Autoregressive power spectral density estimate — Yule-Walker method

returns
the power spectral density estimate, `pxx`

= pyulear(`x`

,`order`

)`pxx`

, of
a discrete-time signal, `x`

, found using the Yule-Walker
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`

= pyulear(`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 `pyulear`

uses a default
DFT length of 256.

`[`

returns a frequency vector, `pxx`

,`f`

] = pyulear(___,`fs`

)`f`

, in cycles per unit time. The
sample rate, `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`

] = pyulear(`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 sample rate, `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`

] = pyulear(___,'ConfidenceLevel',`probability`

)`probability`

× 100%
confidence intervals for the PSD estimate in `pxxc`

.

`pyulear(___)`

with no output
arguments plots the AR PSD estimate in dB per unit frequency in the
current figure window.