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Find and plot the Fourier transform of the Ricker wavelet

asked 2014-11-03 22:14:32 -0500

fomel_sergey gravatar image

updated 2014-11-04 01:46:51 -0500

tmonteil gravatar image
  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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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 gravatar imagetmonteil ( 2014-11-04 01:46:21 -0500 )edit

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

fomel_sergey gravatar imagefomel_sergey ( 2014-11-12 19:44:05 -0500 )edit

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answered 2020-07-02 03:11:10 -0500

updated 2020-07-02 12:31:14 -0500

I will show you how to calculate fourier transform in sage. I am assuming you have theoretical knowledge of the thing.

i will calculate the fourier transform of a sin wave of the form sin(2πft)

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)

The output shall be the fourier transform

Plot:

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

This will give u the plot

norm means the modulus of the complex function.

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Asked: 2014-11-03 22:14:32 -0500

Seen: 1,911 times

Last updated: Jul 02