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Spectrogram Computation

This section lists the spectrogram function called in the Matlab code displayed in Fig.8.11.

function X = spectrogram(x,nfft,fs,window,noverlap,doplot,dbclip);

%SPECTROGRAM Calculate spectrogram from signal.
%     spectrogram for the signal in vector A.  
% NFFT is the FFT size used for each frame of A.  It should be a
% power of 2 for fastest computation of the spectrogram.
% Fs is the sampling frequency. Since all processing parameters are
% in units of samples, Fs does not effect the spectrogram itself,
% but it is used for axis scaling in the plot produced when
% SPECTROGRAM is called with no output argument (see below).
% WINDOW is the length M window function applied, IN ZERO-PHASE
% FORM, to each frame of A.  M cannot exceed NFFT.  For M<NFFT,
% NFFT-M zeros are inserted in the FFT buffer (for interpolated
% zero-phase processing).  The window should be supplied in CAUSAL
% NOVERLAP is the number of samples the sections of A overlap, if
% nonnegative.  If negative, -NOVERLAP is the "hop size", i.e., the
% number of samples to advance successive windows.  (The overlap is
% the window length minus the hop size.)  The hop size is called
% NHOP below.  NOVERLAP must be less than M.
% If doplot is nonzero, or if there is no output argument, the 
% spectrogram is displayed.
% When the spectrogram is displayed, it is "clipped" dbclip dB
% below its maximum magnitude.  The default clipping level is 100 
% dB down.
% Thus, SPECTROGRAM splits the signal into overlapping segments of
% length M, windows each segment with the length M WINDOW vector, in
% zero-phase form, and forms the columns of B with their
% zero-padded, length NFFT discrete Fourier transforms.
% With no output argument B, SPECTROGRAM plots the dB magnitude of
% the spectrogram in the current figure, using
% IMAGESC(T,F,20*log10(ABS(B))), AXIS XY, COLORMAP(JET) so the low
% frequency content of the first portion of the signal is displayed
% in the lower left corner of the axes.
% Each column of B contains an estimate of the short-term,
% time-localized frequency content of the signal A.  Time increases
% linearly across the columns of B, from left to right.  Frequency
% increases linearly down the rows, starting at 0.
% If A is a length NX complex signal, B is returned as a complex
% matrix with NFFT rows and
%      k = floor((NX-NOVERLAP)/(length(WINDOW)-NOVERLAP)) 
%        = floor((NX-NOVERLAP)/NHOP)
% columns.  When A is real, only the NFFT/2+1 rows are needed when
% NFFT even, and the first (NFFT+1)/2 rows are sufficient for
% inversion when NFFT is odd.
% See also: Matlab and Octave's SPECGRAM and STFT functions.

if nargin<7, dbclip=100; end
if nargin<6, doplot=0; end
if nargin<5, noverlap=256; end
if nargin<4, window=hamming(512); end
if nargin<3, fs=1; end
if nargin<2, nfft=2048; end

x = x(:); % make sure it's a column

M = length(window);
if length(x)<M, x = [x;zeros(M-length(x),1)]; end;
if (M<2) 
  % (Matlab's specgram allows window to be a scalar specifying
  % the length of a Hanning window.)
  error('spectrogram: Expect complete window, not just its length'); 
Modd = mod(M,2); % 0 if M even, 1 if odd
Mo2 = (M-Modd)/2;
w = window(:); % Make sure it's a column
zp = zeros(nfft-M,1);
wzp = [w(Mo2+1:M);zp;w(1:Mo2)];

noverlap = round(noverlap); % in case non-integer
if noverlap<0
  nhop = - noverlap;
  noverlap = M-nhop;
  nhop = M-noverlap;

nx = length(x);
nframes = 1+floor((nx-noverlap)/nhop);

X = zeros(nfft,nframes);
xoff = 0;
for m=1:nframes-1
  xframe = x(xoff+1:xoff+M); % extract frame of input data
  xoff = xoff + nhop;   % advance in-pointer by hop size
  xzp = [xframe(Mo2+1:M);zp;xframe(1:Mo2)];
  xw = wzp .* xzp;
  X(:,m) = fft(xw);

if (nargout==0) | doplot
  t = (0:nframes-1)*nhop/fs;
  f = 0.001*(0:nfft-1)*fs/nfft;
  Xdb = 20*log10(abs(X));
  Xmax = max(max(Xdb));
  % Clip lower limit so nulls don't dominate:
  clipvals = [Xmax-dbclip,Xmax];
  % grid;
  xlabel('Time (sec)');
  ylabel('Freq (kHz)');

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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-10-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University