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EST_fft.h
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/*************************************************************************/
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/* */
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/* Centre for Speech Technology Research */
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/* University of Edinburgh, UK */
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/* Copyright (c) 1995,1996 */
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/* All Rights Reserved. */
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/* the following conditions: */
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/* 1. The code must retain the above copyright notice, this list of */
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/* conditions and the following disclaimer. */
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/* 3. Original authors' names are not deleted. */
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/* 4. The authors' names are not used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THE UNIVERSITY OF EDINBURGH AND THE CONTRIBUTORS TO THIS WORK */
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/* DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING */
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/* ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT */
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/* SHALL THE UNIVERSITY OF EDINBURGH NOR THE CONTRIBUTORS BE LIABLE */
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/* FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES */
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/* AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, */
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/* ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF */
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/* THIS SOFTWARE. */
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/* */
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/*************************************************************************/
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#ifndef __EST_FFT_H__
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#define __EST_FFT_H__
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#include "EST_Wave.h"
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#include "EST_Track.h"
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#include "EST_FMatrix.h"
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/**@name Fast Fourier Transform functions
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<para>
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These are the low level functions where the actual FFT is
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performed. Both slow and fast implementations are available for
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historical reasons. They have identical functionality. At this time,
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vectors of complex numbers are handled as pairs of vectors of real and
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imaginary numbers.
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</para>
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<formalpara> <title>What is a Fourier Transform ?</title>
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<para>
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The Fourier transform of a signal gives us a frequency-domain
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representation of a time-domain signal. In discrete time, the Fourier
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Transform is called a Discrete Fourier Transform (DFT) and is given
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by:
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\[y_k = \sum_{t=0}^{n-1} x_t \; \omega_{n}^{kt} \; ; \; k=0...n-1 \]
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where \(y = (y_0,y_1,... y_{n-1})\) is the DFT (of order \(n\) ) of the
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signal \(x = (x_0,x_1,... x_{n-1})\), where
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\(\omega_{n}^{0},\omega_{n}^{1},... \omega_{n}^{n-1}\) are the n
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complex nth roots of 1.
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</para>
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<para>
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The Fast Fourier Transform (FFT) is a very efficient implementation of
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a Discrete Fourier Transform. See, for example "Algorithms" by Thomas
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H. Cormen, Charles E. Leiserson and Ronald L. Rivest (pub. MIT Press),
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or any signal processing textbook.
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</para>
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</formalpara>
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*/
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//@{
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/** Basic in-place FFT.
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<para>There's no point actually using this - use \Ref{fastFFT}
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instead. However, the code in this function closely matches the
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classic FORTRAN version given in many text books, so is at least easy
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to follow for new users.</para>
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<para>The length of <parameter>real</parameter> and
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<parameter>imag</parameter> must be the same, and must be a power of 2
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(e.g. 128).</para>
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@see slowIFFT
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@see FastFFT */
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int
slowFFT(
EST_FVector
&real,
EST_FVector
&imag);
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/** Alternate name for slowFFT
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*/
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inline
int
FFT(
EST_FVector
&real,
EST_FVector
&imag){
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return
slowFFT(real, imag);
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}
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/** Basic inverse in-place FFT
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int slowFFT
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*/
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int
slowIFFT(
EST_FVector
&real,
EST_FVector
&imag);
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/** Alternate name for slowIFFT
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*/
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inline
int
IFFT(
EST_FVector
&real,
EST_FVector
&imag){
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return
slowIFFT(real, imag);
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}
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/** Power spectrum using the fastFFT function.
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The power spectrum is simply the squared magnitude of the
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FFT. The result real and imaginary parts are both set equal
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to the power spectrum (you only need one of them !)
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*/
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int
power_spectrum(
EST_FVector
&real,
EST_FVector
&imag);
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/** Power spectrum using the slowFFT function
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*/
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int
power_spectrum_slow(
EST_FVector
&real,
EST_FVector
&imag);
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/** Fast FFT
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An optimised implementation by Tony Robinson to be used
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in preference to slowFFT
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*/
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int
fastFFT(
EST_FVector
&invec);
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// Auxiliary for fastFFT
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int
fastlog2(
int
);
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//@}
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#endif // __EST_FFT_H__
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include
sigpr
EST_fft.h
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