# WVD Spectrogram (G Dataflow)

Version:

Computes the energy distribution of the input signal in the joint time-frequency domain using the Wigner-Ville distribution (WVD) algorithm.

## x

The input time-domain signal.

## time increment

Time intervals, in units of samples, of the Wigner-Ville Distribution (WVD).

Performance Considerations

Increasing time increment decreases the computation time and reduces memory requirements but also reduces time-domain resolution. Decreasing time increment improves time-domain resolution but increases the computation time and memory requirements.

Default: 1

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## WVD spectrogram

The energy distribution of the input signal in the joint time-frequency domain.

## error out

Error information. The node produces this output according to standard error behavior.

## Using the Wigner-Ville Distribution (WVD) Algorithm to Calculate the Spectrogram

For a discrete signal X, with an analytic associate of Z, the following equation defines the Wigner-Ville Distribution (WVD) of the analytic associate, ${\text{WVD}}_{Z}\left(n,f\right)$:

${\text{WVD}}_{Z}\left(n,f\right)=2\underset{k=-\infty }{\overset{\infty }{\sum }}Z\left(n+k\right)Z*\left(n-k\right){e}^{-j4\pi fk}$

where

• n is the index in the time domain
• f is the index in the frequency domain
• Z is the analytic associate defined as $\text{X}+i*H\left[\text{X}\right]$, where $H\left[\text{X}\right]$ is the Hilbert Transform of X

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported