pcov
Autoregressive power spectral density estimate — covariance method
Syntax
Description
pxx = pcov(x,order)pxx,
of a discrete-time signal, x, found using the
covariance method. When x is a vector, it is
treated as a single channel. When x is a matrix,
the PSD is computed independently for each column and stored in the
corresponding column of pxx. pxx is
the distribution of power per unit frequency. The frequency is expressed
in units of rad/sample. order is the order of
the autoregressive (AR) model used to produce the PSD estimate.
pxx = pcov(x,order,nfft)nfft points
in the discrete Fourier transform (DFT). For real x, pxx has
length (nfft/2+1) if nfft is
even, and (nfft+1)/2 if nfft is
odd. For complex–valued x, pxx always
has length nfft. If you omit nfft,
or specify it as empty, then pcov uses a default
DFT length of 256.
[
returns the vector of normalized angular frequencies, pxx,w] = pcov(___)w, at which the PSD
is estimated. w has units of radians/sample. For real-valued signals,
w spans the interval [0, π] when nfft is even and [0,π) when nfft is odd. For complex–valued signals,
w always spans the interval [0,2π].
[
returns a frequency vector, pxx,f] = pcov(___,fs)f, in cycles per unit time. The sampling
frequency, fs, is the number of samples per unit time. If the unit of time
is seconds, then f is in cycles/second (Hz). For real-valued signals,
f spans the interval [0,fs/2] when
nfft is even and [0,fs/2) when
nfft is odd. For complex-valued signals, f spans the
interval [0,fs).
[
returns the two-sided AR PSD estimates at the frequencies specified in the vector,
pxx,f] = pcov(x,order,f,fs)f. The vector f must contain at least two elements,
because otherwise the function interprets it as nfft. The frequencies in
f are in cycles per unit time. The sampling frequency,
fs, is the number of samples per unit time. If the unit of time is
seconds, then f is in cycles/second (Hz).
[___, returns
the pxxc] = pcov(___,'ConfidenceLevel',probability)probability × 100%
confidence intervals for the PSD estimate in pxxc.
pcov(___) with no output arguments
plots the AR PSD estimate in dB per unit frequency in the current
figure window.
Examples
Covariance-Method PSD Estimate of an AR(4) Process
Create a realization of an AR(4) wide-sense stationary random process. Estimate the PSD using the covariance method. Compare the PSD estimate based on a single realization to the true PSD of the random process.
Create an AR(4) system function. Obtain the frequency response and plot the PSD of the system.
A = [1 -2.7607 3.8106 -2.6535 0.9238]; [H,F] = freqz(1,A,[],1); plot(F,20*log10(abs(H))) xlabel('Frequency (Hz)') ylabel('PSD (dB/Hz)')
Create a realization of the AR(4) random process. Set the random number generator to the default settings for reproducible results. The realization is 1000 samples in length. Assume a sampling frequency of 1 Hz. Use pcov to estimate the PSD for a 4th-order process. Compare the PSD estimate with the true PSD.
rng default x = randn(1000,1); y = filter(1,A,x); [Pxx,F] = pcov(y,4,1024,1); hold on plot(F,10*log10(Pxx)) legend('True Power Spectral Density','pcov PSD Estimate')
Covariance-Method PSD Estimate of a Multichannel Signal
Create a multichannel signal consisting of three sinusoids in additive white Gaussian noise. The sinusoids' frequencies are 100 Hz, 200 Hz, and 300 Hz. The sampling frequency is 1 kHz, and the signal has a duration of 1 s.
Fs = 1000; t = 0:1/Fs:1-1/Fs; f = [100;200;300]; x = cos(2*pi*f*t)'+randn(length(t),3);
Estimate the PSD of the signal using the covariance method with a 12th-order autoregressive model. Use the default DFT length. Plot the estimate.
morder = 12; pcov(x,morder,[],Fs)
