# pspect

two sided cross-spectral estimate between 2 discrete time signals using the Welch's average periodogram method.

### Syntax

sm = pspect(sec_step, sec_leng, wtype, x) sm = pspect(sec_step, sec_leng, wtype, x, y) sm = pspect(sec_step, sec_leng, wtype, nx) sm = pspect(sec_step, sec_leng, wtype, nx, ny) [sm, cwp] = pspect(.., wpar)

### Arguments

- x
vector, the time-domain samples of the first signal.

- y
vector, the time-domain samples of the second signal. If

`y`

is omitted it is supposed to be equal to`x`

(auto-correlation). If it is present, it must have the same number of element than`x`

.- nx
a scalar : the number of samples in the

`x`

signal. In this case the segments of the`x`

signal are loaded by a user defined function named`getx`

(see below).- ny
a scalar : the number of samples in the

`y`

signal. In this case the segments of the y signal are loaded by a user defined function named`gety`

(see below). If present`ny`

must be equal to`nx`

.- sec_step
offset of each data window. The overlap

`D`

is given by`sec_leng - sec_step`

. If`sec_step == sec_leng/2`

50% overlap is made.- sec_leng
Number of points of the window.

- wtype
The window type

`'re'`

: rectangular`'tr'`

: triangular`'hm'`

: Hamming`'hn'`

: Hann`'kr'`

: Kaiser,in this case the wpar argument must be given`'ch'`

: Chebyshev, in this case the wpar argument must be given

- wpar
optional parameters for Kaiser and Chebyshev windows:

'kr':

`wpar`

must be a strictly positive number'ch':

`wpar`

must be a 2 element vector`[main_lobe_width,side_lobe_height]`

with`0<main_lobe_width<.5`

, and`side_lobe_height>0`

- sm
Two sided power spectral estimate in the interval

`[0,1]`

of the normalized frequencies. It is a row array with`sec_len`

elements. The array is real in case of auto-correlation and complex in case of cross-correlation.The associated normalized frequencies array is

`linspace(0,1,sec_len)`

.- cwp
the unspecified Chebyshev window parameter in case of Chebyshev windowing, or an empty matrix.

### Description

Computes the cross-spectrum estimate of two signals
`x`

and `y`

if both are given and the
auto-spectral estimate of `x`

otherwise. Spectral
estimate obtained using the modified periodogram method.

The cross spectrum of two signal `x`

and `y`

is defined as

The modified periodogram method of spectral estimation repeatedly
calculates the periodogram of windowed sub-sections of the data contained
in `x`

and `y`

. These periodograms are
then averaged together and normalized by an appropriate constant to obtain
the final spectral estimate. It is the averaging process which reduces the
variance in the estimate.

For batch processing, the `x`

and
`y`

data may be read segment by segment using the
`getx`

and `gety`

user defined
functions. These functions have the following syntax:

`xk = getx(ns,offset)`

and
`yk = gety(ns,offset)`

where `ns`

is the
segment size and `offset`

is the index of the first
element of the segment in the full signal.

### Reference

Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999

### Examples

rand('normal'); rand('seed',0); x = rand(1:1024-33+1); // make low-pass filter with eqfir nf = 33; bedge = [0 .1;.125 .5]; des = [1 0]; wate = [1 1]; h = eqfir(nf, bedge, des, wate); // filter white data to obtain colored data h1 = [h zeros(1:max(size(x))-1)]; x1 = [x zeros(1:max(size(h))-1)]; hf = fft(h1,-1); xf = fft(x1,-1); y = real(fft(hf.*xf,1)); // plot magnitude of filter h2 = [h zeros(1:968)]; hf2 = fft(h2,-1); hf2 = real(hf2.*conj(hf2)); hsize = max(size(hf2)); fr = (1:hsize) / hsize; plot(fr, log(hf2)); // pspect example sm = pspect(100,200,'tr',y); smsize = max(size(sm)); fr = (1:smsize) / smsize; plot(fr, log(sm), 'r');

### See also

- cspect — two sided cross-spectral estimate between 2 discrete time signals using the correlation method
- pspect — two sided cross-spectral estimate between 2 discrete time signals using the Welch's average periodogram method.
- mese — maximum entropy spectral estimation
- window — compute symmetric window of various type

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