# Pattern Generator (Gaussian Modulated Sine) (G Dataflow)

Version:

Generates a signal containing a Gaussian-modulated sinusoidal pattern.

## attenuation

Drop in power on either side of the center frequency.

attenuation must be greater than zero.

Default: 6 dB

## amplitude

Amplitude of the pattern.

Default: 1

## delay

Shifts the pattern in the time axis.

Default: 0

## center frequency

Center frequency, or frequency of the carrier, in Hz.

center frequency must be greater than zero.

Default: 1

## normalized bandwidth

Value multiplied by the value of the center frequency to normalize the bandwidth at the attenuation in the power spectrum. This input must be greater than zero.

Default: 0.15

## error in

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

Default: No error

## dt

Sampling interval. This input must be greater than zero. If this input is less than or equal to zero, this node sets the output pattern to an empty array and returns an error.

Default: 0.1

## samples

Number of samples in the pattern. If this input is less than 1, the node sets the output pattern to an empty array and returns an error.

Default: 128

## Gaussian modulated sine pattern

Output Gaussian-modulated sine pattern.

## error out

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

## Algorithm for Generating the Gaussian Modulated Sine Pattern

If the sequence Y represents Gaussian modulated sine pattern, this node generates the pattern according to the following equations:

${y}_{i}=A{e}^{-k{\left(i*\mathrm{\Delta }t-d\right)}^{2}\mathrm{cos}\left(2\pi {f}_{c}\left(i*\mathrm{\Delta }t-d\right)\right)}$

and

$\begin{array}{cc}k=\frac{5{\pi }^{2}{b}^{2}{f}_{c}^{2}}{q*\mathrm{ln}\left(10\right)}& \text{for}\text{\hspace{0.17em}}i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}N-1\end{array}$

where

• A is the amplitude
• b is the normalized bandwidth
• q is the attenuation
• fc is the center frequency
• N is the number of samples

The following equation represents the envelope of the Gaussian-modulated sine pattern:

$A{e}^{-k{t}^{2}}$

The following equation represents the Fourier transform of the envelope:

$A{e}^{-\frac{{\omega }^{2}}{4k}}\sqrt{\frac{\pi }{k}}$

In its power spectrum, at frequency point fc, the power spectrum density reaches the peak value $\sqrt{\frac{\pi }{k}}$. When at frequency points ${f}_{c}±\frac{b*{f}_{c}}{2}$, the power spectrum density decreases q dB from the peak value, where q denotes attenuation, as shown by the following figure.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported