# 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.

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

`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'