal x (n) (n is the sampling time) and the filter coefficient h (n) of the prototype filter.

  At the sampling time mM (where m is an integer), the first intermediate signal w1 (n) is calculated from the input signal x (n) by (Equation 11).

  If c (n) calculated in advance in (Equation 12) instead of h (n) is stored in a table and used, (Equation 11) becomes (Equation 13).

  The first intermediate signal generation unit 101 executes (Equation 13) and outputs the first intermediate signal w1 (n).

  The second intermediate signal generation unit 102 executes (Expression 14) (where j is an imaginary unit) from the first intermediate signal w1 (n) output by the first intermediate signal generation unit 101 to obtain the second An intermediate signal w2 (n) is output.

  The FFT unit 103 performs M / K point fast Fourier transform (FFT) on the second intermediate signal w2 (n) output from the second intermediate signal generation unit 102. (FFT: Fast Fourier Transform) Then, the result is output as the third intermediate signal W3 (k).

  In the fourth intermediate signal generation unit 104, from the third intermediate signal w3 (k) output from the FFT unit 103, (Equation 16) when K <L, and (Equation 17) when K> L. ) To calculate and output the fourth intermediate signal W4 (k).

  The FFT unit 105 performs M / L point fast Fourier transform of (Equation 18) on the fourth intermediate signal W4 (k) output from the fourth intermediate signal generation unit 104, and outputs the result to the fifth Output as an intermediate signal w5 (n).

  The sixth intermediate signal generation unit 106 executes (Equation 19) from the fifth intermediate signal w5 (n) output from the FFT unit 105 and outputs a sixth intermediate signal w6 (n).

  The output signal generation unit 107 calculates the output signal y (n) from the sixth intermediate signal w6 (n) output from the sixth intermediate signal generation unit 106 and the filter coefficient h (n) of the prototype filter.

  The output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) from the sixth intermediate signal w6 (n) (Expression 20) Calculated by Here, instead of h (n), c (n) calculated in advance in (Equation 12) is stored in a table and used, (Equation 20) becomes (Equation 21).

  Here, instead of h (n), c (n) calculated in advance in (Equation 12) is stored in a table and used, (Equation 20) becomes (Equation 21).

  The output signal generation unit 107 executes (Expression 21) to calculate and output the output signal y (mM / K + nL / K).

  FIG. 2 is a flowchart showing processing steps of the sampling frequency conversion method according to Embodiment 1 of the present invention.

  In FIG. 2, Step 201 to Step 203 constitute a signal analysis filter bank based on complex exponential modulation, and Step 204 to Step 207 constitute a signal synthesis filter bank based on complex exponential modulation. In the following, n is the sampling time.

  In step 201, at the sampling time mM (where m is an integer), the first intermediate signal w1 (n) is calculated from the input signal x (n) by (Equation 11). If c (n) calculated in advance in (Equation 12) instead of h (n) is stored in a table and used in step 201, (Equation 11) becomes (Equation 13).

  Therefore, the number of real number additions necessary to execute step 201 is (N / 2M-1) (2M / K) = N / K-2M / K times, and the number of real number multiplications is (N / 2M) (2M / K). ) = N / K times.

  In step 202, the second intermediate signal w2 (n) (where 0 ≦ n ≦ (M / K−1)) is obtained from the first intermediate signal w1 (n) to (Equation 14) (where j is an imaginary unit). ) Is calculated.

  Here, if Kexp (−jπnK / (2M)) is stored in a table and used, complex multiplication is required M / K times to execute step 202. If this is converted into a real number calculation, real number addition needs 2M / K times and real number multiplication needs 4M / K times.

  In step 203, the third intermediate signal W3 (k) (where 0 ≦ k ≦ (M / K−1)) is calculated from the second intermediate signal w2 (n) by fast Fourier transform (Equation 15).

In the FFT of M / K points, (M / (2K)) log ₂ (M / K) times of butterfly operations are required. Since one butterfly operation includes two complex additions and one complex multiplication, converting this into a real number operation requires six real number additions and four real number multiplications. Therefore, the number of real number additions required to execute step 203 is (3M / K) log ₂ (M / K) times, and the number of real number multiplications is (2M / K) log ₂ (M / K) times.

  In step 204, the fourth intermediate signal W4 (k) (where 0 ≦ k ≦ (M / L−1)) is calculated from the third intermediate signal W3 (k) using (Equation 16).

  Step 204 is only rearrangement of the third intermediate signal W3 (k), and real number addition and real number multiplication do not occur.

  Note that (Equation 16) is the case where K <L, and when K> L, the fourth intermediate signal W4 (k) (where 0 is calculated from the third intermediate signal W3 (k) to (Equation 17)). ≦ k ≦ (M / L−1)) is calculated.

  In step 205, the fifth intermediate signal w5 (n) (where 0 ≦ n ≦ (M / L−1)) is calculated from the fourth intermediate signal W4 (k) by fast Fourier transform (Equation 18). .

In step 205, the number of real number additions required to execute the M / L point FFT is (3M / L) log ₂ (M / L) times, and the number of real number multiplications is (2M / L) log ₂ (M / L). L) times.

  In step 206, the sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and then 0 ≦ n ≦ (M / L), the sixth intermediate signals w6 (n) and w6 (n + M / L) are calculated from the fifth intermediate signal w5 (n) by (Equation 19).

  If (1 / M) exp (−jπ (Q + Ln / (2M))) is stored in a table and used in step 206, M / L complex multiplications are required to execute step 206. If this is converted into a real number operation, 2M / L real number addition and 4M / L real number multiplication are required.

  In step 207, the output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n). Calculated by (Equation 20).

  Here, instead of h (n), c (n) calculated in advance in (Equation 12) is stored in a table and used, (Equation 20) becomes (Equation 21).

  Therefore, the number of real number additions required to execute step 207 is (N / M-1) (M / L) = (N / LM-L) times, and the number of real number multiplications is (N / 2M) 2 ( M / L) = N / L times.

When the number of calculations required to execute the first embodiment of FIG. 2 is obtained as the sum of the number of calculations in each of the above steps, the real number addition number is (N / K + (3M / K) log ₂ (M / K) + N / L + M / L + (3M / L) log ₂ (M / L)) times, the number of real multiplications is (N / K + 4M / K + (2M / K) log ₂ (M / K) + N / L + 4M / L + (2M / L) log ₂ (M / L)) times. If the order N of the prototype filter is 640, the band division number M is 64, the up-sampling factor K is 1, and the down-sampling factor 1 / L is 1/2, the computations necessary to execute the first embodiment The amount is 2624 real additions and 2432 real multiplications. When this is compared with the conventional example (real number addition number 21088, real number multiplication number 21440), in Embodiment 1, the real number addition number is reduced to about 12% of the conventional example and the real number multiplication number is reduced to about 11% of the conventional example. can do.

  As described above, in the sampling frequency conversion method of the first embodiment, it is possible to reduce the amount of calculation by efficiently applying the fast Fourier transform using the periodicity of the complex exponential function. Further, the calculation amount can be reduced by adopting a configuration that does not depend on the phase of signal analysis and the phase of signal synthesis. From these things, the amount of calculation required for execution of sampling frequency conversion can be reduced. As a result, the operation clock frequency when the sampling frequency conversion is implemented by a digital signal processor or LSI can be reduced, and the sampling frequency conversion can be realized with low power consumption. In addition, it is possible to shorten the processing time when performing sampling frequency conversion by software using a computer, and it is possible to realize high-speed processing.

(Embodiment 2)
FIG. 3 is a block diagram illustrating a configuration of an apparatus that executes the sampling frequency conversion method according to the second embodiment. 3 is obtained by adding a band division signal generation unit 108 to the configuration of FIG. 1 of the first embodiment. As a result, in the second embodiment, sampling frequency conversion can be performed and a complex band division signal having a specified signal analysis phase can be output.

  The band division signal generation unit 108 calculates (Expression 22) when k is an even number (k = 2l) from the third intermediate signal W3 (k) output from the FFT unit 103 (where * is a conjugate complex number and A is When k is an odd number (phase of signal analysis) (k = 2l + 1), (Equation 23) is executed to calculate and output a complex band division signal X (k, mM / K).

  FIG. 4 is a flowchart showing processing steps of the sampling frequency conversion method according to Embodiment 2 of the present invention.

  The second embodiment is the same as the first embodiment except that step 301 for calculating a complex band division signal having the phase of the designated signal analysis is added. As shown in FIG. 4, step 301 is added after step 203. 4, steps having the same numbers as those in FIG. 2 are the same steps as those in FIG.

  In step 301, the complex band division signal X () at the sampling time mM / K in the k-th band (where 0 ≦ k ≦ (M / K−1)) from the third intermediate signal W3 (k) calculated in step 203. k, mM / K) when k is an even number (k = 2l) (Equation 22) (where * is a conjugate complex number, A is a phase of signal analysis), and k is an odd number (k = 2l + 1) Is calculated by (Equation 23) and output.

  Since the input signal is up-sampled K times, the effective band of the complex band division signal is from the 0th band to the (M / K-1) band, and the complex band division signal above the M / K band is Zero.

  In order to execute step 301, M / K complex multiplications are necessary. If this is converted to a real number operation, 2M / K real additions and 4M / K real multiplications are required.

  When the phase A of the signal analysis is a multiple of 8M, (Equation 22) and (Equation 23) become (Equation 24) and (Equation 25), respectively, and real number addition and real number multiplication are performed to execute step 301. Is no longer necessary.

The number of operations required to execute the second embodiment of FIG. 4 is the sum of the number of operations in each of the above steps, and the real number addition number is (N / K + 2M / K + (3M / K) log ₂ (M / K ) + N / L + M / L + (3M / L) log ₂ (M / L)) times, real number of times of multiplication is (N / K + 8M / K + (2M / K) log ₂ (M / K) + N / L + 4M / L + (2M) / L) log ₂ (M / L)) times. Here, when the order N of the prototype filter is 640, the band division number M is 64, the upsampling factor K is 1, and the downsampling factor 1 / L is 1/2, the second embodiment is executed. The required amount of calculation is 2752 real additions and 2688 real multiplications. When this is compared with the conventional example (real number addition number 21088, real number multiplication number 21440), the second embodiment reduces the real number addition number to about 13% of the conventional example and the real number multiplication number to about 13% of the conventional example. can do.

  As described above, in the sampling frequency conversion method using complex exponential modulation according to the second embodiment, the sampling frequency conversion is performed in the same manner as in the first embodiment, and the complex band division signal of the phase of the designated signal analysis is calculated. Can be output.

(Embodiment 3)
FIG. 5 is a flowchart showing processing steps of the sampling frequency conversion method according to Embodiment 3 of the present invention.

  In FIG. 5, Steps 501 to 503 constitute a signal analysis filter bank based on complex exponential modulation, and Steps 504 to 507 constitute a signal synthesis filter bank based on complex exponential modulation.

  The difference between the third embodiment and the first embodiment is that, in the first embodiment, the signal analysis filter bank based on complex exponential modulation is efficiently realized using the fast Fourier transform, whereas the first embodiment is different from the first embodiment. 3 is an efficient implementation by using an inverse fast Fourier transform (IFFT: Inverse Fast Fourier Transform).

  Comparing Embodiment 3 in FIG. 5 with Embodiment 1 in FIG. 2, Step 501, Step 505, Step 506, and Step 507 in Embodiment 3 are the same as Step 201, Step 205, and Step in Embodiment 1, respectively. 206 is the same as step 207, but steps 502 to 504 of the third embodiment are different from steps 202 to 204 of the first embodiment.

  In step 501, at the sampling time mM (where m is an integer), the first intermediate signal w1 (n) is calculated from the input signal x (n) according to (Equation 26).

  If c (n) calculated in advance in (Equation 12) instead of h (n) in step 501 is stored in a table and used, (Equation 26) becomes (Equation 27).

  Therefore, the number of real number additions required to execute step 501 is (N / 2M-1) (2M / K) = (N / K-2M / K) times, and the number of real number multiplications is (N / 2M) (2M / K) = N / K times.

  In step 502, the second intermediate signal w2 (n) (where 0 ≦ n ≦ (M / K−1)) is calculated from the first intermediate signal w1 (n) to (Equation 28) (where j is an imaginary unit). ) Is calculated.

  Here, if Kexp (jπnK / (2M)) is stored in a table and used, complex multiplication is required M / K times to execute step 502. If this is converted into a real number calculation, real number addition needs 2M / K times and real number multiplication needs 4M / K times.

  In step 503, the third intermediate signal W3 (k) (where 0 ≦ k ≦ (M / K−1)) is calculated from the second intermediate signal w2 (n) by inverse fast Fourier transform (Equation 29). .

In step 503, the number of real number additions necessary to execute the IFFT of M / K points is (3M / K) log ₂ (M / K) times, and the number of real number multiplications is (2M / K) log ₂ (M / K) times.

  In step 504, the fourth intermediate signal W4 (k) (where 0 ≦ k ≦ (M / L−1), * is a conjugate complex number) is calculated from the third intermediate signal W3 (k) using (Equation 30). To do.

  Step 504 is taking the conjugate complex number of the third intermediate signal W3 (k) and rearranging, and real number addition and real number multiplication do not occur.

  Note that (Equation 30) is the case where K <L, and in the case of K> L, the fourth intermediate signal W4 (k) (provided that 0 through the third intermediate signal W3 (k) to (Equation 31)). ≦ k ≦ (M / L−1)) is calculated.

  In step 505, the fifth intermediate signal w5 (n) (where 0 ≦ n ≦ (M / L−1)) is calculated from the fourth intermediate signal W4 (k) by the fast Fourier transform (Expression 32). .

The number of real number additions required to execute M / L point FFT in step 505 is (3M / L) log ₂ (M / L) times, and the number of real number multiplications is (2M / L) log ₂ (M / L). ) Times.

  In step 506, the sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and then 0 ≦ n ≦ (M / L), the sixth intermediate signals w6 (n) and w6 (n + M / L) are calculated from the fifth intermediate signal w5 (n) by (Equation 33).

  If (1 / M) exp (−jπ (Q + Ln / (2M))) is stored in a table and used in step 506, M / L complex multiplications are required to execute step 506. If this is converted into a real number operation, 2M / L real number addition and 4M / L real number multiplication are required.

  In step 507, the output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) ( It is calculated by the equation 34).

  Here, if c (n) calculated in advance in (Equation 12) instead of h (n) is stored in a table and used, (Equation 34) becomes (Equation 35).

  Therefore, the number of real number additions necessary to execute Step 507 is (N / M−1) (M / L) = (N / LM−L / L) times, and the number of real number multiplications is (N / 2M) 2 ( M / L) = N / L times.

When the number of computations necessary to execute the third embodiment of FIG. 5 is obtained as the sum of the number of computations in each of the above steps, the real number addition number is (N / K + (3M / K) log ₂ (M / K) + N / L + M / L + (3M / L) log ₂ (M / L)) times, the number of real multiplications is (N / K + 4M / K + (2M / K) log ₂ (M / K) + N / L + 4M / L + (2M / L) log ₂ (M / L)) times. The number of calculations in the third embodiment is the same as the number of calculations in the first embodiment. Here, when the order N of the prototype filter is 640, the band division number M is 64, the upsampling factor K is 1, and the downsampling factor 1 / L is 1/2, the third embodiment is executed. The amount of calculation required is 2624 real additions and 2432 real multiplications. When this is compared with the conventional example (real number addition number 21088, real number multiplication number 21440), in Embodiment 3, the real number addition number is reduced to about 12% of the conventional example and the real number multiplication number is reduced to about 11% of the conventional example. can do.

  As described above, in the sampling frequency conversion method of the third embodiment, it is possible to reduce the amount of calculation by efficiently applying the inverse fast Fourier transform and the fast Fourier transform using the periodicity of the complex exponential function. . Further, the calculation amount can be reduced by adopting a configuration that does not depend on the phase of signal analysis and the phase of signal synthesis. From these things, the amount of calculation required for execution of sampling frequency conversion can be reduced. As a result, the operation clock frequency when the sampling frequency conversion is implemented by a digital signal processor or LSI can be reduced, and the sampling frequency conversion can be realized with low power consumption. In addition, it is possible to shorten the processing time when performing sampling frequency conversion by software using a computer, and it is possible to realize high-speed processing.

(Embodiment 4)
FIG. 6 is a flowchart showing processing steps of the sampling frequency conversion method according to Embodiment 4 of the present invention.

  In FIG. 6, steps 601 to 603 constitute a signal analysis filter bank based on complex exponential modulation, and steps 604 to 607 constitute a signal synthesis filter bank based on complex exponential modulation.

  The difference between the fourth embodiment and the first embodiment is that, in the first embodiment, the signal synthesis filter bank based on complex exponential modulation is efficiently realized by using the fast Fourier transform. 4 is an efficient implementation using inverse fast Fourier transform.

  Comparing Embodiment 4 of FIG. 6 with Embodiment 1 of FIG. 2, Step 601, Step 602, Step 603, and Step 607 of Embodiment 4 are the same as Step 201, Step 202, and Step of Embodiment 1, respectively. 203 is the same as step 207, but steps 604 to 606 of the fourth embodiment are different from steps 204 to 206 of the first embodiment.

  In step 601, at the sampling time mM (where m is an integer), the first intermediate signal w1 (n) is calculated from the input signal x (n) by (Equation 36).

  If c (n) calculated in advance in (Equation 12) instead of h (n) is stored in the table and used in step 601, (Equation 36) becomes (Equation 37).

  Therefore, the number of real number additions required to execute step 601 is (N / 2M-1) (2M / K) = (N / K-2M / K) times, and the number of real number multiplications is (N / 2M) (2M / K) = N / K times.

  In step 602, the second intermediate signal w2 (n) (where 0 ≦ n ≦ (M / K−1)) is obtained from the first intermediate signal w1 (n) to (Equation 38) (where j is an imaginary unit). ) Is calculated.

  Here, if Kexp (−jπnK / (2M)) is stored in a table and used, complex multiplication is required M / K times to execute step 602. If this is converted into a real number calculation, real number addition needs 2M / K times and real number multiplication needs 4M / K times.

  In step 603, the third intermediate signal W3 (k) (where 0 ≦ k ≦ (M / K−1)) is calculated from the second intermediate signal w2 (n) by fast Fourier transform (Equation 39).

In step 603, the number of real number additions required to execute M / K point FFT is (3M / K) log ₂ (M / K) times, and the number of real number multiplications is (2M / K) log ₂ (M / K) times.

  In step 604, the fourth intermediate signal W4 (k) (where 0 ≦ k ≦ (M / L−1), * is a conjugate complex number) is calculated from the third intermediate signal W3 (k) using (Equation 40). To do.

  Step 604 is taking the conjugate complex number of the third intermediate signal W3 (k) and rearranging, and real number addition and real number multiplication do not occur.

  Note that (Equation 40) is the case of K <L, and when K> L, the fourth intermediate signal W4 (k) (where 0 is calculated from the third intermediate signal W3 (k) to (Equation 41)). ≦ k ≦ (M / L−1)) is calculated.

  In step 605, the fifth intermediate signal w5 (n) (where 0 ≦ n ≦ (M / L−1)) is calculated from the fourth intermediate signal W4 (k) by inverse fast Fourier transform (Equation 42). To do.

In step 605, the number of real number additions required to execute IFFT at the M / L point is (3M / L) log ₂ (M / L) times, and the number of real number multiplications is (2M / L) log ₂ (M / L). ) Times.

  In step 606, the sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and then 0 ≦ n ≦ (M / L), the sixth intermediate signals w6 (n) and w6 (n + M / L) are calculated from the fifth intermediate signal w5 (n) by (Equation 43).

  If (1 / M) exp (jπ (Q + Ln / (2M))) is stored in a table and used in step 606, M / L complex multiplications are required to execute step 606. When this is converted into a real number calculation, 2M / L real number addition and 4M / L real number multiplication are required.

  In step 607, the output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) ( It is calculated by equation (44).

  Here, if c (n) calculated in advance in (Equation 12) instead of h (n) is stored in a table and used, (Equation 44) becomes (Equation 45).

  Therefore, the number of real number additions necessary to execute step 607 is (N / M-1) (M / L) = (N / LM-L / L) times, and the number of real number multiplications is (N / 2M) 2 ( M / L) = N / L times.

When the number of computations necessary to execute the fourth embodiment of FIG. 6 is obtained as the sum of the number of computations in the above steps, the real number addition number is (N / K + (3M / K) log ₂ (M / K). + N / L + M / L + (3M / L) log ₂ (M / L)) times, the number of real multiplications is (N / K + 4M / K + (2M / K) log ₂ (M / K) + N / L + 4M / L + (2M / L) log ₂ (M / L)) times. The number of calculations in the fourth embodiment is the same as the number of calculations in the first embodiment. Here, if the order N of the prototype filter is 640, the band division number M is 64, the upsampling factor K is 1, and the downsampling factor 1 / L is 1/2, then the fourth embodiment is executed. The amount of calculation required is 2624 real additions and 2432 real multiplications. When this is compared with the conventional example (real number addition number 21088, real number multiplication number 21440), the fourth embodiment reduces the real number addition number to about 12% of the conventional example and the real number multiplication number to about 11% of the conventional example. can do.

  As described above, in the sampling frequency conversion method of the fourth embodiment, it is possible to reduce the amount of calculation by efficiently applying the fast Fourier transform and the inverse fast Fourier transform using the periodicity of the complex exponential function. . Further, the calculation amount can be reduced by adopting a configuration that does not depend on the phase of signal analysis and the phase of signal synthesis.

  From these things, the amount of calculation required for execution of sampling frequency conversion can be reduced. As a result, the operation clock frequency when the sampling frequency conversion is implemented by a digital signal processor or LSI can be reduced, and the sampling frequency conversion can be realized with low power consumption. In addition, it is possible to shorten the processing time when performing sampling frequency conversion by software using a computer, and it is possible to realize high-speed processing.

(Embodiment 5)
FIG. 7 is a flowchart showing processing steps of the sampling frequency conversion method according to the fifth embodiment of the present invention.

  In FIG. 7, Steps 701 to 703 constitute a signal analysis filter bank based on complex exponential modulation, and Steps 704 to 707 constitute a signal synthesis filter bank based on complex exponential modulation.

  The difference between the fifth embodiment and the first embodiment is that, in the first embodiment, both the signal analysis filter bank and the signal synthesis filter bank by complex exponential modulation are efficiently realized by using the fast Fourier transform. On the other hand, in the fifth embodiment, both are efficiently realized using inverse fast Fourier transform.

  Comparing Embodiment 5 of FIG. 7 with Embodiment 1 of FIG. 2, Step 701, Step 704, and Step 707 of Embodiment 5 are the same as Step 201, Step 204, and Step 207 of Embodiment 1, respectively. However, step 702, step 703, step 705, and step 706 of the fifth embodiment are different from step 202, step 203, step 205, and step 206 of the first embodiment.

  In step 701, at the sampling time mM (where m is an integer), the first intermediate signal w1 (n) is calculated from the input signal x (n) by (Equation 46).

  If c (n) calculated in advance in (Equation 12) instead of h (n) is stored in the table and used in step 701, (Equation 46) becomes (Equation 47).

  Therefore, the number of real number additions required to execute Step 701 is (N / 2M-1) (2M / K) = (N / K-2M / K) times, and the number of real number multiplications is (N / 2M) (2M / K) = N / K times.

  In Step 702, the second intermediate signal w2 (n) (where 0 ≦ n ≦ (M / K−1)) is obtained from the first intermediate signal w1 (n) to (Formula 48) (where j is an imaginary unit). ) Is calculated.

  Here, if Kexp (jπnK / (2M)) is stored in a table and used, complex multiplication is required M / K times to execute step 702. When this is converted to a real number calculation, real number addition requires 2M / K times, and real number multiplication requires 4M / K times.

  In step 703, the third intermediate signal W3 (k) (where 0 ≦ k ≦ (M / K−1)) is calculated from the second intermediate signal w2 (n) by inverse fast Fourier transform (Equation 49). .

In step 703, the number of real number additions necessary to execute the IFFT of M / K points is (3M / K) log ₂ (M / K) times, and the number of real number multiplications is (2M / K) log ₂ (M / K) times.

  In step 704, the fourth intermediate signal W4 (k) (where 0 ≦ k ≦ (M / L−1)) is calculated from the third intermediate signal W3 (k) using (Equation 50).

  Step 704 is a rearrangement of the third intermediate signal W3 (k), and real number addition and real number multiplication do not occur.

  Note that (Equation 50) is the case of K <L, and when K> L, the fourth intermediate signal W4 (k) (where 0 is calculated from the third intermediate signal W3 (k) to (Equation 51)). ≦ k ≦ (M / L−1)) is calculated.

  In step 705, the fifth intermediate signal w5 (n) (where 0 ≦ n ≦ (M / L−1)) is calculated from the fourth intermediate signal W4 (k) by inverse fast Fourier transform (Formula 52). To do.

In step 705, the number of real number additions required to execute the IFFT at the M / L point is (3M / L) log ₂ (M / L) times, and the number of real number multiplications is (2M / L) log ₂ (M / L). ) Times.

  In step 706, the sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and then 0 ≦ n ≦ (M / L), the sixth intermediate signals w6 (n) and w6 (n + M / L) are calculated from the fifth intermediate signal w5 (n) by (Equation 53).

  In step 706, if (1 / M) exp (jπ (Q + Ln / (2M))) is stored in a table and used, executing step 706 requires M / L complex multiplications. When this is converted into a real number calculation, 2M / L real number addition and 4M / L real number multiplication are required.

  In step 707, the output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) ( It is calculated by the equation (54).

  Here, if c (n) calculated in advance in (Equation 12) instead of h (n) is stored in a table and used, (Equation 54) becomes (Equation 55).

  Therefore, the number of real number additions required to execute Step 707 is (N / M-1) (M / L) = (N / LM-L) times, and the number of real number multiplications is (N / 2M) 2 ( M / L) = (N / L) times.

When the number of calculations required to execute the fifth embodiment of FIG. 7 is obtained as the sum of the number of calculations in each of the above steps, the real number addition number is (N / K + (3M / K) log ₂ (M / K) + N / L + M / L + (3M / L) log ₂ (M / L)) times, the number of real multiplications is (N / K + 4M / K + (2M / K) log ₂ (M / K) + N / L + 4M / L + (2M / L) log ₂ (M / L)) times. The number of calculations in the fifth embodiment is the same as the number of calculations in the first embodiment. Here, when the order N of the prototype filter is 640, the band division number M is 64, the upsampling factor K is 1, and the downsampling factor 1 / L is 1/2, the fifth embodiment is executed. The amount of calculation required is 2624 real additions and 2432 real multiplications. When this is compared with the conventional example (real number addition number 21088, real number multiplication number 21440), in Embodiment 5, the real number addition number is reduced to about 12% of the conventional example and the real number multiplication number is reduced to about 11% of the conventional example. can do.

  As described above, in the sampling frequency conversion method according to the fifth embodiment, it is possible to reduce the amount of calculation by efficiently applying the inverse fast Fourier transform using the periodicity of the complex exponential function. Further, the calculation amount can be reduced by adopting a configuration that does not depend on the phase of signal analysis and the phase of signal synthesis. From these things, the amount of calculation required for execution of sampling frequency conversion can be reduced. As a result, the operation clock frequency when the sampling frequency conversion is implemented by a digital signal processor or LSI can be reduced, and the sampling frequency conversion can be realized with low power consumption. In addition, it is possible to shorten the processing time when performing sampling frequency conversion by software using a computer, and it is possible to realize high-speed processing.

  In each of the above embodiments, the step may be modified such that a constant is multiplied in the previous step and a reciprocal of the constant is multiplied in the subsequent step.

  The signal analysis and synthesis method in each of the above embodiments can be realized as a program to be executed by a computer or a digital signal processor, and may be recorded on a computer-readable recording medium.

  As described above, the sampling frequency conversion method according to the present invention is useful for high-efficiency encoding of audio signals and image signals, band expansion, etc., and particularly reduces the amount of calculation and has low power consumption or high sampling frequency. Suitable for realizing conversion.

The block diagram which shows the structure of the apparatus which performs the sampling frequency conversion method in Embodiment 1 of this invention The flowchart which shows the processing step of the sampling frequency conversion method in Embodiment 1 of this invention. The block diagram which shows the structure of the apparatus which performs the sampling frequency conversion method in Embodiment 2 of this invention The flowchart which shows the processing step of the sampling frequency conversion method in Embodiment 2 of this invention. The flowchart which shows the processing step of the sampling frequency conversion method in Embodiment 3 of this invention. The flowchart which shows the processing step of the sampling frequency conversion method in Embodiment 4 of this invention. The flowchart which shows the processing step of the sampling frequency conversion method in Embodiment 5 of this invention. A block diagram showing a configuration of a sampling frequency converter using a conventional signal analysis filter bank and a signal synthesis filter bank Flowchart showing processing steps of a conventional complex exponential modulation filter bank signal analysis method A flowchart showing processing steps of a conventional complex exponential modulation filter bank signal synthesis method

Explanation of symbols

101 first intermediate signal generation unit 102 second intermediate signal generation unit 103 FFT unit (third intermediate signal generation unit)
104 fourth intermediate signal generation unit 105 FFT unit (fifth intermediate signal generation unit)
106 sixth intermediate signal generation unit 107 output signal generation unit 108 band division signal generation unit 801 signal analysis filter bank 802 signal synthesis filter bank 803 sampling frequency K-fold interpolator 804 analysis band pass filter 805 decimation unit 806 interpolator 807 synthesis Band pass filter 808 Adder 809 Sampling frequency 1 / L decimation device

Claims (6)

Input signal x (n) sampled at input sampling frequency fs (n is sampling time) is output sampling frequency (fsK / L) (where M is the number of divisions when the input signal is divided by equal bandwidth, K and L Is a sampling frequency conversion method for converting to an output signal y (n) sampled by a positive divisor including 1 of M), and the filter coefficient of the linear phase acyclic prototype filter is represented by h (n) Where N is the filter order, 0 ≦ n ≦ N, N = 2MQ, Q is a positive integer, and h (0) = h (N) = 0)
Calculating the first intermediate signal w1 (n) from the input signal x (n) at the sampling time mM (where m is an integer) according to (Equation 1);

Calculating the second intermediate signal w2 (n) from the first intermediate signal w1 (n) by (Equation 2) (where j is an imaginary unit);

Calculating the third intermediate signal W3 (k) from the second intermediate signal w2 (n) by fast Fourier transform according to (Equation 3);

The step of calculating the fourth intermediate signal W4 (k) from the third intermediate signal W3 (k) by (Equation 4) when K <L and by (Equation 5) when K> L. When,

Calculating the fifth intermediate signal w5 (n) from the fourth intermediate signal W4 (k) by fast Fourier transform (Equation 6);

The sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and the sixth intermediate signal for 0 ≦ n ≦ M / L From w5 (n) and w6 (n + M / L) to the fifth intermediate signal w5 (n) to (Equation 7) (where Re (x) is the real part of the complex number x and Im (x) is the imaginary part of x) ) To calculate,

The output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) to (number) 8) calculating according to

A sampling frequency conversion method comprising: Input signal x (n) sampled at input sampling frequency fs (n is sampling time) is output sampling frequency (fsK / L) (where M is the number of divisions when the input signal is divided by equal bandwidth, K and L Is a sampling frequency conversion method for converting to an output signal y (n) sampled by a positive divisor including 1 of M), and the filter coefficient of the linear phase acyclic prototype filter is represented by h (n) Where N is the filter order, 0 ≦ n ≦ N, N = 2MQ, Q is a positive integer, and h (0) = h (N) = 0)
Calculating the first intermediate signal w1 (n) from the input signal x (n) at the sampling time mM (where m is an integer) according to (Equation 9);

Calculating the second intermediate signal w2 (n) from the first intermediate signal w1 (n) by (Equation 10) (where j is an imaginary unit);

Calculating the third intermediate signal W3 (k) from the second intermediate signal w2 (n) by inverse fast Fourier transform (Equation 11);

When K <L, (Equation 12) (where * is a conjugate complex number), and when K> L, (Equation 13), the third intermediate signal W3 (k) to the fourth intermediate signal. Calculating W4 (k);

Calculating the fifth intermediate signal w5 (n) from the fourth intermediate signal W4 (k) by the fast Fourier transform (Equation 14);

The sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and the sixth intermediate signal for 0 ≦ n ≦ M / L From w5 (n) and w6 (n + M / L) to the fifth intermediate signal w5 (n) to (Equation 15) (where Re (x) is the real part of the complex number x and Im (x) is the imaginary part of x) ) To calculate,

The output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) to (number) 16) calculating according to

A sampling frequency conversion method comprising: Input signal x (n) sampled at input sampling frequency fs (n is sampling time) is output sampling frequency (fsK / L) (where M is the number of divisions when the input signal is divided by equal bandwidth, K and L Is a sampling frequency conversion method for converting to an output signal y (n) sampled by a positive divisor including 1 of M), and the filter coefficient of the linear phase acyclic prototype filter is represented by h (n) Where N is the filter order, 0 ≦ n ≦ N, N = 2MQ, Q is a positive integer, and h (0) = h (N) = 0)
Calculating the first intermediate signal w1 (n) from the input signal x (n) at the sampling time mM (where m is an integer) according to (Equation 17);

Calculating the second intermediate signal w2 (n) from the first intermediate signal w1 (n) by (Equation 18) (where j is an imaginary unit);

Calculating the third intermediate signal W3 (k) from the second intermediate signal w2 (n) by fast Fourier transform (Equation 19);

When K <L, (Expression 20) (where * is a conjugate complex number), and when K> L, (Expression 21), the third intermediate signal W3 (k) to the fourth intermediate signal Calculating W4 (k);

Calculating the fifth intermediate signal w5 (n) from the fourth intermediate signal W4 (k) by inverse fast Fourier transform (Equation 22);

The sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and the sixth intermediate signal for 0 ≦ n ≦ M / L From w5 (n) and w6 (n + M / L) to the fifth intermediate signal w5 (n) to (Equation 23) (where Re (x) is the real part of the complex number x and Im (x) is the imaginary part of x) ) To calculate,

The output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) 24) calculating according to

A sampling frequency conversion method comprising: Input signal x (n) sampled at input sampling frequency fs (n is sampling time) is output sampling frequency (fsK / L) (where M is the number of divisions when the input signal is divided by equal bandwidth, K and L Is a sampling frequency conversion method for converting to an output signal y (n) sampled by a positive divisor including 1 of M), and the filter coefficient of the linear phase acyclic prototype filter is represented by h (n) Where N is the filter order, 0 ≦ n ≦ N, N = 2MQ, Q is a positive integer, and h (0) = h (N) = 0)
Calculating a first intermediate signal w1 (n) from the input signal x (n) at the sampling time mM (where m is an integer) according to (Equation 25);

Calculating the second intermediate signal w2 (n) from the first intermediate signal w1 (n) by (Equation 26) (where j is an imaginary unit);

Calculating the third intermediate signal W3 (k) from the second intermediate signal w2 (n) by inverse fast Fourier transform (Equation 27);

The step of calculating the fourth intermediate signal W4 (k) from the third intermediate signal W3 (k) according to (Equation 28) when K <L and according to (Equation 29) when K> L. When,

Calculating the fifth intermediate signal w5 (n) from the fourth intermediate signal W4 (k) by inverse fast Fourier transform (Equation 30);

The sixth intermediate signal w6 (n) for 0 ≦ n ≦ (2 (N−M) / L−1) is shifted to w6 (n + 2M / L), and the sixth intermediate signal for 0 ≦ n ≦ M / L From w5 (n) and w6 (n + M / L) to the fifth intermediate signal w5 (n) to (Equation 31) (where Re (x) is the real part of the complex number x and Im (x) is the imaginary part of x) ) To calculate,

The output signal y (mM / K + nL / K) at the sampling time (mM / K + nL / K) (where 0 ≦ n ≦ (M / L−1)) is calculated from the sixth intermediate signal w6 (n) 32) calculating according to

A sampling frequency conversion method comprising: A program for causing a computer to execute the sampling frequency conversion method according to any one of claims 1 to 4. A computer-readable recording medium on which the program according to claim 5 is recorded.

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