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# Find and plot the Fourier transform of the Ricker wavelet

1. The Ricker wavelet, also known as the Mexican hat wavelet, is a popular representation of seismic signals. The Ricker wavelet r(t) is defined as the second derivative of the Gaussian

r(t)=−d2dt2g(t), where g(t)=e−a2t2.

(a) Find and plot the Fourier transform of the Ricker wavelet.

(b) Find the peak frequency: the frequency of the maximum of the Fourier spectrum.

(c) Find the apparent frequency: the frequency corresponding to the period between two minima in the time domain.

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## Comments

1

This looks like homework. If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.

@tmonteil so how do I plot it? I don't know what function to use to plot it.

## 1 Answer

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### code begins from here: f= frequency,t=time

from sage.symbolic.integration.integral import indefinite_integral

amplitude = 1.0

phase = 0.0

Input(f,t) = amplitudesin(2pift + phase)

assume(f>0)

Input_fourier(f,t) = indefinite_integral(exp(-2piItf)*Input(f,t),t) show(Input(f,t)) show(Input_fourier)

### Plot:

plot(norm(Input_fourier(f,2)),f,0,10000,gridlines = True,)

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Asked: 2014-11-04 05:14:32 +0200

Seen: 2,001 times

Last updated: Jul 02 '20