ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 02 Jul 2020 03:11:10 -0500Find and plot the Fourier transform of the Ricker wavelethttp://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/ 2. 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.
Mon, 03 Nov 2014 22:14:32 -0600http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/Comment by fomel_sergey for <ol>
<li>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</li>
</ol>
<p>r(t)=−d2dt2g(t), where g(t)=e−a2t2.</p>
<p>(a) Find and plot the Fourier transform of the Ricker wavelet.</p>
<p>(b) Find the peak frequency: the frequency of the maximum of the Fourier spectrum.</p>
<p>(c) Find the apparent frequency: the frequency corresponding to the period between two minima in the time domain.</p>
http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?comment=24853#post-id-24853@tmonteil so how do I plot it? I don't know what function to use to plot it.Wed, 12 Nov 2014 19:44:05 -0600http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?comment=24853#post-id-24853Comment by tmonteil for <ol>
<li>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</li>
</ol>
<p>r(t)=−d2dt2g(t), where g(t)=e−a2t2.</p>
<p>(a) Find and plot the Fourier transform of the Ricker wavelet.</p>
<p>(b) Find the peak frequency: the frequency of the maximum of the Fourier spectrum.</p>
<p>(c) Find the apparent frequency: the frequency corresponding to the period between two minima in the time domain.</p>
http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?comment=24774#post-id-24774This 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.Tue, 04 Nov 2014 01:46:21 -0600http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?comment=24774#post-id-24774Answer by backchodmaster for <ol>
<li>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</li>
</ol>
<p>r(t)=−d2dt2g(t), where g(t)=e−a2t2.</p>
<p>(a) Find and plot the Fourier transform of the Ricker wavelet.</p>
<p>(b) Find the peak frequency: the frequency of the maximum of the Fourier spectrum.</p>
<p>(c) Find the apparent frequency: the frequency corresponding to the period between two minima in the time domain.</p>
http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?answer=52300#post-id-52300####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) = amplitude*sin(2*pi*f*t + phase)
assume(f>0)
Input_fourier(f,t) = indefinite_integral(exp(-2*pi*I*t*f)*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.Thu, 02 Jul 2020 03:11:10 -0500http://ask.sagemath.org/question/24772/find-and-plot-the-fourier-transform-of-the-ricker-wavelet/?answer=52300#post-id-52300