marytts.util.math

Class FFT

java.lang.Object

marytts.util.math.FFT

public class FFT
extends Object

Author:

Marc Schröder

Constructor Summary

Constructors

Constructor and Description
FFT()

Method Summary

Methods

Modifier and Type	Method and Description
static double[]	autoCorrelate(double[] signal) Compute the autocorrelation of a signal, by inverse transformation of its power spectrum.
static double[]	autoCorrelateWithZeroPadding(double[] signal) Compute the autocorrelation of a signal, by inverse transformation of its power spectrum.
static double[]	computeAmplitudeSpectrum_FD(double[] fft) From the result of the FFT (in the frequency domain), compute the absolute value for each positive frequency, i.e.
static double[]	computeAmplitudeSpectrum(double[] signal) Convenience method for computing the absolute amplitude spectrum of a real signal.
static double[]	computeLogAmplitudeSpectrum_FD(double[] fft) From the result of the FFT (in the frequency domain), compute the log amplitude for each positive frequency.
static double[]	computeLogAmplitudeSpectrum(double[] signal) Convenience method for computing the log amplitude spectrum of a real signal.
static double[]	computeLogPowerSpectrum_FD(double[] fft) From the result of the FFT, compute the log (dB) power for each positive frequency.
static double[]	computeLogPowerSpectrum(double[] signal) Convenience method for computing the log (dB) power spectrum of a real signal.
static double[]	computePhaseSpectrum_FD(double[] fft) From the result of the FFT (in the frequency domain), compute the phase spectrum for each positive frequency.
static double[]	computePowerSpectrum_FD(double[] fft) From the result of the FFT (in the frequency domain), compute the power for each positive frequency.
static double[]	computePowerSpectrum(double[] signal) Convenience method for computing the absolute power spectrum of a real signal.
static double[]	convolve_FD(double[] signal1, double[] fft2) Compute the convolution of two signals, by multiplying them in the frequency domain.
static double[]	convolve_FD(double[] signal1, double[] fft2, double deltaT) Compute the convolution of two signals, by multiplying them in the frequency domain.
static double[]	convolve(double[] signal1, double[] signal2) Compute the convolution of two signals, by multiplying them in the frequency domain.
static double[]	convolve(double[] signal1, double[] signal2, double deltaT) Compute the convolution of two signals, by multiplying them in the frequency domain.
static double[]	convolveWithZeroPadding(double[] signal1, double[] signal2) Compute the convolution of two signals, by multipying them in the frequency domain.
static double[]	convolveWithZeroPadding(double[] signal1, double[] signal2, double deltaT) Compute the convolution of two signals, by multipying them in the frequency domain.
static double[]	correlate(double[] signal1, double[] signal2) Compute the correlation of two signals, by multiplying the transform of signal2 with the conjugate complex of the transform of signal1, in the frequency domain.
static double[]	correlateWithZeroPadding(double[] signal1, double[] signal2) Compute the correlation of two signals, by multipying them in the frequency domain.
static void	main(String[] args)
static void	realTransform(double[] data, boolean inverse) Calculates the Fourier transform of a set of n real-valued data points.
static void	transform(double[] realAndImag, boolean inverse) Carry out the FFT or inverse FFT, and return the result in the same arrays given as parameters.
static void	transform(double[] real, double[] imag, boolean inverse) Carry out the FFT or inverse FFT, and return the result in the same arrays given as parameters.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FFT

public FFT()

Method Detail

computeLogPowerSpectrum

public static double[] computeLogPowerSpectrum(double[] signal)

Convenience method for computing the log (dB) power spectrum of a real signal. The signal can be of any length; internally, zeroes will be added if signal length is not a power of two.

Parameters:

signal - the real signal for which to compute the power spectrum.

Returns:

the power spectrum, as an array of length N/2 (where N is the power of two greater than or equal to signal.length): the log of the squared absolute values of the lower half of the complex fourier transform array.

computeLogPowerSpectrum_FD

public static double[] computeLogPowerSpectrum_FD(double[] fft)

From the result of the FFT, compute the log (dB) power for each positive frequency.

Parameters:

fft - the array of real and imag parts of the complex number array, fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

an array of length real.length/2 containing numbers representing the log of the square of the absolute value of each complex number, p[i] = real[i]*real[i] + imag[i]*imag[i]

computePowerSpectrum

public static double[] computePowerSpectrum(double[] signal)

Convenience method for computing the absolute power spectrum of a real signal. The signal can be of any length; internally, zeroes will be added if signal length is not a power of two.

Parameters:

signal - the real signal for which to compute the power spectrum.

Returns:

the power spectrum, as an array of length N/2 (where N is the power of two greater than or equal to signal.length): the squared absolute values of the lower half of the complex fourier transform array.

computePowerSpectrum_FD

public static double[] computePowerSpectrum_FD(double[] fft)

From the result of the FFT (in the frequency domain), compute the power for each positive frequency.

Parameters:

fft - the array of real and imag parts of the complex number array, fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

an array of length real.length/2 containing numbers representing the square of the absolute value of each complex number, p[i] = real[i]*real[i] + imag[i]*imag[i]

computeLogAmplitudeSpectrum

public static double[] computeLogAmplitudeSpectrum(double[] signal)

Convenience method for computing the log amplitude spectrum of a real signal. The signal can be of any length; internally, zeroes will be added if signal length is not a power of two.

Parameters:

signal - the real signal for which to compute the power spectrum.

Returns:

the log amplitude spectrum, as an array of length N/2 (where N is the power of two greater than or equal to signal.length): the log of the absolute values of the lower half of the complex fourier transform array.

computeLogAmplitudeSpectrum_FD

public static double[] computeLogAmplitudeSpectrum_FD(double[] fft)

From the result of the FFT (in the frequency domain), compute the log amplitude for each positive frequency.

Parameters:

fft - the array of real and imag parts of the complex number array, fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

an array of length real.length/2 containing numbers representing the log of the square of the absolute value of each complex number, p[i] = real[i]*real[i] + imag[i]*imag[i]

computeAmplitudeSpectrum

public static double[] computeAmplitudeSpectrum(double[] signal)

Convenience method for computing the absolute amplitude spectrum of a real signal. The signal can be of any length; internally, zeroes will be added if signal length is not a power of two.

Parameters:

signal - the real signal for which to compute the power spectrum.

Returns:

the power spectrum, as an array of length N/2 (where N is the power of two greater than or equal to signal.length): the absolute values of the lower half of the complex fourier transform array.

computeAmplitudeSpectrum_FD

public static double[] computeAmplitudeSpectrum_FD(double[] fft)

From the result of the FFT (in the frequency domain), compute the absolute value for each positive frequency, i.e. the norm of each complex number in the lower half of the array

Parameters:

fft - the array of real and imag parts of the complex number array, fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

an array of length real.length/2 containing numbers representing the absolute value of each complex number, r[i] = sqrt(real[i]*real[i] + imag[i]*imag[i])

computePhaseSpectrum_FD

public static double[] computePhaseSpectrum_FD(double[] fft)

From the result of the FFT (in the frequency domain), compute the phase spectrum for each positive frequency.

Parameters:

fft - the array of real and imag parts of the complex number array, fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

an array of length real.length/2 containing numbers representing the phases of each complex number, phase[i] = atan(imag[i], real[i])

transform

public static void transform(double[] real,
             double[] imag,
             boolean inverse)

Carry out the FFT or inverse FFT, and return the result in the same arrays given as parameters. In the case of the "forward" FFT, real is the signal to transform, and imag is an empty array. After the call, real will hold the real part of the complex frequency array, and imag will hold the imaginary part. They are ordered such that first come positive frequencies from 0 to fmax, then the negative frequencies from -fmax to 0 (which are the mirror image of the positive frequencies). In the case of the inverse FFT, real and imag are in input the real and imaginary part of the complex frequencies, and in output, real is the signal. The method already computes the division by array length required for the inverse transform.

Parameters:

real - in "forward" FFT: as input=the time-domain signal to transform, as output=the real part of the complex frequencies; in inverse FFT: as input=the real part of the complex frequencies, as output= the time-domain signal.

imag - in "forward" FFT: as input=an empty array, as output=the imaginary part of the complex frequencies; in inverse FFT: as input=the imaginary part of the complex frequencies, as output= not used.

inverse - whether to calculate the FFT or the inverse FFT.

transform

public static void transform(double[] realAndImag,
             boolean inverse)

Carry out the FFT or inverse FFT, and return the result in the same arrays given as parameters. This works exactly like #transform(real, imag, boolean), but data is represented differently: the even indices of the input array hold the real part, the odd indices the imag part of each complex number.

Parameters:

realAndImag - the array of complex numbers to transform

inverse - whether to calculate the FFT or the inverse FFT.

realTransform

public static void realTransform(double[] data,
                 boolean inverse)

Calculates the Fourier transform of a set of n real-valued data points. Replaces this data (which is stored in array data[1..n]) by the positive frequency half of its complex Fourier transform. The real-valued first and last components of the complex transform are returned as elements data[1] and data[2], respectively. n must be a power of 2. This routine also calculates the inverse transform of a complex data array if it is the transform of real data. (Result in this case must be multiplied by 2/n.)

Parameters:

data - data

inverse - inverse

convolveWithZeroPadding

public static double[] convolveWithZeroPadding(double[] signal1,
                               double[] signal2,
                               double deltaT)

Compute the convolution of two signals, by multipying them in the frequency domain. Normalise the result with respect to deltaT (the inverse of the sampling rate). This method applies zero padding where necessary to ensure that the result is not polluted because of assumed periodicity. The two signals need not be of equal length.

Parameters:

signal1 - signal 1

signal2 - signal 2

deltaT - , the time difference between two samples (= 1/samplingrate)

Returns:

the convolved signal, with length signal1.length+signal2.length

convolveWithZeroPadding

public static double[] convolveWithZeroPadding(double[] signal1,
                               double[] signal2)

Compute the convolution of two signals, by multipying them in the frequency domain. This method applies zero padding where necessary to ensure that the result is not polluted because of assumed periodicity. The two signals need not be of equal length.

Parameters:

signal1 - signal 1

signal2 - signal 2

Returns:

the convolved signal, with length signal1.length+signal2.length

convolve

public static double[] convolve(double[] signal1,
                double[] signal2,
                double deltaT)

Compute the convolution of two signals, by multiplying them in the frequency domain. Normalise the result with respect to deltaT (the inverse of the sampling rate). This is the core method, requiring two signals of equal length, which must be a power of two, and not checking for pollution arising from the assumed periodicity of both signals.

Parameters:

signal1 - signal 1

signal2 - signal 2

deltaT - , the time difference between two samples (= 1/samplingrate)

Returns:

the convolved signal, of the same length as the two input signals

Throws:

IllegalArgumentException - if the two input signals do not have the same length.

convolve

public static double[] convolve(double[] signal1,
                double[] signal2)

Compute the convolution of two signals, by multiplying them in the frequency domain. This is the core method, requiring two signals of equal length, which must be a power of two, and not checking for pollution arising from the assumed periodicity of both signals.

Parameters:

signal1 - signal 1

signal2 - signal 2

Returns:

the convolved signal, of the same length as the two input signals

Throws:

IllegalArgumentException - if the two input signals do not have the same length.

convolve_FD

public static double[] convolve_FD(double[] signal1,
                   double[] fft2,
                   double deltaT)

Compute the convolution of two signals, by multiplying them in the frequency domain. Normalise the result with respect to deltaT (the inverse of the sampling rate). This is a specialised version of the core method, requiring two signals of equal length, which must be a power of two, and not checking for pollution arising from the assumed periodicity of both signals. In this version, the first signal is provided in the time domain, while the second is already transformed into the frequency domain.

Parameters:

signal1 - the first input signal, in the time domain

fft2 - the complex transform of the second signal, in the frequency domain fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

deltaT - , the time difference between two samples (= 1/samplingrate)

Returns:

the convolved signal, of the same length as the two input signals

Throws:

IllegalArgumentException - if the two input signals do not have the same length.

convolve_FD

public static double[] convolve_FD(double[] signal1,
                   double[] fft2)

Compute the convolution of two signals, by multiplying them in the frequency domain. This is a specialised version of the core method, requiring two signals of equal length, which must be a power of two, and not checking for pollution arising from the assumed periodicity of both signals. In this version, the first signal is provided in the time domain, while the second is already transformed into the frequency domain.

Parameters:

signal1 - the first input signal, in the time domain

fft2 - the complex transform of the second signal, in the frequency domain fft[0] = real[0], fft[1] = real[N/2], fft[2*i] = real[i], fft[2*i+1] = imag[i] for 1≤i<N/2

Returns:

the convolved signal, of the same length as the two input signals

Throws:

IllegalArgumentException - if the two input signals do not have the same length.

correlateWithZeroPadding

public static double[] correlateWithZeroPadding(double[] signal1,
                                double[] signal2)

Compute the correlation of two signals, by multipying them in the frequency domain. This method applies zero padding where necessary to ensure that the result is not polluted because of assumed periodicity. The two signals need not be of equal length.

Parameters:

signal1 - signal 1

signal2 - signal 2

Returns:

the correlation function, with length signal1.length+signal2.length

correlate

public static double[] correlate(double[] signal1,
                 double[] signal2)

Compute the correlation of two signals, by multiplying the transform of signal2 with the conjugate complex of the transform of signal1, in the frequency domain. Sign convention: If signal2 is shifted by n to the right of signal2, then the correlation function will have a peak at positive n. This is the core method, requiring two signals of equal length, which must be a power of two, and not checking for pollution arising from the assumed periodicity of both signals.

Parameters:

signal1 - signal 1

signal2 - signal 2

Returns:

the correlated signal, of the same length as the two input signals

Throws:

IllegalArgumentException - if the two input signals do not have the same length.

autoCorrelate

public static double[] autoCorrelate(double[] signal)

Compute the autocorrelation of a signal, by inverse transformation of its power spectrum. This is the core method, requiring a signal whose length must be a power of two, and not checking for pollution arising from the assumed periodicity of the signal.

Parameters:

signal - signal

Returns:

the correlated signal, of the same length as the input signal

autoCorrelateWithZeroPadding

public static double[] autoCorrelateWithZeroPadding(double[] signal)

Compute the autocorrelation of a signal, by inverse transformation of its power spectrum. This method applies zero padding where necessary to ensure that the result is not polluted because of assumed periodicity.

Parameters:

signal - signal

Returns:

the correlated signal, of the same length as the input signal

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception