# psd5

Modified power spectral density function.

## Syntax

psd5(time, amplitude, block, overlap)

## Argument

time
The vector of times at which the signal is sampled.
amplitude
The vector of signal amplitudes on which the PSD is to be performed.
block
Block length for spectral averaging.
overlap
Samples of overlap from block to block. The overlap, an integer value, must be smaller than the block size.

## Example

Curve Math Vectors Results
p1w1c1.x = (0:255:1)/512 The vector of sample times.
p1w1c1.y = 6 +

10*cos(2*pi*20*x+pi/6) +

8*cos(2*pi*48*x+pi/3)

The vector of signal amplitude samples.
x = freq(p1w1c1.x[0:numpts(y)-1:1])/2 The vector of frequencies.
y = psd5(p1w1c1.x, p1w1c1.y, 128, 64) The vector of PSD values.

The modified PSD function applies a Hanning window to each block of the PSD. The result is the average PSD per block.

The Hanning function compensates for the bias that it induces by removing the DC component and scaling the data in each block prior to performing an FFT.

The PSD contribution of the sinusoidal components at 20 and 48 hertz are 25 and 16, respectively. See the psd help topic for details on those calculations.

The Hann window spreads each PSD contribution over 3 bins, with 2/3 of the power in the middle bin, and 1/6 in each of the side bins. The output resolution is 4Hz, so the output values are as follows for the 2 block example:

PSD(16) = 1/2 * 1/6 * 25 = 2.0833

PSD(20) = 1/2 * 2/3 * 25 = 8.3333

PSD(24) = 1/2 * 1/6 * 25 = 2.0833

PSD(44) = 1/2 * 1/6 * 16 = 1.3333

PSD(48) = 1/2 * 2/3 * 16 = 5.3333

PSD(52) = 1/2 * 1/6 * 16 = 1.3333