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spectrogram - Spectrogram using short-time Fourier transform

Syntax

S = spectrogram(x) S = spectrogram(x,window) S = spectrogram(x,window,noverlap) S = spectrogram(x,window,noverlap,nfft) S = spectrogram(x,window,noverlap,nfft,fs) [S,F,T] = spectrogram(x,window,noverlap,F) [S,F,T] = spectrogram(x,window,noverlap,F,fs) [S,F,T,P] = spectrogram(...) spectrogram(...)

Description

spectrogram, when used without any outputs, plots a spectrogram or, when used with an S output, returns the short-time Fourier transform of the input signal. To create a spectrogram from the returned short-time Fourier transform data, refer to the [S,F,T,P] syntax described below.

S = spectrogram(x) returns S, the short time Fourier transform of the input signal vector x. By default, x is divided into eight segments. If x cannot be divided exactly into eight segments, it is truncated. These default values are used.

window is a Hamming window of length nfft.
noverlap is the number of samples that each segment overlaps. The default value is the number producing 50% overlap between segments.
nfft is the FFT length and is the maximum of 256 or the next power of 2 greater than the length of each segment of x. (Instead of nfft, you can specify a vector of frequencies, F. See below for more information.)
fs is the sampling frequency, which defaults to normalized frequency.

Each column of S contains an estimate of the short-term, time-localized frequency content of x. Time increases across the columns of S and frequency increases down the rows.

If x is a length Nx complex signal, S is a complex matrix with nfft rows and k columns, where for a scalar window

k = fix((Nx-noverlap)/(window-noverlap))

or if window is a vector

k = fix((Nx-noverlap)/(length(window)-noverlap))

For real x, the output S has (nfft/2+1) rows if nfft is even, and (nfft+1)/2 rows if nfft is odd.

S = spectrogram(x,window) uses the window specified. If window is an integer, x is divided into segments equal to that integer value and a Hamming window is used. If window is a vector, x is divided into segments equal to the length of window and then the segments are windowed using the window functions specified in the window vector. For a list of available windows see Windows.

Note To obtain the same results for the removed specgram function, specify a 'Hann' window of length 256.

S = spectrogram(x,window,noverlap) overlaps noverlap samples of each segment. noverlap must be an integer smaller than window or if window is a vector, smaller than the length of window.

S = spectrogram(x,window,noverlap,nfft) uses the nfft number of sampling points to calculate the discrete Fourier transform. nfft must be a scalar.

S = spectrogram(x,window,noverlap,nfft,fs) uses fs sampling frequency in Hz. If fs is specified as empty [], it defaults to 1 Hz.

[S,F,T] = spectrogram(x,window,noverlap,F) uses a vector F of frequencies in Hz. F must be a vector with at least two elements. This case computes the spectrogram at the frequencies in F using the Goertzel algorithm. The specified frequencies are rounded to the nearest DFT bin commensurate with the signal's resolution. In all other syntax cases where nfft or a default for nfft is used, the short-time Fourier transform is used. The F vector returned is a vector of the rounded frequencies. T is a vector of times at which the spectrogram is computed. The length of F is equal to the number of rows of S. The length of T is equal to k, as defined above and each value corresponds to the center of each segment.

[S,F,T] = spectrogram(x,window,noverlap,F,fs) uses a vector F of frequencies in Hz as above and uses the fs sampling frequency in Hz. If fs is specified as empty [], it defaults to 1 Hz.

[S,F,T,P] = spectrogram(...) returns a matrix P containing the power spectral density (PSD) of each segment. For real x, P contains the one-sided modified periodogram estimate of the PSD of each segment. For complex x and when you specify a vector of frequencies F, P contains the two-sided PSD.

The elements of the PSD matrix P are given by where is a real-valued scalar defined as follows

For the one-sided PSD,

where denotes the window function (Hamming by default) and is the sampling frequency. At zero and the Nyquist frequencies, the factor of 2 in the numerator is replaced by 1.
For the two-sided PSD,

at all frequencies.
If the sampling frequency is not specified, is replaced in the denominator by .

spectrogram(...) plots the PSD estimate for each segment on a surface in a figure window. The plot is created using

surf(T,F,10*log10(abs(P)));
axis tight;
view(0,90);

Using spectrogram(...,'freqloc') syntax and adding a 'freqloc' string (either 'xaxis' or 'yaxis') controls where the frequency axis is displayed. Using 'xaxis' displays the frequency on the x-axis. Using 'yaxis' displays frequency on the y-axis and time on the x-axis. The default is 'xaxis'. If you specify both a 'freqloc' string and output arguments, 'freqloc' is ignored.

Examples

Compute and display the PSD of each segment of a quadratic chirp, which starts at 100 Hz and crosses 200 Hz at t = 1 sec.

T = 0:0.001:2;
X = chirp(T,100,1,200,'q');
spectrogram(X,128,120,128,1E3); 
title('Quadratic Chirp');

Compute and display the PSD of each segment of a linear chirp, which starts at DC and crosses 150 Hz at t = 1 sec. Display the frequency on the y-axis.

T = 0:0.001:2;
X = chirp(T,0,1,150);
[S,F,T,P] = spectrogram(X,256,250,256,1E3);
surf(T,F,10*log10(P),'edgecolor','none'); axis tight; 
view(0,90);
xlabel('Time (Seconds)'); ylabel('Hz');

References

[1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989, pp.713-718.

[2] Rabiner, L.R., and R.W. Schafer, Digital Processing of Speech Signals, Prentice-Hall, Englewood Cliffs, NJ, 1978.

spectrogram - Spectrogram using short-time Fourier transform

Syntax

Description

Examples

References

See Also

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