Fourier and Laplace 371
R.4.126 The MATLAB function spectrum(x) returns the script fi le specpsd is executed and
the resulting plots are shown in Figures 4.20 and 4.21 plot of psd(f) with the default
given by length(f) = 256 or less.
R.4.127 The MATLAB function spectrum(x,y) estimates the power density of the sequences
x and y, and returns the spectral analysis for x and y in a tablelike format, where
the fi rst fi ve columns are denoted by Pxx, Pyy, Pxy, Txy, and Cxy, where
Pxx denotes the psd of x
Pyy represents the psd of y
Pxy represents the cross-spectral density
Txy represents the complex transfer function that relates input x to the output y
Cxy denotes the coherence relation between the system input x and its output y
The remaining three columns provide confi dence ranges.
R.4.128 The coherent relation Cxy indicates by means of the coeffi cients the degree of similar-
ity between the two given sequences x and y, over a normalized range of frequen-
cies. The range of the coeffi cients of similarity are defi ned between 0 and 1, where 0
indicates no similarity and 1 indicates a high degree of similarity between x and y.
R.4.129 The MATLAB function spectrum(x,y), with no explicit output, returns these fi ve
plots: Pxx, Pyy, magnitude [Txy], phase[Txy], and Cxy.
R.4.130 The MATLAB function cohere(x,y) returns the plot of the coeffi cients of similarity
between x and y, indicating how well the input x corresponds to the output y, over
a normalized frequency range.Spectrogram of the speech file mtlb
1
0.8
0.60.40.20
0Frequency500 1000 1500
Time
Specgram of sinusoid + noise
10.80.60.4
0.20Frequency0 500 1000 1500
TimePower spec. den. of mtlbFrequency
Power spec. den. of sinus. + noise20− 20− 40− 600Power spectrum magnitude (dB) (^0) 0.5 1
30
20
10
0
(^0) 0.5 1
− 10
Frequency
Power spectrum magnitude (dB)
FIGURE 4.21
(See color insert following page 374.) Plots of parts 5, 6, 7, and 8 of R.4.125.