Matlab listing: spectrogram.m

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

%SPECTROGRAM Calculate spectrogram from signal.
%   B = SPECTROGRAM(A,NFFT,Fs,WINDOW,NOVERLAP) calculates the 
%   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
%   FORM.
%
%   NOVERLAP is the number of samples the sections of A overlap, if
%   nonnegative.  If negative, -NOVERLAP is the "hop size", \ie, 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.
%
%   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.
%
%   If DOPLOT is nonzero, the spectrogram will be plotted in any case.
%   DBDOWN (default=100) sets the clip level below the maximum in dB.
%
%   See also: Matlab's SPECGRAM function.
%   02/04/02/jos: Created
%   02/12/04/jos: Added dbdown

if nargin<7, dbdown=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(:);

nfft
M = length(window)
if (M<2) error(...
  'spectrogram: Expect complete window, not just its length'); 
end;
Modd = mod(M,2); % 0 if M even, 1 if odd
Mo2 = (M-Modd)/2;
w = window(:); % Make sure its a column
zp = zeros(nfft-M,1);
wzp = [w(Mo2+1:M);zp;w(1:Mo2)];

if noverlap<0
  nhop = - noverlap;
  noverlap = M-nhop;
else
  nhop = M-noverlap;
end

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

X = zeros(nfft,nframes);
x = x(:); % make sure it's a column
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);
end

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 to -dbdown dB so nulls don't dominate:
  clipvals = [Xmax-dbdown,Xmax];
  imagesc(t,f,Xdb,clipvals);
  % grid;
  axis xy;
  colormap(jet);
  xlabel('Time (sec)');
  ylabel('Freq (kHz)');
end

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.