--- /dev/null
+## Copyright (C) 1999-2001 Paul Kienzle <pkienzle@users.sf.net>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## usage: [S [, f [, t]]] = specgram(x [, n [, Fs [, window [, overlap]]]])
+##
+## Generate a spectrogram for the signal. This chops the signal into
+## overlapping slices, windows each slice and applies a Fourier
+## transform to determine the frequency components at that slice.
+##
+## x: vector of samples
+## n: size of fourier transform window, or [] for default=256
+## Fs: sample rate, or [] for default=2 Hz
+## window: shape of the fourier transform window, or [] for default=hanning(n)
+## Note: window length can be specified instead, in which case
+## window=hanning(length)
+## overlap: overlap with previous window, or [] for default=length(window)/2
+##
+## Return values
+## S is complex output of the FFT, one row per slice
+## f is the frequency indices corresponding to the rows of S.
+## t is the time indices corresponding to the columns of S.
+## If no return value is requested, the spectrogram is displayed instead.
+##
+## Example
+## x = chirp([0:0.001:2],0,2,500); # freq. sweep from 0-500 over 2 sec.
+## Fs=1000; # sampled every 0.001 sec so rate is 1 kHz
+## step=ceil(20*Fs/1000); # one spectral slice every 20 ms
+## window=ceil(100*Fs/1000); # 100 ms data window
+## specgram(x, 2^nextpow2(window), Fs, window, window-step);
+##
+## ## Speech spectrogram
+## [x, Fs] = auload(file_in_loadpath("sample.wav")); # audio file
+## step = fix(5*Fs/1000); # one spectral slice every 5 ms
+## window = fix(40*Fs/1000); # 40 ms data window
+## fftn = 2^nextpow2(window); # next highest power of 2
+## [S, f, t] = specgram(x, fftn, Fs, window, window-step);
+## S = abs(S(2:fftn*4000/Fs,:)); # magnitude in range 0<f<=4000 Hz.
+## S = S/max(S(:)); # normalize magnitude so that max is 0 dB.
+## S = max(S, 10^(-40/10)); # clip below -40 dB.
+## S = min(S, 10^(-3/10)); # clip above -3 dB.
+## imagesc(t, f, flipud(log(S))); # display in log scale
+##
+## The choice of window defines the time-frequency resolution. In
+## speech for example, a wide window shows more harmonic detail while a
+## narrow window averages over the harmonic detail and shows more
+## formant structure. The shape of the window is not so critical so long
+## as it goes gradually to zero on the ends.
+##
+## Step size (which is window length minus overlap) controls the
+## horizontal scale of the spectrogram. Decrease it to stretch, or
+## increase it to compress. Increasing step size will reduce time
+## resolution, but decreasing it will not improve it much beyond the
+## limits imposed by the window size (you do gain a little bit,
+## depending on the shape of your window, as the peak of the window
+## slides over peaks in the signal energy). The range 1-5 msec is good
+## for speech.
+##
+## FFT length controls the vertical scale. Selecting an FFT length
+## greater than the window length does not add any information to the
+## spectrum, but it is a good way to interpolate between frequency
+## points which can make for prettier spectrograms.
+##
+## After you have generated the spectral slices, there are a number of
+## decisions for displaying them. First the phase information is
+## discarded and the energy normalized:
+##
+## S = abs(S); S = S/max(S(:));
+##
+## Then the dynamic range of the signal is chosen. Since information in
+## speech is well above the noise floor, it makes sense to eliminate any
+## dynamic range at the bottom end. This is done by taking the max of
+## the magnitude and some minimum energy such as minE=-40dB. Similarly,
+## there is not much information in the very top of the range, so
+## clipping to a maximum energy such as maxE=-3dB makes sense:
+##
+## S = max(S, 10^(minE/10)); S = min(S, 10^(maxE/10));
+##
+## The frequency range of the FFT is from 0 to the Nyquist frequency of
+## one half the sampling rate. If the signal of interest is band
+## limited, you do not need to display the entire frequency range. In
+## speech for example, most of the signal is below 4 kHz, so there is no
+## reason to display up to the Nyquist frequency of 10 kHz for a 20 kHz
+## sampling rate. In this case you will want to keep only the first 40%
+## of the rows of the returned S and f. More generally, to display the
+## frequency range [minF, maxF], you could use the following row index:
+##
+## idx = (f >= minF & f <= maxF);
+##
+## Then there is the choice of colormap. A brightness varying colormap
+## such as copper or bone gives good shape to the ridges and valleys. A
+## hue varying colormap such as jet or hsv gives an indication of the
+## steepness of the slopes. The final spectrogram is displayed in log
+## energy scale and by convention has low frequencies on the bottom of
+## the image:
+##
+## imagesc(t, f, flipud(log(S(idx,:))));
+
+function [S_r, f_r, t_r] = specgram(x, n = min(256, length(x)), Fs = 2, window = hanning(n), overlap = ceil(length(window)/2))
+
+ if nargin < 1 || nargin > 5
+ print_usage;
+ ## make sure x is a vector
+ elseif columns(x) != 1 && rows(x) != 1
+ error ("specgram data must be a vector");
+ end
+ if columns(x) != 1, x = x'; end
+
+ ## if only the window length is given, generate hanning window
+ if length(window) == 1, window = hanning(window); end
+
+ ## should be extended to accept a vector of frequencies at which to
+ ## evaluate the fourier transform (via filterbank or chirp
+ ## z-transform)
+ if length(n)>1,
+ error("specgram doesn't handle frequency vectors yet");
+ endif
+
+ ## compute window offsets
+ win_size = length(window);
+ if (win_size > n)
+ n = win_size;
+ warning ("specgram fft size adjusted to %d", n);
+ end
+ step = win_size - overlap;
+
+ ## build matrix of windowed data slices
+ offset = [ 1 : step : length(x)-win_size ];
+ S = zeros (n, length(offset));
+ for i=1:length(offset)
+ S(1:win_size, i) = x(offset(i):offset(i)+win_size-1) .* window;
+ endfor
+
+ ## compute fourier transform
+ S = fft (S);
+
+ ## extract the positive frequency components
+ if rem(n,2)==1
+ ret_n = (n+1)/2;
+ else
+ ret_n = n/2;
+ end
+ S = S(1:ret_n, :);
+
+ f = [0:ret_n-1]*Fs/n;
+ t = offset/Fs;
+ if nargout==0
+ imagesc(t, f, 20*log10(abs(S)));
+ set (gca (), "ydir", "normal");
+ xlabel ("Time")
+ ylabel ("Frequency")
+ endif
+ if nargout>0, S_r = S; endif
+ if nargout>1, f_r = f; endif
+ if nargout>2, t_r = t; endif
+
+endfunction
+
+%!shared S,f,t,x
+%! Fs=1000;
+%! x = chirp([0:1/Fs:2],0,2,500); # freq. sweep from 0-500 over 2 sec.
+%! step=ceil(20*Fs/1000); # one spectral slice every 20 ms
+%! window=ceil(100*Fs/1000); # 100 ms data window
+%! [S, f, t] = specgram(x);
+
+%! ## test of returned shape
+%!assert (rows(S), 128)
+%!assert (columns(f), rows(S))
+%!assert (columns(t), columns(S))
+%!test [S, f, t] = specgram(x');
+%!assert (rows(S), 128)
+%!assert (columns(f), rows(S));
+%!assert (columns(t), columns(S));
+%!error (isempty(specgram([])));
+%!error (isempty(specgram([1, 2 ; 3, 4])));
+%!error (specgram)
+
+%!demo
+%! Fs=1000;
+%! x = chirp([0:1/Fs:2],0,2,500); # freq. sweep from 0-500 over 2 sec.
+%! step=ceil(20*Fs/1000); # one spectral slice every 20 ms
+%! window=ceil(100*Fs/1000); # 100 ms data window
+%!
+%! ## test of automatic plot
+%! [S, f, t] = specgram(x);
+%! specgram(x, 2^nextpow2(window), Fs, window, window-step);
+%! disp("shows a diagonal from bottom left to top right");
+%! input("press enter:","s");
+%!
+%! ## test of returned values
+%! S = specgram(x, 2^nextpow2(window), Fs, window, window-step);
+%! imagesc(20*log10(flipud(abs(S))));
+%! disp("same again, but this time using returned value");
+
+%!demo
+%! ## Speech spectrogram
+%! [x, Fs] = auload(file_in_loadpath("sample.wav")); # audio file
+%! step = fix(5*Fs/1000); # one spectral slice every 5 ms
+%! window = fix(40*Fs/1000); # 40 ms data window
+%! fftn = 2^nextpow2(window); # next highest power of 2
+%! [S, f, t] = specgram(x, fftn, Fs, window, window-step);
+%! S = abs(S(2:fftn*4000/Fs,:)); # magnitude in range 0<f<=4000 Hz.
+%! S = S/max(max(S)); # normalize magnitude so that max is 0 dB.
+%! S = max(S, 10^(-40/10)); # clip below -40 dB.
+%! S = min(S, 10^(-3/10)); # clip above -3 dB.
+%! imagesc(flipud(20*log10(S)));
+%!
+%! % The image contains a spectrogram of 'sample.wav'
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff