% error: [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,:))));

- hanning % Return the filter coefficients of a Hanning window of length @var{m}.
- window % Create a @var{n}-point windowing from the function @var{f}. The

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