## 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. % % 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'); 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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