Last Modified: March 15, 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.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**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

Timestamp of the output signal. If this input is unwired, this node uses the current time as the timestamp of the output signal.

This input is available only if you configure this node to return a waveform.

Output Gaussian-modulated sine pattern.

This output can return a waveform or an array of double-precision, floating-point numbers.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

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: This product does not support FPGA devices