# pwelch

Computes the power spectral density.

## Syntax

Pxx=pwelch(x)

Pxx=pwelch(x,window)

Pxx=pwelch(x,window,overlap)

Pxx=pwelch(x,window,overlap,nfft)

Pxx=pwelch(x,window,overlap,nfft,fs)

Pxx=pwelch(x,window,overlap,nfft,fs,range)

[Pxx,freq]=pwelch(...)

pwelch(...)

## Inputs

`x`- The signal.
`window`- The window size, or the window vector.
`overlap`- The number of overlapping points in adjacent windows.
`nfft`- The size of the fft.
`fs`- The sampling frequency.
`range`- The spectrum type: 'onesided' or 'twosided'.

## Outputs

- Pxx
- The power spectral density.
- freq
- The vector of frequencies corresponding to the density values.

## Example

```
n = 1000;
fs = 1125;
ts = 1/fs;
t = [0:1:(n-1)]*ts;
f1 = 24;
f2 = 56;
omega1 = 2 * pi * f1;
omega2 = 2 * pi * f2;
signal = 3 + 5 * cos(omega1 * t) + 7 * cos(omega2 * t);
window = hann(250,'periodic');
overlap = 125;
fftsize = 250;
range = 'onesided';
[Pxx,frq]=pwelch(signal,window,overlap,fftsize,fs,range);
f = frq([1, 2, 3, 4, 5, 13, 14, 15])'
p = Pxx([1, 2, 3, 4, 5, 13, 14, 15])'
```

```
f = [Matrix] 1 x 8
0 4 20 24 28 52 56 60
p = [Matrix] 1 x 8
1.50000 0.75000 0.52083 2.08333 0.52083 1.02083 4.08333 1.02083
```

## Comments

With no return arguments, the function will automatically plot.

The 'onesided' output has a length of `nfft/2+1` if `nfft` is even,
or `(nfft+1)/2` if `nfft` is odd.

It is often recommended to remove the signal mean prior to calling pwelch. The function does not remove the mean automatically.

The optional arguments can be defaulted using []. The defaults are as follows:

`window`- A Hamming window with the largest length that produces eight data segments.
`overlap`- One half of the window length.
`nfft`- The window length. A larger value will pad zeros to each block of windowed data.
`fs`- 1.0 Hz.
`range`- 'onesided'

## Comments

When `x` is a 2D matrix pwelch will operate on each column
and the output vectors will be stored in the columns of `Pxx`.