signal (version 0.5)

specgram: Spectogram plot

Description

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.

Usage

specgram(x, n = min(256, length(x)), Fs = 2, window = hanning(n), overlap = length(window)/2)

## S3 method for class 'specgram':
plot(x, ...)

## S3 method for class 'specgram':
print(x, ...)

Arguments

x

the vector of samples.

n

the size of the Fourier transform window.

Fs

the sample rate, Hz.

window

shape of the fourier transform window, defaults to hanning(n). The window length for a hanning window can be specified instead.

overlap

overlap with previous window, defaults to half the window length.

...

additional arguments (ignored).

Value

• For specgram list of class specgram with items:
• S
  complex output of the FFT, one row per slice.
• f
  the frequency indices corresponding to the rows of S.
• t
  the time indices corresponding to the columns of S..

Details

When results of specgram are printed, a spectogram will be plotted. As with lattice plots, automatic printing does not work inside loops and function calls, so explicit calls to print or plot are needed there. 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)<="" code=""> 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.

References

Octave Forge http://octave.sf.net

See Also

fft, image

Examples

specgram(chirp(seq(-2, 15, by = .001), 400, 10, 100, 'quadratic'))
specgram(chirp(seq(0, 5, by = 1/8000), 200, 2, 500, "logarithmic"), Fs = 8000)

data(wav)  # contains wav$rate, wav$sound
Fs = wav$rate
step = trunc(5*Fs/1000);     # one spectral slice every 5 ms
window = trunc(40*Fs/1000);  # 40 ms data window
fftn = 2^nextpow2(window); # next highest power of 2
spg = specgram(wav$sound, fftn, Fs, window, window-step)
S = abs(spg$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[S < 10^(-40/10)] = 10^(-40/10)   # clip below -40 dB.
S[S > 10^(-3/10)] = 10^(-3/10)    # clip above -3 dB.
image(t(20*log10(S)), axes = FALSE) #, col = gray(0:255 / 255))