Version:

Last Modified: January 9, 2017

Generates a signal containing a Gaussian-modulated sinusoidal pattern.

Drop in power on either side of the center frequency.

**attenuation** must be greater than zero.

**Default: **6 dB

Amplitude of the pattern.

**Default: **1

Shifts the pattern in the time axis.

**Default: **0

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

**center frequency** must be greater than zero.

**Default: **1

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

**Default: **No error

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

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

Output Gaussian-modulated sine pattern.

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

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

and

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

where

*A*is the**amplitude***b*is the**normalized bandwidth***q*is the**attenuation***f*_{c}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 *f*_{c}, the power spectrum density reaches the peak value
$\sqrt{\frac{\pi}{k}}$. When at frequency points
${f}_{c}\pm \frac{b*{f}_{c}}{2}$, 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