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Periodogram power spectral density estimate

`pxx = periodogram(x)`

`pxx = periodogram(x,window)`

`pxx = periodogram(x,window,nfft)`

`[pxx,w] = periodogram(___)`

`[pxx,f] = periodogram(___,fs)`

`[pxx,w] = periodogram(x,window,w)`

`[pxx,f] = periodogram(x,window,f,fs)`

`[___] = periodogram(x,window,___,freqrange)`

`[___] = periodogram(x,window,___,spectrumtype)`

`[___,pxxc] = periodogram(___,'ConfidenceLevel',probability)`

```
[rpxx,f]
= periodogram(___,'reassigned')
```

```
[rpxx,f,pxx,fc]
= periodogram(___,'reassigned')
```

`periodogram(___)`

returns
the periodogram power spectral density (PSD) estimate, `pxx`

= periodogram(`x`

)`pxx`

,
of the input signal, `x`

, found using a rectangular
window. 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`

. If `x`

is real-valued, `pxx`

is
a one-sided PSD estimate. If `x`

is complex-valued, `pxx`

is
a two-sided PSD estimate. The number of points, `nfft`

,
in the discrete Fourier transform (DFT) is the maximum of 256 or the
next power of two greater than the signal length.

uses `pxx`

= periodogram(`x`

,`window`

,`nfft`

)`nfft`

points
in the discrete Fourier transform (DFT). If `nfft`

is
greater than the signal length, `x`

is zero-padded
to length `nfft`

. If `nfft`

is
less than the signal length, the signal is wrapped modulo `nfft`

and
summed using `datawrap`

. For example, the input
signal `[1 2 3 4 5 6 7 8]`

with `nfft`

equal
to 4 results in the periodogram of ```
sum([1 5; 2 6; 3 7; 4
8],2)
```

.

`[`

returns
a frequency vector, `pxx`

,`f`

] = periodogram(___,`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`

). `fs`

must
be the fourth input to `periodogram`

. To input
a sample rate and still use the default values of the preceding optional
arguments, specify these arguments as empty, `[]`

.

`[`

returns
the two-sided periodogram estimates at the frequencies specified in
the vector, `pxx`

,`f`

] = periodogram(`x`

,`window`

,`f`

,`fs`

)`f`

. `f`

must contain
at least two elements. 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).

`[___] = periodogram(`

returns
the PSD estimate if `x`

,`window`

,___,`spectrumtype`

)`spectrumtype`

is specified
as `'psd'`

and returns the power spectrum if `spectrumtype`

is
specified as `'power'`

.

`[___,`

returns
the `pxxc`

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

)`probability`

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

.

`periodogram(___)`

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

[1] Fulop, Sean A., and Kelly Fitz. "Algorithms for
computing the time-corrected instantaneous frequency (reassigned)
spectrogram, with applications." *Journal of the
Acoustical Society of America*. Vol. 119,
January 2006, pp. 360–371.

[2] Auger, François, and Patrick Flandrin. "Improving
the Readability of Time-Frequency and Time-Scale Representations by
the Reassignment Method." *IEEE ^{®} Transactions
on Signal Processing*. Vol. 43, May 1995,
pp. 1068–1089.

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