Gaussian Modulated Sine Pattern VI

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Updated2025-01-28
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Gaussian Modulated Sine Pattern VI

Generates an array that contains a Gaussian-modulated sinusoidal pattern.

Inputs/Outputs

attenuation (dB) —

attenuation (dB) is related to the drop in power on either side of the center frequency, which must be greater than zero. The default is 6 dB.

center frequency (Hz) —

center frequency (Hz) is the center frequency, or frequency of the carrier, in Hertz. The default is 1.

samples —

samples is the number of samples of the Gauss-Mod Sine Pattern. If samples is less than 1, the VI sets Gauss-Mod Sine Pattern to an empty array and returns an error. The default is 128.

amplitude —

amplitude is the amplitude of the Gauss-Mod Sine Pattern. The default is 1.

delay (s) —

delay (s) shifts the peak of the Gauss-Mod Sine Pattern. The default is 0.

delta t (s) —

delta t (s) is the sampling interval. delta t (s) must be greater than zero. If delta t (s) is less than or equal to zero, the VI sets Gauss-Mod Sine Pattern to an empty array and returns an error. The default is 0.1.

normalized bandwidth —

normalized bandwidth is the value multiplied by center frequency to normalize the bandwidth at attenuation (dB) in the power spectrum. normalized bandwidth must be greater than zero. The default is 0.15.

Gauss-Mod Sine Pattern —

Gauss-Mod Sine Pattern is an array that contains a Gaussian-modulated sinusoidal pattern of samples.

error —

error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

If the sequence Y represents Gauss-Mod Sine Pattern, the Gaussian Modulated Sine Pattern VI generates the pattern according to the following equations:

and

where A is the amplitude, b is the normalized bandwidth, q is the attenuation, f_c is the center frequency (Hz), d is the delay, and N is the samples.

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

The following equation represents the Fourier transform of the envelope:

In its power spectrum, at frequency point f_c, the power spectrum density reaches the peak value . When at frequency points , the power spectrum density decreases q dB from the peak value, where q denotes attenuation, as shown by the following screenshot.