## 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.
% 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", 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.
%

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');
end;
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;
else
nhop = M-noverlap;
end

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

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