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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 overlapping segments that produces 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.

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(F,T,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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