MFCC——Java版

只有花钱可以下，贴在这位大家谋点福利，同时也是希望能跟大家探讨一下（尴尬的没提取出来）

如有侵犯版权请及时告知删除（好多人拿去发资源赚积分我觉得还不如公开），让我们一起膜拜一下原创大神。

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MFCC.java

/**Calculates the mel-based cepstra coefficients for one frame of speech.
 * Based on the original MFCC implementation described in:
 * [1] Davis & Mermelstein - IEEE Transactions on ASSP, August 1980.
 * Additional references are:
 * [2] Joseph Picone, Proceedings of the IEEE, Sep. 1993.
 * [3] Jankowski et al. IEEE Trans. on Speech and Audio Processing. July, 1995.
 * [4] Cardin et al, ICASSP'93 - pp. II-243
 *
 * Notice that there are several different implementations of the mel filter
 * bank. For example, the log is usually implementated after having the filter
 * outputs calculated, but could be implemented before filtering. Besides, there are
 * differences in the specification of the filter frequencies. [1]
 * suggested linear scale until 1000 Hz and logarithm scale afterwards.
 * This implementation uses the equation (10) in [2]:
 *      mel frequency = 2595 log(1 + (f/700)), where log is base 10
 * to find the filter bank center frequencies.
 *
 * @author Aldebaro Klautau
 * @version 2.0 - March 07, 2001
 * @see MFCCPatternGenerator
 */




//if m_oisZeroThCepstralCoefficientCalculated is true,
//this class decrements m_nnumberOfParameters by 1 and
//adds the 0-th coefficient to complete a vector with
//the number of MFCC's specified by the user.
public class MFCC {


// parameter USEPOWER in HTK, where default is false
private static final boolean m_ousePowerInsteadOfMagnitude = false;


// Number of MFCCs per speech frame.
private final int m_nnumberOfParameters;
/**
* Sampling frequency.
*/
private final double m_dsamplingFrequency;
/**
* Number of filter in mel filter bank.
*/
private final int m_nnumberOfFilters;
/**
* Number of FFT points.
*/
private final int m_nFFTLength;
/**
* Coefficient of filtering performing in cepstral domain (called
* 'liftering' operation). It is not used if m_oisLifteringEnabled is false.
*/
private final int m_nlifteringCoefficient;
/**
* True enables liftering.
*/
private final boolean m_oisLifteringEnabled;
/**
* Minimum value of filter output, otherwise the log is not calculated and
* m_dlogFilterOutputFloor is adopted. ISIP implementation assumes
* m_dminimumFilterOutput = 1 and this value is used here.
*/
private final double m_dminimumFilterOutput = 1.0;


/**
* True if the zero'th MFCC should be calculated.
*/
private final boolean m_oisZeroThCepstralCoefficientCalculated;


/**
* Floor value for filter output in log domain. ISIP implementation assumes
* m_dlogFilterOutputFloor = 0 and this value is used here.
*/
private final double m_dlogFilterOutputFloor = 0.0;
private int[][] m_nboundariesDFTBins;
private double[][] m_dweights;
private FFT m_fft;
private double[][] m_ddCTMatrix;


private double[] m_dfilterOutput;
private final double[] m_nlifteringMultiplicationFactor;


// things to be calculated just once:
private final double m_dscalingFactor;


/**
* The 0-th coefficient is included in nnumberOfParameters. So, if one wants
* 12 MFCC's and additionally the 0-th coefficient, one should call the
* constructor with nnumberOfParameters = 13 and
* oisZeroThCepstralCoefficientCalculated = true
*/
public MFCC(int nnumberOfParameters, double dsamplingFrequency,
int nnumberofFilters, int nFFTLength, boolean oisLifteringEnabled,
int nlifteringCoefficient,
boolean oisZeroThCepstralCoefficientCalculated) {


m_oisZeroThCepstralCoefficientCalculated = oisZeroThCepstralCoefficientCalculated;
if (m_oisZeroThCepstralCoefficientCalculated) {
// the user shouldn't notice that nnumberOfParameters was
// decremented internally
m_nnumberOfParameters = nnumberOfParameters - 1;
} else {
m_nnumberOfParameters = nnumberOfParameters;
}


m_dsamplingFrequency = dsamplingFrequency;
m_nnumberOfFilters = nnumberofFilters;
m_nFFTLength = nFFTLength;


// the filter bank weights, FFT's cosines and sines
// and DCT matrix are initialized once to save computations.


// initializes the mel-based filter bank structure
calculateMelBasedFilterBank(dsamplingFrequency, nnumberofFilters,
nFFTLength);
m_fft = new FFT(m_nFFTLength); // initialize FFT
initializeDCTMatrix();
m_nlifteringCoefficient = nlifteringCoefficient;
m_oisLifteringEnabled = oisLifteringEnabled;


// avoid allocating RAM space repeatedly, m_dfilterOutput is
// going to be used in method getParameters()
m_dfilterOutput = new double[m_nnumberOfFilters];


// needed in method getParameters()
// m_dscalingFactor shouldn't be necessary because it's only
// a scaling factor, but I'll implement it
// for the sake of getting the same numbers ISIP gets
m_dscalingFactor = Math.sqrt(2.0 / m_nnumberOfFilters);


// for liftering method
if (m_oisLifteringEnabled) {
// note that:
@SuppressWarnings("unused")
int nnumberOfCoefficientsToLift = m_nnumberOfParameters;
// even when m_oisZeroThCepstralCoefficientCalculated is true
// because if 0-th cepstral coefficient is included,
// it is not liftered
m_nlifteringMultiplicationFactor = new double[m_nlifteringCoefficient];
double dfactor = m_nlifteringCoefficient / 2.0;
double dfactor2 = Math.PI / m_nlifteringCoefficient;
for (int i = 0; i < m_nlifteringCoefficient; i++) {
m_nlifteringMultiplicationFactor[i] = 1.0 + dfactor
* Math.sin(dfactor2 * (i + 1));
}
if (m_nnumberOfParameters > m_nlifteringCoefficient) {
new Error(
"Liftering is enabled and the number "
+ "of parameters = "
+ m_nnumberOfParameters
+ ", while "
+ "the liftering coefficient is "
+ m_nlifteringCoefficient
+ ". In this case some cepstrum coefficients would be made "
+ "equal to zero due to liftering, what does not make much "
+ "sense in a speech recognition system. You may want to "
+ "increase the liftering coefficient or decrease the number "
+ "of MFCC parameters.");
}
} else {
m_nlifteringMultiplicationFactor = null;
}
}


/** Initializes the DCT matrix. */
private void initializeDCTMatrix() {
m_ddCTMatrix = new double[m_nnumberOfParameters][m_nnumberOfFilters];
for (int i = 0; i < m_nnumberOfParameters; i++) {
for (int j = 0; j < m_nnumberOfFilters; j++) {
m_ddCTMatrix[i][j] = Math.cos((i + 1.0) * (j + 1.0 - 0.5)
* (Math.PI / m_nnumberOfFilters));
}
}
}


/**
* Converts frequencies in Hz to mel scale according to mel frequency = 2595
* log(1 + (f/700)), where log is base 10 and f is the frequency in Hz.
*/
public static double[] convertHzToMel(double[] dhzFrequencies,
double dsamplingFrequency) {
double[] dmelFrequencies = new double[dhzFrequencies.length];
for (int k = 0; k < dhzFrequencies.length; k++) {
dmelFrequencies[k] = 2595.0 * (Math
.log(1.0 + (dhzFrequencies[k] / 700.0)) / Math.log(10));
}
return dmelFrequencies;
}


/**
* Calculates triangular filters. 三角带通滤波器（Triangular Bandpass
* Filters）：将能量频谱能量乘以一组 20 个三角带通滤波器，求得每一个滤波器输出的对数能量（Log
* Energy），共20个。必须注意的是：这 20 个三角带通滤波器在「梅尔频率」（Mel Frequency）上是平均分布的，而梅尔频率和一般频率
* f 的关系式如下： mel(f)=2595*log10(1+f/700) 或是 mel(f)=1125*ln(1+f/700)
* 梅尔频率代表一般人耳对于频率的感受度，由此也可以看出人耳对于频率 f 的感受是呈对数变化的： 在低频部分，人耳感受是比较敏锐 。
* 在高频部分，人耳的感受就会越来越粗糙 。 三角带通滤波器有两个主要目的： 对频谱进行平滑化，并消除谐波的作用，突显原先语音的共振峰。
* （因此一段语音的音调或音高，是不会呈现在 MFCC 参数内，换句话说，以 MFCC为特征的语音辨识系统，并不会受到输入语音的音调不同而有所影响。）
*/
@SuppressWarnings("static-access")
private void calculateMelBasedFilterBank(double dsamplingFrequency,
int nnumberofFilters, int nfftLength) {


// frequencies for each triangular filter
@SuppressWarnings("unused")
double[][] dfrequenciesInMelScale = new double[nnumberofFilters][3];
// the +1 below is due to the sample of frequency pi (or fs/2)
double[] dfftFrequenciesInHz = new double[nfftLength / 2 + 1];
// compute the frequency of each FFT sample (in Hz):
double ddeltaFrequency = dsamplingFrequency / nfftLength;
for (int i = 0; i < dfftFrequenciesInHz.length; i++) {
dfftFrequenciesInHz[i] = i * ddeltaFrequency;
}
// convert Hz to Mel
double[] dfftFrequenciesInMel = this.convertHzToMel(
dfftFrequenciesInHz, dsamplingFrequency);


// compute the center frequencies. Notice that 2 filters are
// "artificially" created in the endpoints of the frequency
// scale, correspondent to 0 and fs/2 Hz.
double[] dfilterCenterFrequencies = new double[nnumberofFilters + 2];
// implicitly: dfilterCenterFrequencies[0] = 0.0;
ddeltaFrequency = dfftFrequenciesInMel[dfftFrequenciesInMel.length - 1]
/ (nnumberofFilters + 1);
for (int i = 1; i < dfilterCenterFrequencies.length; i++) {
dfilterCenterFrequencies[i] = i * ddeltaFrequency;
}


// initialize member variables
m_nboundariesDFTBins = new int[m_nnumberOfFilters][2];
m_dweights = new double[m_nnumberOfFilters][];


// notice the loop starts from the filter i=1 because i=0 is the one
// centered at DC
for (int i = 1; i <= nnumberofFilters; i++) {
m_nboundariesDFTBins[i - 1][0] = Integer.MAX_VALUE;
// notice the loop below doesn't include the first and last FFT
// samples
for (int j = 1; j < dfftFrequenciesInMel.length - 1; j++) {
// see if frequency j is inside the bandwidth of filter i
if ((dfftFrequenciesInMel[j] >= dfilterCenterFrequencies[i - 1])
& (dfftFrequenciesInMel[j] <= dfilterCenterFrequencies[i + 1])) {
// the i-1 below is due to the fact that we discard the
// first filter i=0
// look for the first DFT sample for this filter
if (j < m_nboundariesDFTBins[i - 1][0]) {
m_nboundariesDFTBins[i - 1][0] = j;
}
// look for the last DFT sample for this filter
if (j > m_nboundariesDFTBins[i - 1][1]) {
m_nboundariesDFTBins[i - 1][1] = j;
}
}
}
}
// check for consistency. The problem below would happen just
// in case of a big number of MFCC parameters for a small DFT length.
for (int i = 0; i < nnumberofFilters; i++) {
if (m_nboundariesDFTBins[i][0] == m_nboundariesDFTBins[i][1]) {
new Error(
"Error in MFCC filter bank. In filter "
+ i
+ " the first sample is equal to the last sample !"
+ " Try changing some parameters, for example, decreasing the number of filters.");
}
}


// allocate space
for (int i = 0; i < nnumberofFilters; i++) {
m_dweights[i] = new double[m_nboundariesDFTBins[i][1]
- m_nboundariesDFTBins[i][0] + 1];
}


// calculate the weights
for (int i = 1; i <= nnumberofFilters; i++) {
for (int j = m_nboundariesDFTBins[i - 1][0], k = 0; j <= m_nboundariesDFTBins[i - 1][1]; j++, k++) {
if (dfftFrequenciesInMel[j] < dfilterCenterFrequencies[i]) {
m_dweights[i - 1][k] = (dfftFrequenciesInMel[j] - dfilterCenterFrequencies[i - 1])
/ (dfilterCenterFrequencies[i] - dfilterCenterFrequencies[i - 1]);
} else {
m_dweights[i - 1][k] = 1.0 - ((dfftFrequenciesInMel[j] - dfilterCenterFrequencies[i]) / (dfilterCenterFrequencies[i + 1] - dfilterCenterFrequencies[i]));
}
}
}
}


/**
* Returns the MFCC coefficients for the given speech frame. If calculated,
* the 0-th coefficient is added to the end of the vector (for compatibility
* with HTK). The order of an output vector x with 3 MFCC's, including the
* 0-th, would be: x = {MFCC1, MFCC2, MFCC0}
*/
public double[] getParameters(double[] fspeechFrame) {


// use mel filter bank
for (int i = 0; i < m_nnumberOfFilters; i++) {
m_dfilterOutput[i] = 0.0;
// Notice that the FFT samples at 0 (DC) and fs/2 are not considered
// on this calculation
if (m_ousePowerInsteadOfMagnitude) {
double[] fpowerSpectrum = m_fft.calculateFFTPower(fspeechFrame);
for (int j = m_nboundariesDFTBins[i][0], k = 0; j <= m_nboundariesDFTBins[i][1]; j++, k++) {
m_dfilterOutput[i] += fpowerSpectrum[j] * m_dweights[i][k];
}
} else {
double[] fmagnitudeSpectrum = m_fft
.calculateFFTMagnitude(fspeechFrame);
for (int j = m_nboundariesDFTBins[i][0], k = 0; j <= m_nboundariesDFTBins[i][1]; j++, k++) {
m_dfilterOutput[i] += fmagnitudeSpectrum[j]
* m_dweights[i][k];
}
}


// ISIP (Mississipi univ.) implementation
if (m_dfilterOutput[i] > m_dminimumFilterOutput) {// floor power to
// avoid log(0)
m_dfilterOutput[i] = Math.log(m_dfilterOutput[i]); // using ln
} else {
m_dfilterOutput[i] = m_dlogFilterOutputFloor;
}
}


// need to allocate space for output array
// because it allows the user to call this method
// many times, without having to do a deep copy
// of the output vector
double[] dMFCCParameters = null;
if (m_oisZeroThCepstralCoefficientCalculated) {
dMFCCParameters = new double[m_nnumberOfParameters + 1];
// calculates zero'th cepstral coefficient and pack it
// after the MFCC parameters of each frame for the sake
// of compatibility with HTK
double dzeroThCepstralCoefficient = 0.0;
for (int j = 0; j < m_nnumberOfFilters; j++) {
dzeroThCepstralCoefficient += m_dfilterOutput[j];
}
dzeroThCepstralCoefficient *= m_dscalingFactor;
dMFCCParameters[dMFCCParameters.length - 1] = dzeroThCepstralCoefficient;
} else {
// allocate space
dMFCCParameters = new double[m_nnumberOfParameters];
}


/*
* cosine transform 
*/
for (int i = 0; i < m_nnumberOfParameters; i++) {
for (int j = 0; j < m_nnumberOfFilters; j++) {
dMFCCParameters[i] += m_dfilterOutput[j] * m_ddCTMatrix[i][j];
// the original equations have the first index as 1
}
// could potentially incorporate liftering factor and
// factor below to save multiplications, but will not
// do it for the sake of clarity
dMFCCParameters[i] *= m_dscalingFactor;
}


// debugging purposes
// System.out.println("Windowed speech");
// IO.DisplayVector(fspeechFrame);
// System.out.println("FFT spectrum");
// IO.DisplayVector(fspectrumMagnitude);
// System.out.println("Filter output in dB");
// IO.DisplayVector(dfilterOutput);
// System.out.println("DCT matrix");
// IO.DisplayMatrix(m_ddCTMatrix);
// System.out.println("MFCC before liftering");
// IO.DisplayVector(dMFCCParameters);


if (m_oisLifteringEnabled) {
// Implements liftering to smooth the cepstral coefficients
// according to
// [1] Rabiner, Juang, Fundamentals of Speech Recognition, pp. 169,
// [2] The HTK Book, pp 68 and
// [3] ISIP package - Mississipi Univ. Picone's group.
// if 0-th coefficient is included, it is not liftered
for (int i = 0; i < m_nnumberOfParameters; i++) {
dMFCCParameters[i] *= m_nlifteringMultiplicationFactor[i];
}
}


return dMFCCParameters;
} // end method


/**
* Returns the sampling frequency.
*/
public double getSamplingFrequency() {
return this.m_dsamplingFrequency;
}


/**
* Returns the number of points of the Fast Fourier Transform (FFT) used in
* the calculation of this MFCC.
*/
public int getFFTLength() {
return m_nFFTLength;
}


/**
* Returns the number of MFCC coefficients, including the 0-th if required
* by user in the object construction.
*/
public int getNumberOfCoefficients() {
return (m_oisZeroThCepstralCoefficientCalculated ? (m_nnumberOfParameters + 1)
: m_nnumberOfParameters);
}


/**
* Return a string with all important parameters of this object.
*/
public String toString() {
return "MFCC.nnumberOfParameters = "
+ (m_oisZeroThCepstralCoefficientCalculated ? (m_nnumberOfParameters + 1)
: m_nnumberOfParameters) + "\n"
+ "MFCC.nnumberOfFilters = " + m_nnumberOfFilters + "\n"
+ "MFCC.nFFTLength = " + m_nFFTLength + "\n"
+ "MFCC.dsamplingFrequency = " + m_dsamplingFrequency + "\n"
+ "MFCC.nlifteringCoefficient = " + m_nlifteringCoefficient
+ "\n" + "MFCC.oisLifteringEnabled = " + m_oisLifteringEnabled
+ "\n" + "MFCC.oisZeroThCepstralCoefficientCalculated = "
+ m_oisZeroThCepstralCoefficientCalculated;
}


public double[] getFilterBankOutputs(double[] fspeechFrame) {
// use mel filter bank
double dfilterOutput[] = new double[m_nnumberOfFilters];
for (int i = 0; i < m_nnumberOfFilters; i++) {
// Notice that the FFT samples at 0 (DC) and fs/2 are not considered
// on this calculation
if (m_ousePowerInsteadOfMagnitude) {
double[] fpowerSpectrum = m_fft.calculateFFTPower(fspeechFrame);
for (int j = m_nboundariesDFTBins[i][0], k = 0; j <= m_nboundariesDFTBins[i][1]; j++, k++) {
dfilterOutput[i] += fpowerSpectrum[j] * m_dweights[i][k];
}
} else {
double[] fmagnitudeSpectrum = m_fft
.calculateFFTMagnitude(fspeechFrame);
for (int j = m_nboundariesDFTBins[i][0], k = 0; j <= m_nboundariesDFTBins[i][1]; j++, k++) {
dfilterOutput[i] += fmagnitudeSpectrum[j]
* m_dweights[i][k];
}
}


// ISIP (Mississipi univ.) implementation
if (dfilterOutput[i] > m_dminimumFilterOutput) {// floor power to
// avoid log(0)
dfilterOutput[i] = Math.log(dfilterOutput[i]); // using ln
} else {
dfilterOutput[i] = m_dlogFilterOutputFloor;
}
}
return dfilterOutput;
}


} // end of class

FFT.java

public final class FFT {
public int logm;
final int MAXLOGM = 20; /* max FFT length 2^MAXLOGM */
final double TWOPI = 6.28318530717958647692;
final double SQHALF = 0.707106781186547524401;
int brseed[] = new int[4048];
float tab[][];


public FFT(int nlength) {
double dtemp = Math.log(nlength) / Math.log(2);
if ((dtemp - (int) dtemp) != 0.0) {
throw new Error("FFT length must be a power of 2.");
} else {
this.logm = (int) dtemp;
}
if (logm >= 4) {
creattab(logm);
}
}


/**
* Calculates the magnitude spectrum of a real signal. The returned vector
* contains only the positive frequencies.
*/
public float[] calculateFFTMagnitude(float x[]) {
int i, n;
n = 1 << this.logm;


if (x.length > n) {
throw new Error("Tried to use a " + n
+ "-points FFT for a vector with " + x.length + " samples!");
}


rsfft(x);


float[] mag = new float[n / 2 + 1];
mag[0] = x[0]; // DC frequency must be positive always


if (n == 1) {
return mag;
}
mag[n / 2] = (float) Math.abs(x[n / 2]); // pi (meaning: fs / 2)


// System.out.println("FFT before magnitude");
// IO.DisplayVector(x);


for (i = 1; i < n / 2; i++) {
mag[i] = (float) Math.sqrt(x[i] * x[i] + x[n - i] * x[n - i]);
// System.out.println(mag[i] + " " + x[i] + " " + x[n-i]);
}


// IO.DisplayVector(mag);
return mag;
}


/**
* Calculates the magnitude spectrum of a real signal. The returned vector
* contains only the positive frequencies.
*/
public double[] calculateFFTMagnitude(double inputData[]) {
int i, n;
n = 1 << this.logm;
if (inputData.length > n) {
throw new Error("Tried to use a " + n
+ "-points FFT for a vector with " + inputData.length
+ " samples!");
}


// System.out.println("magnitude test");
// double[] dtest = DSP.DFTMagnitude(inputData);
// IO.DisplayVector(dtest);


float[] x = new float[n];
for (i = 0; i < inputData.length; i++) {
x[i] = (float) inputData[i];
}


rsfft(x);


// System.out.println("FFT before magnitude");
// IO.DisplayVector(x);


double[] mag = new double[n / 2 + 1];
mag[0] = x[0]; // DC frequency must be positive always


if (n == 1) {
return mag;
}
mag[n / 2] = Math.abs(x[n / 2]); // pi (meaning: fs / 2)


for (i = 1; i < n / 2; i++) {
mag[i] = Math.sqrt(x[i] * x[i] + x[n - i] * x[n - i]);
// System.out.println(mag[i] + " " + x[i] + " " + x[n-i]);
}


// IO.DisplayVector(mag);
return mag;
}


/**
* Calculates the power (magnitude squared) spectrum of a real signal. The
* returned vector contains only the positive frequencies.
*/
public double[] calculateFFTPower(double inputData[]) {
int i, n;
n = 1 << this.logm;


// System.out.println("magnitude test");
// double[] dtest = DSP.DFTMagnitude(inputData);
// IO.DisplayVector(dtest);


float[] x = new float[n];
for (i = 0; i < inputData.length; i++) {
x[i] = (float) inputData[i];
}


rsfft(x);


// System.out.println("FFT before magnitude");
// IO.DisplayVector(x);


double[] mag = new double[n / 2 + 1];
mag[0] = x[0]; // DC frequency must be positive always


if (n == 1) {
return mag;
}
mag[n / 2] = Math.abs(x[n / 2]); // pi (meaning: fs / 2)


for (i = 1; i < n / 2; i++) {
mag[i] = x[i] * x[i] + x[n - i] * x[n - i];
// mag[i] = Math.sqrt(x[i]*x[i]+x[n-i]*x[n-i]);
// System.out.println(mag[i] + " " + x[i] + " " + x[n-i]);
}


// IO.DisplayVector(mag);
return mag;
}


/**
* In place calculation of FFT magnitude.
*/
public void FFTMagnitude(float x[]) {
int i, n;
rsfft(x);
n = 1 << this.logm;
if (n == 1)
return;
for (i = 1; i < n / 2; i++) {
x[i] = (float) Math.sqrt(x[i] * x[i] + x[n - i] * x[n - i]);
x[n - i] = x[i];
}
// Aldebaro modification:
x[n / 2] = Math.abs(x[n / 2]);
}


void rsfft(float x[]) {
/* creat table */
// if(logm>=4) creattab(logm);
/* Call recursive routine */


rsrec(x, logm);


/* Output array unshuffling using bit-reversed indices */
if (logm > 1) {
BR_permute(x, logm);
return;
}
}


/*
* -------------------------------------------------------------------- *
* Inverse transform for real inputs *
* --------------------------------------------------------------------
*/


void rsifft(float x[]) {
int i, m;
float fac;
int xp;


/* Output array unshuffling using bit-reversed indices */
if (logm > 1) {
BR_permute(x, logm);
}
x[0] *= 0.5;
if (logm > 0)
x[1] *= 0.5;
/* creat table */
// if(logm>=4) creattab(logm);
/* Call recursive routine */


rsirec(x, logm);


/* Normalization */
m = 1 << logm;
fac = (float) 2.0 / m;
xp = 0;


for (i = 0; i < m; i++) {
x[xp++] *= fac;
}
}


/*
* -------------------------------------------------------------------- *
* Creat multiple fator table *
* --------------------------------------------------------------------
*/


void creattab(int logm) {
int m, m2, m4, m8, nel, n, rlogm;
int cn, spcn, smcn, c3n, spc3n, smc3n;
double ang, s, c;
tab = new float[logm - 4 + 1][6 * ((1 << logm) / 4 - 2)];
for (rlogm = logm; rlogm >= 4; rlogm--)


{
m = 1 << rlogm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;
nel = m4 - 2;
/* Initialize pointers */


cn = 0;
spcn = cn + nel;
smcn = spcn + nel;
c3n = smcn + nel;
spc3n = c3n + nel;
smc3n = spc3n + nel;


/* Compute tables */
for (n = 1; n < m4; n++) {
if (n == m8)
continue;
ang = n * TWOPI / m;
c = Math.cos(ang);
s = Math.sin(ang);
tab[rlogm - 4][cn++] = (float) c;
tab[rlogm - 4][spcn++] = (float) (-(s + c));
tab[rlogm - 4][smcn++] = (float) (s - c);


ang = 3 * n * TWOPI / m;
c = Math.cos(ang);
s = Math.sin(ang);
tab[rlogm - 4][c3n++] = (float) c;
tab[rlogm - 4][spc3n++] = (float) (-(s + c));
tab[rlogm - 4][smc3n++] = (float) (s - c);
}
}
}


/*
* -------------------------------------------------------------------- *
* Recursive part of the RSFFT algorithm. Not externally * callable. *
* --------------------------------------------------------------------
*/


void rsrec(float x[], int logm) {
int m, m2, m4, m8, nel, n;
int x0 = 0;
int xr1, xr2, xi1;
int cn = 0;
int spcn = 0;
int smcn = 0;
float tmp1, tmp2;
double ang, c, s;


/* Check range of logm */
try {
if ((logm < 0) || (logm > MAXLOGM)) {
System.err.println("FFT length m is too big: log2(m) = " + logm
+ "is out of bounds [" + 0 + "," + MAXLOGM + "]");


throw new OutofborderException(logm);
}
} catch (OutofborderException e) {
throw new OutOfMemoryError();
}


/* Compute trivial cases */


if (logm < 2) {
if (logm == 1) { /* length m = 2 */
xr2 = x0 + 1;
tmp1 = x[x0] + x[xr2];
x[xr2] = x[x0] - x[xr2];
x[x0] = tmp1;
return;
} else if (logm == 0)
return; /* length m = 1 */
}


/* Compute a few constants */
m = 1 << logm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;


/* Build tables of butterfly coefficients, if necessary */
// if ((logm >= 4) && (tab[logm-4][0] == 0)) {


/* Allocate memory for tables */
// nel = m4 - 2;


/*
* if ((tab[logm-4] = (float *) calloc(3 * nel, sizeof(float))) == NULL)
* { printf("Error : RSFFT : not enough memory for cosine tables.\n");
* error_exit(); }
*/


/* Initialize pointers */
// tabi=logm-4;
// cn =0; spcn = cn + nel; smcn = spcn + nel;


/* Compute tables */
/*
* for (n = 1; n < m4; n++) { if (n == m8) continue; ang = n *
* (float)TWOPI / m; c = Math.cos(ang); s = Math.sin(ang);
* tab[tabi][cn++] = (float)c; tab[tabi][spcn++] = (float)(- (s + c));
* tab[tabi][smcn++] =(float)( s - c); } }
* 
* /* Step 1
*/
xr1 = x0;
xr2 = xr1 + m2;
for (n = 0; n < m2; n++) {
tmp1 = x[xr1] + x[xr2];
x[xr2] = x[xr1] - x[xr2];
x[xr1] = tmp1;
xr1++;
xr2++;
}


/* Step 2 */
xr1 = x0 + m2 + m4;
for (n = 0; n < m4; n++) {
x[xr1] = -x[xr1];
xr1++;
}


/* Steps 3 & 4 */
xr1 = x0 + m2;
xi1 = xr1 + m4;
if (logm >= 4) {
nel = m4 - 2;
cn = 0;
spcn = cn + nel;
smcn = spcn + nel;
}


xr1++;
xi1++;
for (n = 1; n < m4; n++) {
if (n == m8) {
tmp1 = (float) (SQHALF * (x[xr1] + x[xi1]));
x[xi1] = (float) (SQHALF * (x[xi1] - x[xr1]));
x[xr1] = tmp1;
} else {// System.out.println ("logm-4="+(logm-4));
tmp2 = tab[logm - 4][cn++] * (x[xr1] + x[xi1]);
tmp1 = tab[logm - 4][spcn++] * x[xr1] + tmp2;
x[xr1] = tab[logm - 4][smcn++] * x[xi1] + tmp2;
x[xi1] = tmp1;
}
// System.out.println ("logm-4="+(logm-4));
xr1++;
xi1++;
}


/* Call rsrec again with half DFT length */
rsrec(x, logm - 1);


/*
* Call complex DFT routine, with quarter DFT length. Constants have to
* be recomputed, because they are static!
*/
m = 1 << logm;
m2 = m / 2;
m4 = 3 * (m / 4);
srrec(x, x0 + m2, x0 + m4, logm - 2);


/* Step 5: sign change & data reordering */
m = 1 << logm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;
xr1 = x0 + m2 + m4;
xr2 = x0 + m - 1;
for (n = 0; n < m8; n++) {
tmp1 = x[xr1];
x[xr1++] = -x[xr2];
x[xr2--] = -tmp1;
}
xr1 = x0 + m2 + 1;
xr2 = x0 + m - 2;
for (n = 0; n < m8; n++) {
tmp1 = x[xr1];
x[xr1++] = -x[xr2];
x[xr2--] = tmp1;
xr1++;
xr2--;
}
if (logm == 2)
x[3] = -x[3];
}


/*
* --------------------------------------------------------------------- *
* Recursive part of the inverse RSFFT algorithm. Not externally * callable.
* * --------------------------------------------------------------------
*/


void rsirec(float x[], int logm) {
int m, m2, m4, m8, nel, n;
int xr1, xr2, xi1;
int x0 = 0;
int cn, spcn, smcn;
float tmp1, tmp2;
cn = 0;
smcn = 0;
spcn = 0;


/* Check range of logm */
try {
if ((logm < 0) || (logm > MAXLOGM)) {
System.err.println("FFT length m is too big: log2(m) = " + logm
+ "is out of bounds [" + 0 + "," + MAXLOGM + "]");
throw new OutofborderException(logm);
}
} catch (OutofborderException e) {
throw new OutOfMemoryError();
}


/* Compute trivial cases */
if (logm < 2) {
if (logm == 1) { /* length m = 2 */
xr2 = x0 + 1;
tmp1 = x[x0] + x[xr2];
x[xr2] = x[x0] - x[xr2];
x[0] = tmp1;
return;
} else if (logm == 0)
return; /* length m = 1 */
}


/* Compute a few constants */
m = 1 << logm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;


/* Build tables of butterfly coefficients, if necessary */
// if((logm >= 4) && (tab[logm-4] == NULL)) {


/* Allocate memory for tables */
/*
* el = m4 - 2; if ((tab[logm-4] = (float *) calloc(3 * nel,
* sizeof(float))) == NULL) {
* printf("Error : RSFFT : not enough memory for cosine tables.\n");
* error_exit(); }
* 
* /* Initialize pointers
*/
// cn = tab[logm-4] ; spcn = cn + nel; smcn = spcn + nel;


/* Compute tables */
/*
* (n = 1; n < m4; n++) { if (n == m8) continue; ang = n * TWOPI / m; c
* = cos(ang); s = sin(ang);cn++ = c; *spcn++ = - (s + c); *smcn++ = s -
* c; } } /* Reverse Step 5: sign change & data reordering
*/
if (logm == 2)
x[3] = -x[3];
xr1 = x0 + m2 + 1;
xr2 = x0 + m - 2;
for (n = 0; n < m8; n++) {
tmp1 = x[xr1];
x[xr1++] = x[xr2];
x[xr2--] = -tmp1;
xr1++;
xr2--;
}
xr1 = x0 + m2 + m4;
xr2 = x0 + m - 1;
for (n = 0; n < m8; n++) {
tmp1 = x[xr1];
x[xr1++] = -x[xr2];
x[xr2--] = -tmp1;
}
/* Call rsirec again with half DFT length */
rsirec(x, logm - 1);


/*
* Call complex DFT routine, with quarter DFT length. Constants have to
* be recomputed, because they are static!
*/


/* Now in Java version, we set the multiple Constant to be global */
m = 1 << logm;
m2 = m / 2;
m4 = 3 * (m / 4);
srrec(x, x0 + m4, x0 + m2, logm - 2);


/* Reverse Steps 3 & 4 */
m = 1 << logm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;
xr1 = x0 + m2;
xi1 = xr1 + m4;
if (logm >= 4) {
nel = m4 - 2;
cn = 0;
spcn = cn + nel;
smcn = spcn + nel;
}
xr1++;
xi1++;
for (n = 1; n < m4; n++) {
if (n == m8) {
tmp1 = (float) (SQHALF * (x[xr1] - x[xi1]));
x[xi1] = (float) (SQHALF * (x[xi1] + x[xr1]));
x[xr1] = tmp1;
} else {
tmp2 = tab[logm - 4][cn++] * (x[xr1] + x[xi1]);
tmp1 = tab[logm - 4][smcn++] * x[xr1] + tmp2;
x[xr1] = tab[logm - 4][spcn++] * x[xi1] + tmp2;
x[xi1] = tmp1;
}
xr1++;
xi1++;
}


/* Reverse Step 2 */
xr1 = x0 + m2 + m4;
for (n = 0; n < m4; n++) {
x[xr1] = -x[xr1];
xr1++;
}


/* Reverse Step 1 */
xr1 = x0;
xr2 = xr1 + m2;
for (n = 0; n < m2; n++) {
tmp1 = x[xr1] + x[xr2];
x[xr2] = x[xr1] - x[xr2];
x[xr1] = tmp1;
xr1++;
xr2++;
}
}


/*
* -------------------------------------------------------------------- *
* Recursive part of the SRFFT algorithm. *
* --------------------------------------------------------------------
*/


void srrec(float x[], int xr, int xi, int logm) {
int m, m2, m4, m8, nel, n;
// int x0=0;
int xr1, xr2, xi1, xi2;
int cn, spcn, smcn, c3n, spc3n, smc3n;
float tmp1, tmp2;
cn = 0;
spcn = 0;
smcn = 0;
c3n = 0;
spc3n = 0;
smc3n = 0;


/* Check range of logm */
try {
if ((logm < 0) || (logm > MAXLOGM)) {
System.err.println("FFT length m is too big: log2(m) = " + logm
+ "is out of bounds [" + 0 + "," + MAXLOGM + "]");


throw new OutofborderException(logm);
}
} catch (OutofborderException e) {
throw new OutOfMemoryError();
}


/* Compute trivial cases */
if (logm < 3) {
if (logm == 2) { /* length m = 4 */
xr2 = xr + 2;
xi2 = xi + 2;
tmp1 = x[xr] + x[xr2];
x[xr2] = x[xr] - x[xr2];
x[xr] = tmp1;
tmp1 = x[xi] + x[xi2];
x[xi2] = x[xi] - x[xi2];
x[xi] = tmp1;
xr1 = xr + 1;
xi1 = xi + 1;
xr2++;
xi2++;
tmp1 = x[xr1] + x[xr2];
x[xr2] = x[xr1] - x[xr2];
x[xr1] = tmp1;
tmp1 = x[xi1] + x[xi2];
x[xi2] = x[xi1] - x[xi2];
x[xi1] = tmp1;
xr2 = xr + 1;
xi2 = xi + 1;
tmp1 = x[xr] + x[xr2];
x[xr2] = x[xr] - x[xr2];
x[xr] = tmp1;
tmp1 = x[xi] + x[xi2];
x[xi2] = x[xi] - x[xi2];
x[xi] = tmp1;
xr1 = xr + 2;
xi1 = xi + 2;
xr2 = xr + 3;
xi2 = xi + 3;
tmp1 = x[xr1] + x[xi2];
tmp2 = x[xi1] + x[xr2];
x[xi1] = x[xi1] - x[xr2];
x[xr2] = x[xr1] - x[xi2];
x[xr1] = tmp1;
x[xi2] = tmp2;
return;
}


else if (logm == 1) { /* length m = 2 */
xr2 = xr + 1;
xi2 = xi + 1;
tmp1 = x[xr] + x[xr2];
x[xr2] = x[xr] - x[xr2];
x[xr] = tmp1;
tmp1 = x[xi] + x[xi2];
x[xi2] = x[xi] - x[xi2];
x[xi] = tmp1;
return;
} else if (logm == 0)
return; /* length m = 1 */
}


/* Compute a few constants */
m = 1 << logm;
m2 = m / 2;
m4 = m2 / 2;
m8 = m4 / 2;


/* Build tables of butterfly coefficients, if necessary */
// if ((logm >= 4) && (tab[logm-4] == NULL)) {


/* Allocate memory for tables */
/*
* nel = m4 - 2; if ((tab[logm-4] = (float *) calloc(6 * nel,
* sizeof(float))) == NULL) { exit(1); } /* Initialize pointers
*/


/*
* cn = tab[logm-4]; spcn = cn + nel; smcn = spcn + nel; c3n = smcn +
* nel; spc3n = c3n + nel; smc3n = spc3n + nel;
* 
* 
* /* Compute tables
*/
/*
* for (n = 1; n < m4; n++) { if (n == m8) continue; ang = n * TWOPI /
* m; c = cos(ang); s = sin(ang);cn++ = c; *spcn++ = - (s + c); *smcn++
* = s - c; ang = 3 * n * TWOPI / m; c = cos(ang); s = sin(ang);c3n++ =
* c; *spc3n++ = - (s + c); *smc3n++ = s - c; } }
* 
* 
* /* Step 1
*/
xr1 = xr;
xr2 = xr1 + m2;
xi1 = xi;
xi2 = xi1 + m2;


for (n = 0; n < m2; n++) {
tmp1 = x[xr1] + x[xr2];
x[xr2] = x[xr1] - x[xr2];
x[xr1] = tmp1;
tmp2 = x[xi1] + x[xi2];
x[xi2] = x[xi1] - x[xi2];
x[xi1] = tmp2;
xr1++;
xr2++;
xi1++;
xi2++;
}
/* Step 2 */
xr1 = xr + m2;
xr2 = xr1 + m4;
xi1 = xi + m2;
xi2 = xi1 + m4;
for (n = 0; n < m4; n++) {
tmp1 = x[xr1] + x[xi2];
tmp2 = x[xi1] + x[xr2];
x[xi1] = x[xi1] - x[xr2];
x[xr2] = x[xr1] - x[xi2];
x[xr1] = tmp1;
x[xi2] = tmp2;
xr1++;
xr2++;
xi1++;
xi2++;
}


/* Steps 3 & 4 */
xr1 = xr + m2;
xr2 = xr1 + m4;
xi1 = xi + m2;
xi2 = xi1 + m4;
if (logm >= 4) {
nel = m4 - 2;
cn = 0;
spcn = cn + nel;
smcn = spcn + nel;
c3n = smcn + nel;
spc3n = c3n + nel;
smc3n = spc3n + nel;
}
xr1++;
xr2++;
xi1++;
xi2++;
for (n = 1; n < m4; n++) {
if (n == m8) {
tmp1 = (float) (SQHALF * (x[xr1] + x[xi1]));
x[xi1] = (float) (SQHALF * (x[xi1] - x[xr1]));
x[xr1] = tmp1;
tmp2 = (float) (SQHALF * (x[xi2] - x[xr2]));
x[xi2] = (float) (-SQHALF * (x[xr2] + x[xi2]));
x[xr2] = tmp2;
} else {
tmp2 = tab[logm - 4][cn++] * (x[xr1] + x[xi1]);
tmp1 = tab[logm - 4][spcn++] * x[xr1] + tmp2;
x[xr1] = tab[logm - 4][smcn++] * x[xi1] + tmp2;
x[xi1] = tmp1;
tmp2 = tab[logm - 4][c3n++] * (x[xr2] + x[xi2]);
tmp1 = tab[logm - 4][spc3n++] * x[xr2] + tmp2;
x[xr2] = tab[logm - 4][smc3n++] * x[xi2] + tmp2;
x[xi2] = tmp1;
}
// System.out.println ("logm-4="+(logm-4));
xr1++;
xr2++;
xi1++;
xi2++;
}
/* Call ssrec again with half DFT length */
srrec(x, xr, xi, logm - 1);


/*
* Call ssrec again twice with one quarter DFT length. Constants have to
* be recomputed, because they are static!
*/
m = 1 << logm;
m2 = m / 2;
srrec(x, xr + m2, xi + m2, logm - 2);
m = 1 << logm;
m4 = 3 * (m / 4);
srrec(x, xr + m4, xi + m4, logm - 2);
}


/*
* -------------------------------------------------------------------- *
* Data unshuffling according to bit-reversed indexing. * * * Bit reversal
* is done using Evan's algorithm (Ref: D. M. W. * Evans,
* "An improved digit-reversal permutation algorithm...", * IEEE Trans.
* ASSP, Aug. 1987, pp. 1120-1125). *
* --------------------------------------------------------------------
*/


// static int brseed[256]; /* Evans' seed table */
// static int brsflg; /* flag for table building */


void creatbrseed(int logm) {
int lg2, n;
lg2 = logm >> 1;
n = 1 << lg2;
if (logm != (logm >> 1) << 1)
lg2++;
brseed[0] = 0;
brseed[1] = 1;
for (int j = 2; j <= lg2; j++) {
int imax = 1 << (j - 1);
for (int i = 0; i < imax; i++) {
brseed[i] <<= 1;
brseed[i + imax] = brseed[i] + 1;
}
}
}


void BR_permute(float x[], int logm) {
int i, j, imax, lg2, n;
int off, fj, gno;
float tmp;
int xp, xq, brp;
int x0 = 0;


lg2 = logm >> 1;
n = 1 << lg2;
if (logm != (logm >> 1) << 1)
lg2++;


/* Create seed table if not yet built */
/*
* if (brsflg != logm) { brsflg = logm; brseed[0] = 0; brseed[1] = 1;
* for (j=2; j <= lg2; j++) { imax = 1 << (j-1); for (i = 0; i < imax;
* i++) { brseed[i] <<= 1; brseed[i + imax] = brseed[i] + 1; } } }
*/
creatbrseed(logm);


/* Unshuffling loop */
for (off = 1; off < n; off++) {
fj = n * brseed[off];
i = off;
j = fj;
tmp = x[i];
x[i] = x[j];
x[j] = tmp;
xp = i;
brp = 1;


for (gno = 1; gno < brseed[off]; gno++) {
xp += n;
j = fj + brseed[brp++];
xq = x0 + j;
tmp = x[xp];
x[xp] = x[xq];
x[xq] = tmp;
}
}


}


class OutofborderException extends Exception {
public OutofborderException(int logm) {
super();
}
}
}

最后附带一个读取WAV文件：

// filename: WaveFileReader.java  // RobinTang  // 2012-08-23  import java.io.*;  public class WaveFileReader {    private String filename = null;    private int[][] data = null;    private int len = 0;    private String chunkdescriptor = null;    static private int lenchunkdescriptor = 4;    private long chunksize = 0;    static private int lenchunksize = 4;    private String waveflag = null;    static private int lenwaveflag = 4;    private String fmtubchunk = null;    static private int lenfmtubchunk = 4;    private long subchunk1size = 0;    static private int lensubchunk1size = 4;    private int audioformat = 0;    static private int lenaudioformat = 2;    private int numchannels = 0;    static private int lennumchannels = 2;    private long samplerate = 0;    static private int lensamplerate = 2;    private long byterate = 0;    static private int lenbyterate = 4;    private int blockalign = 0;    static private int lenblockling = 2;    private int bitspersample = 0;    static private int lenbitspersample = 2;    private String datasubchunk = null;    static private int lendatasubchunk = 4;    private long subchunk2size = 0;    static private int lensubchunk2size = 4;    private FileInputStream fis = null;    private BufferedInputStream bis = null;    private boolean issuccess = false;    public WaveFileReader(String filename) {      this.initReader(filename);    }    // 判断是否创建wav读取器成功    public boolean isSuccess() {      return issuccess;    }    // 获取每个采样的编码长度，8bit或者16bit    public int getBitPerSample(){      return this.bitspersample;    }    // 获取采样率    public long getSampleRate(){      return this.samplerate;    }    // 获取声道个数，1代表单声道 2代表立体声    public int getNumChannels(){      return this.numchannels;    }    // 获取数据长度，也就是一共采样多少个    public int getDataLen(){      return this.len;    }    // 获取数据    // 数据是一个二维数组，[n][m]代表第n个声道的第m个采样值    public int[][] getData(){      return this.data;    }    private void initReader(String filename){      this.filename = filename;      try {        fis = new FileInputStream(this.filename);        bis = new BufferedInputStream(fis);        this.chunkdescriptor = readString(lenchunkdescriptor);        if(!chunkdescriptor.endsWith("RIFF"))          throw new IllegalArgumentException("RIFF miss, " + filename + " is not a wave file.");        this.chunksize = readLong();        this.waveflag = readString(lenwaveflag);        if(!waveflag.endsWith("WAVE"))          throw new IllegalArgumentException("WAVE miss, " + filename + " is not a wave file.");        this.fmtubchunk = readString(lenfmtubchunk);        if(!fmtubchunk.endsWith("fmt "))          throw new IllegalArgumentException("fmt miss, " + filename + " is not a wave file.");        this.subchunk1size = readLong();        this.audioformat = readInt();        this.numchannels = readInt();        this.samplerate = readLong();        this.byterate = readLong();        this.blockalign = readInt();        this.bitspersample = readInt();        this.datasubchunk = readString(lendatasubchunk);        if(!datasubchunk.endsWith("data"))          throw new IllegalArgumentException("data miss, " + filename + " is not a wave file.");        this.subchunk2size = readLong();        this.len = (int)(this.subchunk2size/(this.bitspersample/8)/this.numchannels);        this.data = new int[this.numchannels][this.len];                 for(int i=0; i        for(int n=0; n          if(this.bitspersample == 8){              this.data[n][i] = bis.read();            }            else if(this.bitspersample == 16){              this.data[n][i] = this.readInt();            }          }        }        issuccess = true;      } catch (Exception e) {        e.printStackTrace();      }      finally{        try{        if(bis != null)          bis.close();        if(fis != null)          fis.close();        }        catch(Exception e1){          e1.printStackTrace();        }      }    }    private String readString(int len){      byte[] buf = new byte[len];      try {        if(bis.read(buf)!=len)          throw new IOException("no more data!!!");      } catch (IOException e) {        e.printStackTrace();      }      return new String(buf);    }    private int readInt(){      byte[] buf = new byte[2];      int res = 0;      try {        if(bis.read(buf)!=2)          throw new IOException("no more data!!!");        res = (buf[0]&0x000000FF) | (((int)buf[1])<<8);      } catch (IOException e) {        e.printStackTrace();      }      return res;    }    private long readLong(){      long res = 0;      try {        long[] l = new long[4];        for(int i=0; i<4; ++i){          l[i] = bis.read();          if(l[i]==-1){            throw new IOException("no more data!!!");          }        }        res = l[0] | (l[1]<<8) | (l[2]<<16) | (l[3]<<24);      } catch（IOException e）{        e.printStackTrace（）;      }      return res;    }    私人字节[]的ReadBytes（INT LEN）{      字节[] buf中=新的字节[长度];        尝试     {  （！bis.read（BUF）= LEN）如果          抛出新的IOException异常（“没有更多的数据!!!” ）;      } catch（IOException e）{        e.printStackTrace（）;      }      return buf;    }  }