Main Content

Autoregressive power spectral density estimate — covariance method

returns
the power spectral density (PSD) estimate, `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.

uses `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 [0,2*π*].

`[`

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.