CN113933590A - Method, system, medium, and apparatus for calculating frequency spectrum of wave - Google Patents
Method, system, medium, and apparatus for calculating frequency spectrum of wave Download PDFInfo
- Publication number
- CN113933590A CN113933590A CN202010674824.2A CN202010674824A CN113933590A CN 113933590 A CN113933590 A CN 113933590A CN 202010674824 A CN202010674824 A CN 202010674824A CN 113933590 A CN113933590 A CN 113933590A
- Authority
- CN
- China
- Prior art keywords
- frequency
- filter
- fst
- spectrum
- fed
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000001228 spectrum Methods 0.000 title claims abstract description 87
- 238000000034 method Methods 0.000 title claims abstract description 31
- 230000004044 response Effects 0.000 claims description 31
- 239000011159 matrix material Substances 0.000 claims description 22
- 238000004590 computer program Methods 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 11
- 230000003595 spectral effect Effects 0.000 claims description 3
- 230000008901 benefit Effects 0.000 abstract description 4
- 238000004458 analytical method Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 238000002955 isolation Methods 0.000 description 3
- 238000005070 sampling Methods 0.000 description 3
- 230000008094 contradictory effect Effects 0.000 description 2
- 210000005069 ears Anatomy 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000006870 function Effects 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 238000003491 array Methods 0.000 description 1
- 230000002146 bilateral effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
- 238000000638 solvent extraction Methods 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/165—Spectrum analysis; Fourier analysis using filters
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Pure & Applied Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Discrete Mathematics (AREA)
- Measurement And Recording Of Electrical Phenomena And Electrical Characteristics Of The Living Body (AREA)
- Complex Calculations (AREA)
Abstract
The invention provides a method, a system, a medium and a device for calculating a frequency spectrum of a waveform, wherein the method comprises the following steps: inputting a time domain signal of a wave into a filter bank, wherein the filter bank consists of N band-pass filters; the frequency range of the wave is denoted as [ Fst, Fed]N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying: upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N(ii) a Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N(ii) a Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N(ii) a The passband ripple range of the filter is (1-6)]Within the dB range, the stop band attenuation is more than 30 dB; a period for acquiring the center frequency of each filter, calculating a statistical index for the output of each filter with an integral multiple length of half the period as a window length,and splicing the statistical results of the filters into an output frequency spectrum in sequence according to the filter numbers. The invention is used for calculating the frequency spectrum of the wave, and has the advantages that: decoupling time resolution and frequency resolution of the frequency spectrum, dividing frequency points in an equal ratio, and eliminating frequency spectrum leakage.
Description
Technical Field
The present invention relates to the field of processing technology of wave spectrum, and in particular, to a method, system, medium, and apparatus for calculating a wave spectrum.
Background
The discrete fourier transform and STFT implementation algorithms commonly used in the analysis of waves today have the following inherent disadvantages:
the contradiction between time resolution and frequency resolution. The product of time resolution and frequency resolution is a fixed value, of which one must be sacrificed to the other. And the capability of the device is much poorer than that of human ears, so that the application requirement is difficult to meet. Largely from the assumption that the fourier spectrum is invariant over time to the frequency components.
The frequency band rows can be divided only according to equal difference, the number and the interval of the divided frequency bands are completely determined by the length of a sampling window, the frequency points are not consistent with requirements, and the low-frequency points are too sparse to provide information required by application. Meanwhile, the high-frequency points are too dense, so that the calculation power is wasted. Applications such as machine hearing/machine music analysis require more equal-ratio frequency bin partitioning (logarithmic distribution). This problem stems from the fact that the discrete fourier transform is computationally simplified by the orthogonality of the trigonometric function system. The time resolution and frequency resolution of the low frequency band are low.
The problem of energy leakage, energy at frequencies that are not integer multiples of the fundamental frequency, is spread over almost the entire frequency band. Therefore, the linear combination of the time domain is not equal to the linear combination of the frequency domain, and nonlinear aliasing exists between frequency points with quite long frequency distance, thereby bringing great difficulty to subsequent frequency domain analysis.
Therefore, it is desirable to solve the contradiction between the time resolution and the frequency resolution of the spectrum of the wave and the problems of non-compliance and energy leakage caused by the equal-difference frequency division.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a method, a system, a medium and a device for calculating a frequency spectrum of a wave, which are used to solve the problems of the prior art that the time resolution and the frequency resolution of the frequency spectrum of the wave are contradictory, and the isobaric frequency band division causes non-compliance and energy leakage.
To achieve the above and other related objects, the present invention provides a method for calculating a frequency spectrum of a wave, comprising the steps of: inputting a time domain signal of a wave into a filter bank, wherein the filter bank consists of N filters; frequency range [ Fst, Fed ] of the said wave]Where Fst is the frequency rangeA lower bound of the enclosure, Fed being an upper bound of the frequency range, N satisfying N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying: upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N(ii) a Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N(ii) a Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N(ii) a The passband ripple range of the filter is (1-6)]Within the dB range, the stop band attenuation is more than 30 dB; and the period is used for acquiring the center frequency of each filter, the integral multiple length of half of the period is used as the output calculation statistical index of the window length to each filter, and the statistical results of each filter are sequentially spliced into an output frequency spectrum according to the filter number.
In an embodiment of the invention, the method further includes performing a convolution operation on the output spectrum by using an inverse convolution kernel to further eliminate spectrum leakage.
In an embodiment of the present invention, the inverse convolution kernel is obtained based on the following steps: acquiring a frequency response curve of the filter, acquiring frequency responses close to M frequency points on one side of the central frequency of the frequency response curve, and acquiring a number array [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
and inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
In an embodiment of the invention, the filter is an IIR band-pass filter.
To achieve the above object, the present invention also provides a system for calculating a frequency spectrum of a wave, comprising: an input module and an output module; the input module is used for inputting a time domain signal of a wave into a filter bank, and the filter bank consists of N filters; frequency range [ Fst, Fed ] of the said wave]Which isFst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying: upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N(ii) a Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N(ii) a Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N(ii) a The passband ripple range of the filter is (1-6)]Within the dB range, the stop band attenuation is more than 30 dB; the output module is used for acquiring the period of the center frequency of each filter, calculating the statistical index of the output of each filter by taking the integral multiple length of half of the period as the window length, and splicing the statistical results of each filter into an output frequency spectrum in sequence according to the serial numbers of the filters.
In an embodiment of the present invention, the apparatus further includes a convolution module, where the convolution module is configured to perform a convolution operation on the output spectrum by using a deconvolution kernel to further eliminate spectrum leakage.
In an embodiment of the present invention, the inverse convolution kernel is obtained based on the following steps: acquiring a frequency response curve of the filter, acquiring the frequency responses of M adjacent frequency points on one side of the central frequency of the frequency response curve, and acquiring a number array [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
and inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
In an embodiment of the invention, the filter is an IIR band-pass filter.
To achieve the above object, the present invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method of calculating a frequency spectrum of any of the above waves.
To achieve the above object, the present invention also provides a device for calculating a frequency spectrum of a wave, including: a processor and a memory; the memory is used for storing a computer program; the processor is connected with the memory and is used for executing the computer program stored in the memory so as to enable the calculating device of the wave spectrum to execute any one of the calculating methods of the wave spectrum.
As described above, the method, system, medium, and apparatus for calculating a spectrum of a wave according to the present invention have the following advantageous effects: the method is used for decoupling the time resolution and the frequency resolution of the frequency spectrum, dividing frequency points in an equal ratio and eliminating frequency spectrum leakage.
Drawings
FIG. 1a is a flow chart of a method of calculating a spectrum of a wave according to an embodiment of the present invention;
FIG. 1b is a flow chart of a method of calculating a spectrum of a wave according to the present invention in yet another embodiment;
FIG. 1c is a flow chart of a method of calculating a spectrum of a wave according to the present invention in yet another embodiment;
FIG. 2 is a schematic diagram of a computing system for calculating a spectrum of a wave according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a device for calculating a spectrum of a wave according to an embodiment of the present invention.
Description of the element reference numerals
21 input module
22 output module
31 processor
32 memory
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, so that the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, the type, quantity and proportion of the components in actual implementation can be changed freely, and the layout of the components can be more complicated.
The method, the system, the medium and the device for calculating the frequency spectrum of the wave are used for decoupling the time resolution and the frequency resolution of the frequency spectrum, dividing frequency points in an equal ratio and eliminating frequency spectrum leakage.
As shown in fig. 1a, in an embodiment, the method for calculating the spectrum of a wave of the present invention includes the following steps:
and step S11, inputting the time domain signal of the wave into a filter bank, wherein the filter bank consists of N filters.
In particular, the frequency range [ Fst, Fed ] of the waves]The frequency range of the wave is larger than or equal to Fst and smaller than or equal to Fed, wherein Fst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying:
upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N；
Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N；
Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N；
The passband ripple range of the filter is within the range of [ 1-6 ] dB, and the stopband attenuation is greater than 30 dB.
In particular, in order to determine the number of filters of the filter bank, the frequency range [ Fst, Fed ] to be processed is determined by the specific application requirements]The equal ratio is divided into N frequency bands. In order to achieve excellent transition band attenuation characteristics, N should satisfy: n is a radical of>＝log2(Fed/Fst)。I.e. N is greater than or equal to log2(Fed/Fst). N is the number of filters.
Specifically, the calculation of the upper and lower bounds of the pass band frequency of each filter includes numbering from 0 to N-1 for N filters, i belongs to 0 to N-1 for the ith filter, and the ith filter satisfies:
upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N；
Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N；
Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N。
Specifically, parameters of pass band ripple and stop band attenuation of each filter need to be consistent, the pass band ripple range of the filter is in a range of [ 1-6 ] dB, and the stop band attenuation is greater than 30 dB. The passband neighborhood frequency response curves of each filter are the same after being aligned according to the center frequency. The passband neighborhood frequency response curves of each filter are symmetric about the center frequency. More accords with the application requirement and is closer to the auditory rule of human ears. Which makes the latter deconvolution operation easier and thus allows excellent inter-band isolation to be achieved with a relatively low filter order, e.g. 2. A lower filter order can result in better time resolution, fast start-up and shorter ringing.
And step S12, obtaining the period of the center frequency of each filter, calculating the output statistical index of each filter by taking the integral multiple length of half of the period as the window length, and splicing the statistical results of each filter into an output frequency spectrum according to the filter number.
Specifically, a period of the center frequency of each filter is obtained, and a statistical index is calculated for the output of each filter with an integral multiple length of half of the period as a window length, where the statistical index includes but is not limited to: amplitude, standard deviation, root mean square. And obtaining a statistical result based on the statistical index. And splicing the statistical results of the filters into an output frequency spectrum in sequence according to the filter numbers. And splicing the statistical results of the filters into an output frequency spectrum in sequence according to the serial numbers of the filters, namely, taking the integral multiple length of half the period of the central frequency as an x-axis to obtain the frequency spectrum of each corresponding filter, counting the output of each filter by taking the integral multiple length of half the period of the central frequency as a window, taking the counted result as the component of the output frequency spectrum on the frequency point, and splicing the result into the output frequency spectrum in sequence according to the serial numbers of the N filters from 0 to N-1. The statistics may be classical statistics such as RMS, meanabs, peak, or a combination of more than one, depending on the particular application. The calculation method of the classical statistic is not described herein. The period of the center frequency refers to a period corresponding to the center frequency, and the reciprocal of the center frequency is the period.
Specifically, the method further comprises the step of performing convolution operation on the output spectrum by utilizing an inverse convolution core so as to further eliminate spectrum leakage. And the frequency spectrum leakage is further eliminated by applying an inverse convolution kernel, and the isolation between bands is improved. If the target application is sensitive to performance and not sensitive to the inter-band separation index, this part may be skipped, step S12 is directly used to obtain the period of the center frequency of each filter, and the length of the integral multiple of half of the period is used as the window length to calculate the statistical index for the output of each filter, and different statistical indexes include but are not limited to: amplitude, standard deviation, root mean square, etc. And counting the results of the filters. And splicing the statistical results of the filters into an output frequency spectrum in sequence according to the filter numbers.
Specifically, the inverse convolution kernel is obtained based on the following steps:
obtaining a frequency response curve of the filter, taking a horizontal axis of the frequency response curve as a frequency difference, obtaining the frequency response of M adjacent frequency points on one side of the central frequency of the frequency response curve, and obtaining a number sequence [ M ] based on the frequency response1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix A is arranged, the N center frequencies are divided in an equal ratio mode, and the special (equal ratio) division mode ensures that the frequency response curves of all the filters are the same and are symmetrical left and right. And conditions are created for using the same convolution kernel to resist aliasing. The frequency response of M frequency points adjacent to the single side of the central frequency is recorded as M1,m2,...,mM]. As followsAnd (4) acquiring frequency response of the frequency points as shown in the table. The larger M is, the higher the accuracy is, but the larger the calculation amount is, the more the application is focused on.
And inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
Specifically, a frequency response curve is calculated based on the determined digital filter coefficients. The frequency response corresponding to the center frequency of each m filters adjacent to each other at one side (symmetry or bilateral average) is recorded as a sequence [ m ] from near to far1,m2,m3,...,mM-1,mM]. The larger M is, the higher the accuracy is, but the larger the calculation amount is, the more the application is focused on. The angularly symmetric matrix a is rearranged with the elements in this series, for example when M is 3:
and taking the integral multiple length of half of the central frequency period of each filter as a window to obtain an output spectrum. And performing convolution operation on the output frequency spectrum by utilizing a deconvolution core to further eliminate frequency spectrum leakage, wherein the output obtained after the convolution operation is the final output, and if various statistics are analyzed simultaneously, various statistics are calculated respectively.
The method has the following characteristics, relative to discrete fourier transform, and has significant advantages in many wave analysis applications, represented by machine hearing.
The frequency point quantity and distribution are completely decoupled from the length of the sampling window. The two contradictory targets of the short sampling window and the high frequency point density in the discrete Fourier transform can be simultaneously achieved. The advantage is more remarkable when a low-frequency fast-rhythm signal is analyzed.
The frequency points may be configured in a logarithmic distribution. The high frequency part can be provided with a broadband, and the low frequency part is provided with a narrow band, so that the calculation resources are distributed to meet the requirements better.
The problem of frequency spectrum leakage is effectively solved. A band isolation of better than 60 db attenuation per 34% frequency deviation can be achieved (see data curve for details). Most of the energy (above 99%) is concentrated in the frequency bin with a radius of 0.7%. Providing a plurality of convenience and possibility for subsequent analysis.
Specifically, a time domain signal of a wave is input into a 2-order elliptic band-pass filter bank, wherein the 2-order elliptic band-pass filter bank consists of 384 filters;
the frequency range of the wave is [65.41 Hz-16744.04 Hz), wherein 65.41Hz is the lower boundary of the frequency range, 16744.04Hz is the upper boundary of the frequency range, 384 meets 384>＝log2(16744.04/65.41) numbered from 0 to 383 for the 384 filters, for an ith filter, i belongs to 0 to 383, the ith filter satisfying:
upper bound fh (i) ═ 65.41 (16744.04/65.41)(i+1)/384；
Center frequency fc (i) ═ 65.41 (16744.04/65.41)(i+0.5)/384；
Lower bound of passband fl (i) 65.41 (16744.04/65.41)i/384；
The passband ripple of the filter is 3dB, and the stopband attenuation is 80 dB; the pass band width is 50 minutes.
Batch designed digital filter coefficients: (wherein// the text behind is a comment)
//radius:2.500000e-01,db:3
3f21adacaef45127,bffffe8a196adeb0,3feffdca4a6a2174,3f21ef7e3494e5a0,bffffe83516773e0,3feffdc210396d65,3f223244bde48403,bffffe7c66119782,3feffdb9b768436d,3f227603dab7c277,bffffe75569a3bec,3feffdb13f84a90a,//15
3f22babf2822b64c,bffffe6e222d1a14,3feffda8a81afba9,3f23007a50aa2b8e,bffffe66c7f08d9e,3feffd9ff0b5eab7,3f2347390c759524,bffffe5f47056fcc,3feffd9718de714f,3f238eff2181b4c1,bffffe579e86f158,3feffd8e201bcfc9,//16
3f23d7d063d3fc3b,bffffe4fcd8a7366,3feffd8505f38581,3f2421b0b5aeb0d2,bffffe47d31f5f30,3feffd7bc9e94a29,3f246ca407c5ce70,bffffe3fae4efcb1,3feffd726b7f0744,3f24b8ae5974acfd,bffffe375e1c4815,3feffd68ea34d169,//17
3f2505d3b8f470bb,bffffe2ee183c5f8,3feffd5f4588e16d,3f25541843933edd,bffffe26377b567a,3feffd557cf78d95,3f25a38025ec426f,bffffe1d5ef206f4,3feffd4b8ffb4276,3f25f40f9c2081e4,bffffe1456cfe278,3feffd417e0c7bec,//18
3f2645caf2108254,bffffe0b1df5c0f3,3feffd3746a1bdf0,3f2698b68396c362,bffffe01b33d14e2,3feffd2ce92f8d29,3f26ecd6bcc313d7,bffffdf81577b7b0,3feffd226528679e,3f2742301a16c249,bffffdee436fb496,3feffd17b9fcbd2b,//19
3f2798c728c1aa15,bffffde43be711ee,3feffd0ce71ae7c9,3f27f0a086e023c5,bffffdd9fd979920,3feffd01ebef23fc,3f2849c0e3b9ddf1,bffffdcf87329cc3,3feffcf6c7e388c5,3f28a42d000198ae,bffffdc4d760bd51,3feffceb7a5fffce,//20
3f28ffe9ae15d0d7,bffffdb9ecc1ac08,3feffce002ca3d45,3f295cfbd2425b56,bffffdaec5ebec2a,3feffcd46085b7b5,3f29bb686302f0c0,bffffda3616c925e,3feffcc892f39f9d,3f2a1b346946b0d8,bffffd97bdc7025a,3feffcbc9972d72a,//21
3f2a7c6500b49ed7,bffffd8bd974aa84,3feffcb0735fe96c,3f2adeff57f11ae4,bffffd7fb2e4bdd4,3feffca4201501df,3f2b4308b0e45ef8,bffffd73487beb8a,3feffc979ee9e374,3f2ba8866101ff2b,bffffd6698941502,3feffc8aef33dfc3,//22
3f2c0f7dd1916f6d,bffffd59a17c0140,3feffc7e1045cdd1,3f2c77f47ff79a69,bffffd4c61770e80,3feffc710170010d,3f2ce1effe01869e,bffffd3ed6bce164,3feffc63c2003fd2,3f2d4d75f2300d74,bffffd30ff7911ea,3feffc565141b9fe,//23
3f2dba8c1804adc8,bffffd22d9cad60c,3feffc48ae7cff6c,3f2e2938404f7778,bffffd1463c4a9db,3feffc3ad8f7f611,3f2e9980517e18d0,bffffd059b6bf538,3feffc2ccff5d043,3f2f0b6a47ec116c,bffffcf67eb8aed6,3feffc1e92b7027e,//24
3f2f7efc3634070c,bffffce70b94fccd,3feffc1020793981,3f2ff43c45825035,bffffcd73fdcd234,3feffc0178774fb7,3f3035985af4552c,bffffcc7195d8a24,3feffbf299e942ea,3f3071efef599147,bffffcb695d57fc0,3feffbe38404299b,//25
3f30af28175f20f6,bffffca5b2f3a348,3feffbd435fa2837,3f30ed4416673628,bffffc946e570c29,3feffbc4aefa6633,3f312c473bf4445b,bffffc82c58e87e2,3feffbb4ee3102ef,3f316c34e3d5f97a,bffffc70b61825b5,3feffba4f2c70a81,//26
3f31ad107656d8d4,bffffc5e3d60bf04,3feffb94bbe26a4c,3f31eedd686a8174,bffffc4b58c37c3c,3feffb8448a5e560,3f32319f3bdc9ff5,bffffc3805895652,3feffb73983108d7,3f3275597f808b01,bffffc2440e8948c,3feffb62a9a01fdc,//27
3f32ba0fcf619001,bffffc100804469c,3feffb517c0c279b,3f32ffc5d4f3f4f8,bffffbfb57ebbaea,3feffb400e8ac305,3f33467f4746ab80,bffffbe62d99f0e2,3feffb2e602e2e53,3f338e3feb35bc8a,bffffbd085f50752,3feffb1c7005328f,//28
3f33d70b939d6fce,bffffbba5dcda675,3feffb0a3d1b18a6,3f3420e6218e2c7f,bffffba3b1de65ce,3feffaf7c6779c74,3f346bd384811b95,bffffb8c7ecb2da2,3feffae50b1edfb6,3f34b7d7ba8d8c82,bffffb74c12093cf,3feffad20a115c9f,//29
3f3504f6d09f1e0b,bffffb5c755333fe,3feffabec24bd837,3f355334e2acac20,bffffb4397bf0324,3feffaab32c754d7,3f35a2961bf00e5a,bffffb2a24a69de0,3feffa975a7903fc,3f35f31eb71e9e90,bffffb10183291f6,3feffa833852385a,//30
3f3644d2fea28f7f,bffffaf56e70a262,3feffa6ecb40575c,3f3697b74cd51bdf,bffffada23530630,3feffa5a122ccab8,3f36ebd00c3985db,bffffabe32afa1ac,3feffa450bfcf1a0,3f374121b7b8f3c6,bffffaa1983f39ea,3feffa2fb79211c5,//31
3f3797b0dadf2720,bffffa844f9ca27a,3feffa1a13c94835,3f37ef82121813ea,bffffa665443e50a,3feffa041f7b79fc,3f38489a0aee5abc,bffffa47a19162cc,3feff9edd97d446a,3f38a2fd844aa8a3,bffffa2832c0ef8c,3feff9d7409eed54,//32
3f38feb14eb40009,bffffa0802ece628,3feff9c053ac52fe,3f395bba4c90ede4,bffff9e70d0d3643,3feff9a9116cdbc4,3f39ba1d7269b07a,bffff9c54bf66b0a,3feff99178a36594,3f3a19dfc72b4ed5,bffff9a2ba58aad2,3feff979880e352d,//33
3f3a7b06646ba73c,bffff97f52beaf52,3feff9613e66e518,3f3add9676ae7b7e,bffff95b0f8cb64f,3feff9489a625462,3f3b41953dab7653,bffff935eaff6a7e,3feff92f9ab09523,3f3ba7080c953350,bffff90fdf2ac45a,3feff9163dfcdab2,//34
3f3c0df44a614f4e,bffff8e8e5f8e2c6,3feff8fc82ed67ac,3f3c765f72117ce2,bffff8c0f928db21,3feff8e268237ba4,3f3ce04f12fda5c5,bffff898124d80aa,3feff8c7ec3b4098,3f3d4bc8d11f21a9,bffff86e2acc22ec,3feff8ad0dcbb838,//35
3f3db8d2655cfaaa,bffff8433bdb42e0,3feff891cb66a8c5,3f3e27719dd94a7a,bffff8173e813e88,3feff876239889ae,3f3e97ac5e3fb9fd,bffff7ea2b92f2d8,3feff85a14e87010,3f3f0988a0151aa6,bffff7bbfbb25374,3feff83d9dd7fab9,//36
3f3f7d0c730821c7,bffff78ca74cf81c,3feff820bce33df9,3f3ff23dfd43538f,bffff75c269a9f6e,3feff8037080af28,3f403491bde00b0f,bffff72a719ba6be,3feff7e5b7210ff7,3f4070e1a14d78f8,bffff6f78017768b,3feff7c78f2f5943,//37
3f40ae11deb487eb,bffff6c3499ae36a,3feff7a8f710a5bd,3f40ec25b7c77306,bffff68dc5768302,3feff789ed241c49,3f412b207a4c13e3,bffff656eabcf4b4,3feff76a6fc2d9f7,3f416b0580487dd9,bffff61eb0411da7,3feff74a7d3fdbbe,//38
3f41abd830303714,bffff5e50c9457d2,3feff72a13e7e7e5,3f41ed9bfd121a45,bffff5a9f6049394,3feff709320176f2,3f42305466c6e2c3,bffff56d629a6ba8,3feff6e7d5cc9c90,3f427404fa205dc2,bffff52f48172ace,3feff6c5fd82efd3,//39
3f42b8b151194a36,bffff4ef9bf2c2fa,3feff6a3a757735c,3f42fe5d1305eaac,bffff4ae5359b57a,3feff680d1767d0d,3f43450bf4c5443e,bffff46b632aebac,3feff65d7a059d5b,3f438cc1b8f313d0,bffff426bff57fea,3feff6399f238675,//40
3f43d582301a7a13,bffff3e05df67604,3feff6153ee7f2c4,3f441f5138e95f38,bffff3983116630a,3feff5f057638b52,3f446a32c064939d,bffff34e2ce703c6,3feff5cae69fcdb3,3f44b62ac21caddf,bffff30244a0c174,3feff5a4ea9ef1a9,//41
3f45033d4863aae8,bffff2b46b20241e,3feff57e615bce2c,3f45516e6c834f03,bffff26492e33246,3feff55748c9be59,3f45a0c256f451fc,bffff212ae06bd24,3feff52f9ed485d5,3f45f13d3f965032,bffff1beae439902,3feff507616034d9,//42
3f4642e36de8871c,bffff16884ebc112,3feff4de8e490bbc,3f4695b93943662e,bffff11022e7664e,3feff4b523635e4d,3f46e9c30912ea23,bffff0b578b1e88a,3feff48b1e7b7688,3f473f055511d281,bffff0587656b95b,3feff4607d557719,//43
3f479584a585ac0b,bfffeff90b6e27ed,3feff4353dad3d29,3f47ed45937bb489,bfffef97271a1570,3feff4095d364226,3f48464cc9069f31,bfffef32b802910d,3feff3dcd99b7cb0,3f48a09f017d3851,bfffeecbac525b0f,3feff3afb07f4164,//44
3f48fc4109b9eab7,bfffee61f1b34e46,3feff381df7b230b,3f495937c05b2e79,bfffedf5754aaf0c,3feff353641fd268,3f49b7881604e241,bfffed8623b55f1b,3feff3243bf4fd8d,3f4a17370da28e83,bfffed13e903f572,3feff2f464792eb6,//45
3f4a7849bcaa9b7d,bfffec9eb0b6b982,3feff2c3db21aab6,3f4adac54b627d08,bfffec2665b980b0,3feff2929d5a4ec4,3f4b3eaef523d1c9,bfffebaaf25f6d9f,3feff260a8856e17,3f4ba40c08a27d7d,bfffeb2c405e9008,3feff22df9fbaec3,//46
3f4c0ae1e833c5d9,bfffeaaa38cb646e,3feff1fa8f0be61d,3f4c73360a166c3a,bfffea24c41432d3,3feff1c664faf4ca,3f4cdd0df8bbcbbf,bfffe99bc9fc4b46,3feff1917903a219,3f4d486f531206a3,bfffe90f31971f8c,3feff15bc85676fb,//47
3f4db55fcccf382d,bfffe87ee14338b6,3feff12550199864,3f4e23e52ebdbb7b,bfffe7eabea507ba,3feff0ee0d68a122,3f4e9405570983f3,bfffe752aea19001,3feff0b5fd547b41,3f4f05c6398e8e15,bfffe6b69558eab8,3feff07d1ce338ba,//48
3f4f792de0286e97,bfffe6165620a1fa,3feff043690febc9,3f4fee426b02f4c9,bfffe571d37de275,3feff008deca7e86,3f5032850876010c,bfffe4c8ef1f828e,3fefefcd7af789fe,3f506ec58fd33eda,bfffe41b89d7ddae,3fefef913a702cc0,//49
3f50abe5fe1f36b9,bfffe36983968290,3fefef541a01e0c5,3f50e9e991af26ab,bfffe2b2bb61b342,3fefef16166e50d7,3f5128d394d2c996,bfffe1f70f4fb57b,3fefeed72c6b2d36,3f5168a75e002f0b,bfffe1365c7ff212,3fefee9758a1ffd3,//50
3f51a96850003bc3,bfffe0707f13e20d,3fefee5697afffc5,3f51eb19da1bc431,bfffdfa55227c7fe,3fefee14e625e43f,3f522dbf784943b8,bfffded4afcb3414,3fefedd24087b6bb,3f52715cb35b44a2,bfffddfe70f95196,3fefed8ea34ca4bd,//51
3f52b5f5212f65fa,bfffdd226d90fbf2,3fefed4a0aded098,3f52fb8c64de0938,bfffdc407c4c9a30,3fefed04739b21f7,3f5342262eeab14f,bfffdb5872b9beb9,3fefecbdd9d1154d,3f5389c63d750bca,bfffda6a25308a2e,3fefec7639c28aef,//52
3f53d2705c6aa56f,bfffd97566cacf5c,3fefec2d8fa3955d,3f541c2865b9596e,bfffd87a095af680,3fefebe3d79a46a4,3f5466f24182700d,bfffd777dd629e6c,3fefeb990dbe7d8f,3f54b2d1e64e6f7f,bfffd66eb208f926,3fefeb4d2e19b190,//53
3f54ffcb5941b145,bfffd55e5510e298,3fefeb0034a6be4f,3f554de2ae51ab36,bfffd44692ceaf16,3fefeab21d51ae56,3f559d1c087af4e0,bfffd327361dafd3,3fefea62e3f7850b,3f55ed7b99f816ca,bfffd20008556b34,3fefea12846607e7,//54
3f563f05a47915ea,bfffd0d0d13e86e6,3fefe9c0fa5b86e7,3f5691be795bc330,bfffcf9957076186,3fefe96e4186a43d,3f56e5aa79e4db86,bfffce595e3859aa,3fefe91a55861b23,3f573ace1779eeaf,bfffcd10a9a7c010,3fefe8c531e88610,//55
3f57912dd3dc0f69,bfffcbbefa6d7280,3fefe86ed22c23f6,3f57e8ce41635cbc,bfffca640fd61d08,3fefe81731be9ca4,3f5841b4033b5b49,bfffc8ffa7561f48,3fefe7be4bfcc4a7,3f589be3cda01e7a,bfffc7917c7c12ec,3fefe7641c325fe2,//56
3f58f762661c547c,bfffc61948e2f120,3fefe7089d99e3a9,3f595434a3c82bcf,bfffc496c423d41d,3fefe6abcb5c37d2,3f59b25f6f890d00,bfffc309a3c7522a,3fefe64da09076f5,3f5a11e7c45244fe,bfffc1719b366f42,3fefe5ee183badbb,//57
3f5a72d2af668d54,bfffbfce5bab22a4,3fefe58d2d509972,3f5ad525509a73f5,bfffbe1f94206d2c,3fefe52adaaf658e,3f5b38e4da97bd0a,bfffbc64f141fd9c,3fefe4c71b256843,3f5b9e169321a868,bfffba9e1d5b5fca,3fefe461e96cde5a,//58
3f5c04bfd35a23d4,bfffb8cac046b366,3fefe3fb402ca5de,3f5c6ce60807fc75,bfffb6ea7f5ae758,3fefe39319f7f805,3f5cd68eb1de008d,bfffb4fcfd597634,3fefe329714e21fe,3f5d41bf65c3162c,bfffb301da5ba09a,3fefe2be409a3ceb,//59
3f5dae7dcd1b599a,bfffb0f8b3bf21d6,3fefe2518232e4a8,3f5e1ccfa61236e6,bfffaee124125b71,3fefe1e33059edca,3f5e8cbac3e58302,bfffacbac2fff3f0,3fefe173453c1a7c,3f5efe450f31a3bc,bfffaa852539e51b,3fefe101baf0ce5a,//60
3f5f7174863ebf1d,bfffa83fdc63f606,3fefe08e8b79c142,3f5fe64f3d4ef095,bfffa5ea76fd9cf4,3fefe019b0c2b10e,3f602e6daf76cf8b,bfffa384804b4544,3fefdfa324a11264,3f606a8f961feef4,bfffa10d803ef515,3fefdf2ae0d3c020,//61
3f60a7907eaaeee1,bfff9e84fb604ef0,3fefdeb0df02aa23,3f60e573a0bec653,bfff9bea72b3eaba,3fefde3518be8275,3f61243c3fcb24a8,bfff993d63a2021c,3fefddb7878069b9,3f6163edab32d88d,bfff967d47dc6bb2,3fefdd3824a99a4d,//62
3f61a48b3e76d446,bfff93a99543e0a0,3fefdcb6e9831257,3f61e6186161c19b,bfff90c1bdcc87e1,3fefdc33cf3d3c7f,3f6228988834265e,bfff8dc52f61c2d1,3fefdbaeceef97b4,3f626c0f33d12ed1,bfff8ab353c93606,3fefdb27e1985da0,//63
3f62b07ff1ec09bc,bfff878b908509b0,3fefda9f001c27eb,3f62f5ee5d35df99,bfff844d46b55c86,3fefda1423459441,3f633c5e1d8c7000,bfff80f7d2f8e444,3fefd98743c4e721,3f6383d2e82949b2,bfff7d8a8d4cb686,3fefd8f85a2fad6c,//64
3f63cc507fd1a441,bfff7a04c8eb34e4,3fefd8675f005cb8,3f6415dab506e329,bfff7665d42a16cf,3fefd7d44a95f239,3f6460756637bafe,bfff72acf8578c08,3fefd73f15339087,3f64ac247ff1fd33,bfff6ed979967202,3fefd6a7b7001c05,//65
3f64f8ebfd151623,bfff6aea96b996a0,3fefd60e2805d5d2,3f6546cfe7052fcb,bfff66df891e02d5,3fefd5726031f5a0,3f6595d455df029e,bfff62b784844726,3fefd4d4575441fc,3f65e5fd70ac5f73,bfff5e71b6e8c462,3fefd434051ea745,//66
3f66374f6d99645b,bfff5a0d485aeaa2,3fefd3916124cd36,3f6689ce922a640a,bfff55895ad368a5,3fefd2ec62dbab38,3f66dd7f33728dec,bfff50e50a094540,3fefd24501991ae2,3f673265b64b4958,bfff4c1f6b45dd18,3fefd19b3493696f,//67
3f6788868f8c46d2,bfff47378d37be2e,3fefd0eef2e0e770,3f67dfe644445977,bfff422c77c45b3a,3fefd0403377774d,3f68388969f30b23,bfff3cfd2bd89040,3fefcf8eed2c19e9,3f689274a6c2eb35,bfff37a8a337f264,3fefcedb16b27a2b,//68
3f68edacb1c4ae47,bfff322dd04ae438,3fefce24a69c76a2,3f694a36532b0ef6,bfff2c8b9deb6864,3fefcd6b9359a9e0,3f69a81664876de8,bfff26c0ef30ac08,3fefccafd336f124,3f6a0751d1074cd9,bfff20cc9f394266,3fefcbf15c5df165,//69
3f6a67ed95b28ddd,bfff1aad80f40b72,3fefcb3024d49ae7,3f6ac9eec1aa7be3,bfff14625ee7be9c,3fefca6c227cab05,3f6b2d5a7669b49b,bfff0de9faf9139a,3fefc9a54b132c95,3f6b9235e804db83,bfff07430e2f8270,3fefc8db942ff64b,//70
3f6bf8865d6c20ce,bfff006c48789494,3fefc80ef34527be,3f6c605130adabe0,bffef9645069c0af,3fefc73f5d9ea4ab,3f6cc99bcf38da52,bffef229c300ca90,3fefc66cc8618e4c,3f6d346bba2258ed,bffeeabb3362a15e,3fefc597288bbb50,//71
3f6da0c686692611,bffee3172a98b590,3fefc4be72f32db4,3f6e0eb1dd3c7107,bffedb3c274cc0ec,3fefc3e29c45871c,3f6e7e337c425a30,bffed3289d82fa8c,3fefc30399077b4e,3f6eef5135dfa41e,bffecadaf652b113,3fefc2215d9440b7,//72
3f6f6210f1804929,bffec2518f9d45d1,3fefc13bde1cff6d,3f6fd678abe0f66c,bffeb98abbc38322,3fefc0530ea83e13,3f7026473bacc2a5,bffeb084c1594919,3fefbf66e3114cf5,3f70622c3e142d92,bffea73ddad78ba2,3fefbe774f07af47,//73
3f709eee7c5f5c49,bffe9db4364c9d6c,3fefbd84460e828e,3f70dc9121070656,bffe93e5f50ac356,3fefbc8dbb7be3e8,3f711b1761eb1c54,bffe89d12b550c96,3fefbb93a278538c,3f715a84807a63a6,bffe7f73e00a6c10,3fefba95edfe1670,//74
3f719adbc9da9a43,bffe74cc0c4f0f8d,3fefb99490d89598,3f71dc20971114e2,bffe69d79b33f296,3fefb88f7da3bbac,3f721e564d2bd9d0,bffe5e94695caaa2,3fefb786a6cb5098,3f7261805d6b4ad4,bffe530044a36b02,3fefb679fe8a52d3,//75
3f72a5a2456c48f2,bffe4718ebbb3fd8,3fefb56976ea4edc,3f72eabf8f52de6d,bffe3adc0dd07fb6,3fefb45501c2b485,3f7330dbd1f574e5,bffe2e474a27746c,3fefb33c90b82a2c,3f7377fab1088f1e,bffe21582fb93c54,3fefb220153bddc5,//76
3f73c01fdd4b08fc,bffe140c3ccee648,3fefb0ff808ad3de,3f74094f14b2e98a,bffe0660de9acb3c,3fefafdac3ad3458,3f74538c229abba2,bffdf85370d029b2,3fefaeb1cf759512,3f749edadfef6f15,bffde9e13d390810,3fefad8494804244,//77
3f74eb3f335ed41a,bffddb077b4a643e,3fefac53033284af,3f7538bd11869c1c,bffdcbc34fb6b81c,3fefab1d0bb9e58e,3f7587587d23ea66,bffdbc11cbfedbbe,3fefa9e29e0b7056,3f75d71587438107,bffdabefee014fb8,3fefa8a3a9e2f1fb,//78
3f7627f84f7277d4,bffd9b5a9f87fb8e,3fefa7601ec2361e,3f767a0503ef861c,bffd8a4eb5d46dcc,3fefa617ebf041e8,3f76cd3fe1dcec78,bffd78c8f12aad04,3fefa4cb00788c4f,3f7721ad3572ee58,bffd66c5fc5aab48,3fefa3794b2a3447,//79
3f7777515a32e039,bffd54426c486f3a,3fefa222ba973482,3f77ce30bb1ad84d,bffd413abf73083b,3fefa0c73d13949d,3f78264fd2d9f624,bffd2dab5d7a65be,3fef9f66c0b4982c,3f787fb32c053f65,bffd199096a42be1,3fef9e01334feb02,//80
3f78da5f614d2400,bffd04e6a35fa288,3fef9c96827acb71,3f7936591db39f14,bffcefa9a3c8de8b,3fef9b269b893183,3f7993a51cc2ea5e,bffcd9d59f2b4834,3fef99b16b8cf456,3f79f2482ac4e49b,bffcc3668383a4b8,3fef9836df54ec70,//81
3f7a524724fb101f,bffcac582501cc7c,3fef96b6e36c13c0,3f7ab3a6f9d72e4c,bffc94a63d8a3b44,3fef95316418a34a,3f7b166ca9348dbf,bffc7c4c6c37ab0a,3fef93a64d5b2dc9,3f7b7a9d4491f35a,bffc634634dcef10,3fef92158aedb832,//82
3f7be03def4c2751,bffc498eff874856,3fef907f0842cf60,3f7c4753ded93262,bffc2f22180171be,3fef8ee2b0849b3a,3f7cafe45b043f77,bffc13faad57a6da,3fef8d406e93ef05,3f7d19f4be2a2069,bffbf813d15cede3,3fef8b982d07577d,//83
3f7d858a757686da,bffbdb687831f256,3fef89e9d62a25e3,3f7df2ab0121e39f,bffbbdf377cdc41c,3fef883553fb7873,3f7e615bf4afeea3,bffb9faf8788d50c,3fef867a902d4044,3f7ed1a2f72ee570,bffb80973faa9532,3fef84b97423446a,//84
3f7f4385c3777017,bffb60a518fa1534,3fef82f1e8f22242,3f7fb70a286d3135,bffb3fd36c521da4,3fef8123d75e4b3d,3f80161b04a00ae5,bffb1e1c72393182,3fef7f4f27daffaa,3f805187aed723b5,bffafb7a427dface,3fef7d73c28946e5,//85
3f808dce192366fa,bffad7e6d3d8a852,3fef7b918f36e4c6,3f80caf1545678d4,bffab35bfb91cd09,3fef79a8755d4c38,3f8108f47bee235c,bffa8dd36d2f5b37,3fef77b85c208ee4,3f8147dab636b28a,bffa6746ba285f78,3fef75c12a4e4a6c,//86
3f8187a7346db337,bffa3faf51a02a40,3fef73c2c65c926a,3f81c85d32e50705,bffa17068029a24e,3fef71bd1668d7c3,3f8209fff9264e38,bff9ed456f9385e0,3fef6fb00036cd8f,3f824c92da16b864,bff9c26526be6c92,3fef6d9b692f4a3e,//87
3f829019341b26f0,bff9965e897d6a18,3fef6b7f365f26c6,3f82d496713caae1,bff9692a58823e6c,3fef695b4c761aa8,3f831a0e074d64aa,bff93ac131560f20,3fef672f8fc594d8,3f836083780dbb20,bff90b1b8e5fb4d0,3fef64fbe43f9224,//88
3f83a7fa5151eb78,bff8da31c6f8b708,3fef62c02d7570a4,3f83f0762d27fcaf,bff8a7fc0f9221ea,3fef607c4e96c01a,3f8439fab1fe0a5a,bff8747279ea7252,3fef5e302a700fac,3f84848b92c8e78c,bff83f8cf555e74c,3fef5bdba369b8c4,//89
3f84d02c8f2b27ae,bff809434f1a9a98,3fef597e9b86a6c0,3f851ce1739c7c60,bff7d18d32e1d675,3fef5718f4631c1c,3f856aae19916c7b,bff798622b403305,3fef54aa8f33749c,3f85b99667a370dd,bff75db9a2561bab,3fef52334cc2e479,//90
3f86099e51b96632,bff7218ae28a7384,3fef4fb30d7234cc,3f865ac9d93056f5,bff6e3cd17612750,3fef4d29b1367d47,3f86ad1d0d04a9ce,bff6a4774e6f93cd,3fef4a971797dab6,3f87009c09fba70c,bff663807870c0fc,3fef47fb1fb022c6,//91
3f87554afacd5390,bff620df6a7b8d8a,3fef4555a8299564,3f87ab2e184eaf26,bff5dc8adf5d0016,3fef42a68f3d8a8a,3f880249a99c4a8a,bff59679791911d4,3fef3fedb2b31dad,3f885aa204452fac,bff54ea1c294625d,3fef3d2aefddd685,//92
3f88b43b8c762db7,bff504fa3169634a,3fef3a5e239c4e91,3f890f1ab5257bfa,bff4b97927eba9b4,3fef37872a56d420,3f896b44003eaa7d,bff46c14f75c3410,3fef34a5dffe0aaa,3f89c8bbfecef93d,bff41cc3e251937c,3fef31ba20098834,//93
3f8a27875131ffd0,bff3cb7c1f570aee,3fef2ec3c5767000,3f8a87aaa73ea3aa,bff37833dbc5d88f,3fef2bc2aac60ae4,3f8ae92ac07472d4,bff322e13edc0209,3fef28b6a9fc5c6e,3f8b4c0c6c294a98,bff2cb7a6d142126,3fef259f9c9eb5ac,//94
3f8bb05489b74e48,bff271f58bc1d32c,3fef227d5bb2458e,3f8c160808ab3a01,bff21648c4f6933e,3fef1f4fbfbaa62d,3f8c7d2be8f3040d,bff1b86a4bb2eec2,3fef1c16a0b867e2,3f8ce5c53b0cc996,bff1585060682917,3fef18d1d62799b4,//95
3f8d4fd92036135a,bff0f5f155ce8b38,3fef158136fe4f64,3f8dbb6cca9b6276,bff091439614c2e0,3fef122499ab24eb,3f8e28857d8810cc,bff02a3da86cdba2,3fef0ebbd413bf77,3f8e97288d96762a,bfef81ac6df70713,3fef0b46bb934c4d,//96
3f8f075b60e0560d,bfeeaa082a5ce4fa,3fef07c524f8fd50,3f8f79236f2fa9a2,bfedcd7c8cfde2ee,3fef0436e48682b7,3f8fec86422f9899,bfecebf80b4b4694,3fef009bcdee833c,3f9030c4bacedece,bfec05699889a604,3feefcf3b4531212,//97
3f906c195bbde1c0,bfeb19c0b61d5c06,3feef93e6a4421e2,3f90a843e42093cc,bfea28ed84d9dec0,3feef57bc1bdf6c3,3f90e5473d86a35e,bfe932e0d75f3bd5,3feef1ab8c2795cd,3f9123265aecde2d,bfe8378c45913263,3feeedcd9a51321e,//98
3f9161e438d66eae,bfe736e241338f9e,3feee9e1bc729914,3f91a183dd663d71,bfe630d62bb79592,3feee5e7c2299c27,3f91e208587878d3,bfe5255c6d4650fe,3feee1df7a787870,3f922374c3bc2507,bfe4146a8d13d2c2,3feeddc8b3c43db0,//99
3f9265cc42cccec0,bfe2fdf74b074384,3feed9a33bd33314,3f92a912034c5ebf,bfe1e1fabac3c154,3feed56edfcb3a13,3f92ed493cfcf291,bfe0c06e601ddb33,3feed12b6c3030d9,3f93327531dad62d,bfdf329a9a12a60c,3feeccd8ace2529d,//100
3f9378992e3695db,bfdcd9288215218d,3feec8766d1c96a2,3f93bfb888cf1561,bfda7483946db63c,3feec40477730eab,3f9407d6a2ebc08b,bfd804accf9bf83f,3feebf8295d143f7,3f9450f6e876d09d,bfd589a95ceedfac,3feebaf0917892f9,//101
3f949b1cd01793fd,bfd30382dc5927bd,3feeb64e32fe86be,3f94e64bdb4cc627,bfd07247b3b10a21,3feeb19b424b339d,3f9532879686fcd7,bfcbac16c2d5b522,3feeacd786979031,3f957fd399430c98,bfc65dcda5b7b834,3feea802c66bcf37,//102
3f95ce3386247be0,bfc0f9f17c20473e,3feea31cc79db841,3f961dab0b100599,bfb70197fcee04bc,3fee9e254f4effaa,3f966e3de1460a28,bfa7cacfce50c730,3fee991c21eb9f5b,3f96bfefcd7d0e05,bf64037e88cd4980,3fee940103282f20,//103
3f9712c49ffc3cd9,3fa59aca9b0166b0,3fee8ed3b6003c34,3f9766c034b5d6a6,3fb662164f85b6e4,3fee8993fcb4a298,3f97bbe67361a494,3fc10e686280dcf2,3fee844198c9e5b4,3f98123b4f976a91,3fc6fe25ebc5b26e,3fee7edc4b068957,//104
3f9869c2c8e93c2e,3fccff8d271416f0,3fee7963d3716c40,3f98c280eafdd2a5,3fd188ea29dd7773,3fee73d7f15022d6,3f991c79cdaad5ea,3fd49a0ec9e428dd,3fee6e38632552a0,3f9977b1950f0601,3fd7b2baf69f597c,3fee6884e6af0fa0,//105
3f99d42c71ac574d,3fdad26a2301acb5,3fee62bd38e53a88,3f9a31eea082004b,3fddf88c2d894711,3fee5ce115f7dff9,3f9a90fc6b265ba7,3fe092426ce743dc,3fee56f0394d9a46,3f9af15a27e0b4b3,3fe22ad5a432e524,3fee50ea5d81f4b4,//106
3f9b530c39c2ff1e,3fe3c5a4b6c02036,3fee4acf3c63d00e,3f9bb61710c35664,3fe5624dc3636901,3fee449e8ef3ca97,3f9c1a7f29d562a0,3fe70067c87cfc52,3fee3e580d62a9d6,3f9c80490f039ce9,3fe89f825ef96af7,3fee37fb6f0fc636,//107
3f9ce77957885225,3fea3f2575da3241,3fee31886a877ade,3f9d5014a7e680e4,3febded10ea7cd56,3fee2afeb58197f7,3f9dba1fb2028e20,3fed7dfcfb3958da,3fee245e04dfd71d,3f9e259f353aadfb,3fef1c189d4950fd,3fee1da60cac551f,//108
3f9e9297fe7f1a52,3ff05c45542d8b08,3fee16d680180e58,3f9f010ee86a1a34,3ff129587340e6f1,3fee0fef11795e5e,3f9f7108db57b0ab,3ff1f4f000537296,3fee08ef724a84f8,3f9fe28acd7d0991,3ff2beb1a57e7291,3fee01d753282f64,//109
3fa02acce17fda3e,3ff3863e4b2d405d,3fedfaa663d004b6,3fa0651d67063943,3ff44b3203a4d9c6,3fedf35c531f38da,3fa0a0398776deb5,3ff50d23f9d3bb34,3fedebf8cf11242a,3fa0dc23da1106de,3ff5cba663e0f33a,3fede47b84bddf24,//110
To achieve optimal precision and avoid rounding errors caused by interconversion between binary floating point values and decimal literal values, the coefficients are represented in 16-ary text corresponding to the IEEE 75464bit precision binary values.
And taking the integral multiple length of half of the central frequency period of each filter as a window to obtain an output spectrum.
Further comprising convolving the output spectrum with an inverse convolution kernel to further remove spectral leakage. The inverse convolution kernel coefficients: -0.00105783637474566-0.00114793935365354-0.00125199018526776-0.00137322722841485-0.00151594171242436-0.00168579725115534-0.00189091077180455-0.00214118812780976-0.00245665809900512-0.00284393511088502-0.00340513189236233-0.00393642641183259-0.00556693372117235-0.00439700676031480-0.01685286124734420.0198449665281736-0.1467930186890450.466314748234934-1.914077889830803.39074111941880-1.914077889830800.466314748234934-0.1467930186890460.0198449665281744-0.0168528612473447-0.00439700676031477-0.00556693372117244-0.00393642641183231-0.00340513189236235-0.00284393511088510-0.00245665809900537-0.00214118812780948-0.00189091077180488-0.00168579725115488-0.00151594171242466-0.00137322722841482-0.00125199018526771-0.00114793935365354-0.00105783637474564.
Specifically, the time domain signal of the wave is input to a filter bank consisting of N filters as shown in fig. 1 b. Frequency range [ Fst, Fed ] of the said wave]Where Fst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst) numbering said N filters from 0 to N-1, for the ith filter i belongs to0 to N-1, the ith filter satisfying:
upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N；
Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N；
Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N；
The passband ripple range of the filter is in the range of [ 1-6 ] dB, and the stopband attenuation is more than 30 dB;
narrow-band signals are output through the respective filters, each narrow-band range of the narrow-band signals being determined by an upper passband boundary and a lower passband boundary. And acquiring the period of the center frequency of each filter, taking the integral multiple length of half of the period as the window length to calculate statistical indexes for the output of each filter, and splicing the statistical results of each filter into an output frequency spectrum according to the filter number in sequence. And splicing the statistical results of the filters into an output frequency spectrum in sequence according to the filter numbers. The signal intensity in the pass band (each narrow band range is determined by the upper and lower limits of the pass band, namely the upper and lower limits of the pass band) is counted according to a time slice (the period of the center frequency), and the signal intensity is spliced in parallel according to the frequency bands, so that a spectrogram with time as a horizontal axis, frequency as a vertical axis and color as the signal intensity is obtained.
Specifically, as shown in fig. 1c, the method further includes performing a convolution operation on the output spectrum by using an inverse convolution kernel to further eliminate the spectrum leakage.
Acquiring a frequency response curve of the filter (the graph of the arrow pointing to the frequency response curve of the band-pass filter in fig. 1c is the frequency response curve), acquiring the frequency responses of M adjacent frequency points on one side of the central frequency of the frequency response curve, and acquiring a sequence [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
the matrix a is inverted to obtain a matrix IA, and a row or a column at the center of IA is taken to be the inverse convolution kernel (the diagram in fig. 1c in which the arrow points to the inverse convolution kernel is the inverse convolution kernel).
And then, based on the set deconvolution kernel, performing convolution operation on the output spectrum by using the deconvolution kernel to further eliminate spectrum leakage, thereby obtaining a high-frequency and high-resolution spectrogram.
As shown in fig. 2, in an embodiment, the system for calculating the spectrum of a wave of the present invention includes: an input module 21, and an output module 22; the input module 21 is configured to input a time domain signal of a wave into a filter bank, where the filter bank is composed of N filters; frequency range [ Fst, Fed ] of the said wave]Where Fst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying: upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N(ii) a Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N(ii) a Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N(ii) a The passband ripple range of the filter is (1-6)]Within the dB range, the stop band attenuation is more than 30 dB; the output module 22 is configured to obtain a period of the center frequency of each filter, calculate a statistical index for the output of each filter by using an integral multiple length of a half of the period as a window length, and sequentially splice the statistical results of each filter into an output frequency spectrum according to the filter numbers.
In an embodiment of the present invention, the statistical indicators include, but are not limited to: amplitude, standard deviation, root mean square.
In an embodiment of the present invention, the apparatus further includes a convolution module, where the convolution module is configured to perform a convolution operation on the output spectrum by using a deconvolution kernel to further eliminate spectrum leakage.
In an embodiment of the present invention, the inverse convolution kernel is obtained based on the following steps: acquiring a frequency response curve of the filter, acquiring the frequency responses of M adjacent frequency points on one side of the central frequency of the frequency response curve, and acquiring a number array [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
and inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
In an embodiment of the invention, the filter is an IIR band-pass filter.
It should be noted that the structures and principles of the input module 21 and the output module 22 correspond to the steps in the above-mentioned wave spectrum calculation method one to one, and therefore, the details are not repeated herein.
It should be noted that the division of the modules of the above system is only a logical division, and the actual implementation may be wholly or partially integrated into one physical entity, or may be physically separated. And these modules can be realized in the form of software called by processing element; or may be implemented entirely in hardware; and part of the modules can be realized in the form of calling software by the processing element, and part of the modules can be realized in the form of hardware. For example, the x module may be a processing element that is set up separately, or may be implemented by being integrated in a chip of the apparatus, or may be stored in a memory of the apparatus in the form of program code, and the function of the x module may be called and executed by a processing element of the apparatus. Other modules are implemented similarly. In addition, all or part of the modules can be integrated together or can be independently realized. The processing element described herein may be an integrated circuit having signal processing capabilities. In implementation, each step of the above method or each module above may be implemented by an integrated logic circuit of hardware in a processor element or an instruction in the form of software.
For example, the above modules may be one or more integrated circuits configured to implement the above methods, such as: one or more Specific Integrated circuits (ASICs), or one or more Microprocessors (MPUs), or one or more Field Programmable Gate Arrays (FPGAs), etc. For another example, when one of the above modules is implemented in the form of a Processing element scheduler code, the Processing element may be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. For another example, these modules may be integrated together and implemented in the form of a system-on-a-chip (SOC).
In an embodiment of the present invention, the present invention further includes a computer-readable storage medium, on which a computer program is stored, and the computer program is executed by a processor to implement any of the above-mentioned methods for calculating a wave spectrum.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the above method embodiments may be performed by hardware associated with a computer program. The aforementioned computer program may be stored in a computer readable storage medium. When executed, the program performs steps comprising the method embodiments described above; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
As shown in fig. 3, in an embodiment, the device for calculating the spectrum of the wave of the present invention includes: a processor 31 and a memory 32; the memory 32 is for storing a computer program; the processor 31 is connected to the memory 32 and is configured to execute the computer program stored in the memory 32, so that the computing device of the spectrum of the wave executes the computing method of the spectrum of any of the waves.
Specifically, the memory 32 includes: various media that can store program codes, such as ROM, RAM, magnetic disk, U-disk, memory card, or optical disk.
Preferably, the Processor 31 may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the Integrated Circuit may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, or discrete hardware components.
In summary, the method, system, medium and apparatus for calculating the frequency spectrum of the wave are used for decoupling the time resolution and the frequency resolution of the frequency spectrum, dividing the frequency points in an equal ratio, and eliminating the frequency spectrum leakage. Therefore, the invention effectively overcomes various defects in the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (10)
1. A method of calculating a spectrum of a wave, comprising the steps of:
inputting a time domain signal of a wave into a filter bank, the filter bank consisting of N band-pass filters;
frequency range [ Fst, Fed ] of the said wave]Where Fst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying:
upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N；
Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N；
Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N；
The passband ripple range of the filter is in the range of [ 1-6 ] dB, and the stopband attenuation is more than 30 dB;
and the period is used for acquiring the center frequency of each filter, the integral multiple length of half of the period is used as the output calculation statistical index of the window length to each filter, and the statistical results of each filter are sequentially spliced into an output frequency spectrum according to the filter number.
2. The method of calculating the spectrum of waves of claim 1, further comprising convolving said output spectrum with a deconvolution kernel to further eliminate spectral leakage.
3. Method for calculating the spectrum of waves according to claim 2, characterized in that said inverse convolution kernel is obtained on the basis of the following steps:
acquiring a frequency response curve of the filter, acquiring frequency responses close to M frequency points on one side of the central frequency of the frequency response curve, and acquiring a number array [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
and inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
4. The method of calculating a spectrum of waves according to claim 1, characterized in that the filter is an IIR band-pass filter.
5. A system for calculating a spectrum of a wave, comprising: an input module and an output module;
the input module is used for inputting a time domain signal of a wave into a filter bank, and the filter bank consists of N band-pass filters;
frequency range [ Fst, Fed ] of the said wave]Where Fst is the lower bound of the frequency range, Fed is the upper bound of the frequency range, and N satisfies N>＝log2(Fed/Fst), numbering the N filters from 0 to N-1, for the ith filter, i belongs to 0 to N-1, the ith filter satisfying:
upper bound fh (i) ═ Fst (Fed/Fst)(i+1)/N；
Center frequency fc (i) ═ Fst (Fed/Fst)(i+0.5)/N；
Lower band boundary fl (i) ═ Fst (Fed/Fst)i/N；
The passband ripple range of the filter is in the range of [ 1-6 ] dB, and the stopband attenuation is more than 30 dB;
the output module is used for acquiring the period of the center frequency of each filter, calculating the statistical index of the output of each filter by taking the integral multiple length of half of the period as the window length, and splicing the statistical results of each filter into an output frequency spectrum in sequence according to the serial numbers of the filters.
6. The system for computing the spectrum of waves of claim 5, further comprising a convolution module for convolving the output spectrum with a deconvolution kernel to further eliminate spectral leakage.
7. System for computing the spectrum of waves according to claim 5, characterized in that said inverse convolution kernel is obtained on the basis of the following steps:
acquiring a frequency response curve of the filter, acquiring frequency responses close to M frequency points on one side of the central frequency of the frequency response curve, and acquiring a number array [ M ] based on the frequency responses1,m2,m3,...,mM-1,mM]Based on said sequence of numbers [ m ]1,m2,m3,...,mM-1,mM]The angular symmetric matrix a is arranged such that,
and inverting the matrix A to obtain a matrix IA, and taking a row or a column at the center of the IA, namely the inverse convolution kernel.
8. The system for computing the spectrum of waves of claim 5, wherein the filter is an IIR band-pass filter.
9. A computer-readable storage medium on which a computer program is stored, the computer program being executed by a processor to implement a method of calculating a spectrum of a wave according to any one of claims 1 to 4.
10. An apparatus for calculating a frequency spectrum of a wave, comprising: a processor and a memory;
the memory is used for storing a computer program;
the processor is connected to the memory for executing the computer program stored in the memory to cause the computing means of the spectrum of the wave to perform the computing method of the spectrum of the wave according to any one of claims 1 to 4.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010674824.2A CN113933590B (en) | 2020-07-14 | 2020-07-14 | Method, system, medium and device for calculating frequency spectrum of wave |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010674824.2A CN113933590B (en) | 2020-07-14 | 2020-07-14 | Method, system, medium and device for calculating frequency spectrum of wave |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113933590A true CN113933590A (en) | 2022-01-14 |
| CN113933590B CN113933590B (en) | 2024-07-30 |
Family
ID=79273861
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010674824.2A Active CN113933590B (en) | 2020-07-14 | 2020-07-14 | Method, system, medium and device for calculating frequency spectrum of wave |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113933590B (en) |
Citations (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4599567A (en) * | 1983-07-29 | 1986-07-08 | Enelf Inc. | Signal representation generator |
| WO1995002929A1 (en) * | 1993-07-16 | 1995-01-26 | Dolby Laboratories Licensing Corporation | Computationally efficient adaptive bit allocation for encoding method and apparatus with allowance for decoder spectral distortions |
| US5581654A (en) * | 1993-05-25 | 1996-12-03 | Sony Corporation | Method and apparatus for information encoding and decoding |
| CN102506994A (en) * | 2011-11-21 | 2012-06-20 | 嘉兴中科声学科技有限公司 | Digitized acoustic detection system |
| CN103366749A (en) * | 2012-03-28 | 2013-10-23 | 北京天籁传音数字技术有限公司 | Sound coding and decoding apparatus and sound coding and decoding method |
| CN103403710A (en) * | 2011-02-10 | 2013-11-20 | 雅虎公司 | Extraction and matching of characteristic fingerprints from audio signals |
| CN103973324A (en) * | 2014-04-17 | 2014-08-06 | 电子科技大学 | Broadband digital receiver and real-time frequency spectrum processing method thereof |
| CN105551501A (en) * | 2016-01-22 | 2016-05-04 | 大连民族大学 | Harmonic signal fundamental frequency estimation algorithm and device |
| CN107274888A (en) * | 2017-06-14 | 2017-10-20 | 大连海事大学 | A kind of Emotional speech recognition method based on octave signal intensity and differentiation character subset |
| CN107798283A (en) * | 2016-08-31 | 2018-03-13 | 西安英诺视通信息技术有限公司 | A kind of neural network failure multi classifier based on the acyclic figure of decision-directed |
| CN108198545A (en) * | 2017-12-19 | 2018-06-22 | 安徽建筑大学 | A kind of audio recognition method based on wavelet transformation |
| CN108427032A (en) * | 2018-01-29 | 2018-08-21 | 中国电子科技网络信息安全有限公司 | Inversion method when a kind of spectral decomposition method and frequency |
| CN108918965A (en) * | 2018-05-23 | 2018-11-30 | 成都玖锦科技有限公司 | Multi channel signals phase, amplitude high-precision measuring method |
| CN110289006A (en) * | 2018-03-16 | 2019-09-27 | 音乐集团公司 | Frequency spectrum-dynamic of audio signal |
| CN111246484A (en) * | 2020-01-21 | 2020-06-05 | 中国空间技术研究院 | Spectrum self-adaptive high-performance communication system and method |
-
2020
- 2020-07-14 CN CN202010674824.2A patent/CN113933590B/en active Active
Patent Citations (16)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4599567A (en) * | 1983-07-29 | 1986-07-08 | Enelf Inc. | Signal representation generator |
| US5581654A (en) * | 1993-05-25 | 1996-12-03 | Sony Corporation | Method and apparatus for information encoding and decoding |
| WO1995002929A1 (en) * | 1993-07-16 | 1995-01-26 | Dolby Laboratories Licensing Corporation | Computationally efficient adaptive bit allocation for encoding method and apparatus with allowance for decoder spectral distortions |
| CN103403710A (en) * | 2011-02-10 | 2013-11-20 | 雅虎公司 | Extraction and matching of characteristic fingerprints from audio signals |
| CN102506994A (en) * | 2011-11-21 | 2012-06-20 | 嘉兴中科声学科技有限公司 | Digitized acoustic detection system |
| CN103366749A (en) * | 2012-03-28 | 2013-10-23 | 北京天籁传音数字技术有限公司 | Sound coding and decoding apparatus and sound coding and decoding method |
| CN103973324A (en) * | 2014-04-17 | 2014-08-06 | 电子科技大学 | Broadband digital receiver and real-time frequency spectrum processing method thereof |
| CN109410980A (en) * | 2016-01-22 | 2019-03-01 | 大连民族大学 | A kind of application of fundamental frequency estimation algorithm in the fundamental frequency estimation of all kinds of signals with harmonic structure |
| CN105551501A (en) * | 2016-01-22 | 2016-05-04 | 大连民族大学 | Harmonic signal fundamental frequency estimation algorithm and device |
| CN107798283A (en) * | 2016-08-31 | 2018-03-13 | 西安英诺视通信息技术有限公司 | A kind of neural network failure multi classifier based on the acyclic figure of decision-directed |
| CN107274888A (en) * | 2017-06-14 | 2017-10-20 | 大连海事大学 | A kind of Emotional speech recognition method based on octave signal intensity and differentiation character subset |
| CN108198545A (en) * | 2017-12-19 | 2018-06-22 | 安徽建筑大学 | A kind of audio recognition method based on wavelet transformation |
| CN108427032A (en) * | 2018-01-29 | 2018-08-21 | 中国电子科技网络信息安全有限公司 | Inversion method when a kind of spectral decomposition method and frequency |
| CN110289006A (en) * | 2018-03-16 | 2019-09-27 | 音乐集团公司 | Frequency spectrum-dynamic of audio signal |
| CN108918965A (en) * | 2018-05-23 | 2018-11-30 | 成都玖锦科技有限公司 | Multi channel signals phase, amplitude high-precision measuring method |
| CN111246484A (en) * | 2020-01-21 | 2020-06-05 | 中国空间技术研究院 | Spectrum self-adaptive high-performance communication system and method |
Non-Patent Citations (3)
| Title |
|---|
| 万英平: "声频测量技术", vol. 1, 31 October 2006, 国防工业出版社, pages: 10 - 12 * |
| 宋知用: "MATLAB在语音信号分析与合成中的应用", vol. 1, 30 November 2013, 北京航空航天大学出版社, pages: 204 * |
| 庞建丽;高丽娜;: "基于Matlab的IIR数字滤波器设计方法比较及应用", 现代电子技术, no. 11, 1 June 2010 (2010-06-01), pages 103 - 110 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113933590B (en) | 2024-07-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Selesnick et al. | Generalized digital Butterworth filter design | |
| Sreenivas et al. | FFT algorithm for both input and output pruning | |
| Deng | Design and parallel implementation of FIR digital filters with simultaneously variable magnitude and non-integer phase-delay | |
| Kwong | Some results on matrix monotone functions | |
| Lu et al. | Two-dimensional digital filters with sparse coefficients | |
| CN109510609B (en) | Design method of low-complexity sparse FIR low-pass filter | |
| US9787288B2 (en) | Optimal factoring of FIR filters | |
| Penedo et al. | Designing digital filter banks using wavelets | |
| Mehrnia et al. | Optimal factoring of FIR filters | |
| Thesni et al. | Implementation and performance comparison of digital filter in FPGA | |
| CN113933590A (en) | Method, system, medium, and apparatus for calculating frequency spectrum of wave | |
| CN110086452B (en) | Design method of low-complexity sparse FIR notch filter | |
| Jiang et al. | Optimization design of two-channel biorthogonal graph filter banks | |
| Ignjatović et al. | Chromatic derivatives and approximations in practice—part i: A general framework | |
| Soleimani | Combine particle swarm optimization algorithm and canonical sign digit to design finite impulse response filter | |
| Zhou et al. | Optimization design of M-channel oversampled graph filter banks via successive convex approximation | |
| Barakat | The calculation of integrals encountered in optical diffraction theory | |
| López-Parrado et al. | OpenRISC-based System-on-Chip for digital signal processing | |
| Karimov et al. | Compact Fixed-Point Filter Implementation | |
| Ignjatovic | Chromatic derivatives and local approximations | |
| Claasen et al. | Remarks on the zero-input behavior of second-order digital filters designed with one magnitude truncation quatizer | |
| Damian et al. | A low area FIR filter for FPGA implementation | |
| Babic et al. | Optimum low-order windows for discrete Fourier transform systems | |
| Shi et al. | The Companion Model--a Canonical Model in Graph Signal Processing | |
| Dolecek et al. | Low power non-recursive comb-based decimation filter design |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |