Find and plot the Fourier transform of the Ricker wavelet

asked 10 years ago

fomel_sergey
1 ●3 ●3 ●4

updated 10 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

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.

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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 ( 10 years ago )

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

fomel_sergey ( 10 years ago )

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answered 4 years ago

backchodmaster
1 ●1

updated 4 years ago

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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Find and plot the Fourier transform of the Ricker wavelet

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1 Answer

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

The output shall be the fourier transform

Plot:

This will give u the plot

norm means the modulus of the complex function.

Your Answer

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Comments

1 Answer

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

The output shall be the fourier transform

Plot:

This will give u the plot

norm means the modulus of the complex function.

Your Answer

Question Tools

Stats

Related questions

Find and plot the Fourier transform of the Ricker wavelet