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Jeffrey Love

Calculate and plot Fourier spectrum using W|A?

Jeffrey Love
Posted 8 months ago
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Does Wolframalpha have commands that (easily) allow me to supply a mathematical function and, then, have outputted a plot of the Fourier spectrum? Or do I have to go through the process of myself of Fourier transforming and extracting amplitudes from that and, then, plotting?
POSTED BY: Jeffrey Love
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What have you tried? This is the sort of thing one should first experiment with, and go to a forum if nothing suitable was found.
POSTED BY: Daniel Lichtblau
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Jeffrey Love
Jeffrey Love
Posted 8 months ago

Hi Daniel, I've been using the Fourier transform command to obtain a frequency domain expression of my function, then taken its absolute value by multiplying by the complex conjugate, then plotted the result. It's all just standard stuff, so I guess I thought there would be a sort of signal-processing toolbox to do this, and other related things. I'm just exploring.

By the way, why is that the following command gives me a result (FT of a Dawson function):

Fourier transform of Dawson(sqrt(t)*theta(t))

but the following (same thing, but with time multiplied by a constant:

Fourier transform of Dawson(sqrt(at)theta(t))

does not? This difference is just an example of how sometimes Wolframalpha works well, but at other times, for reasons I don't understand, it doesn't.

Thank you,

Jeff
POSTED BY: Jeffrey Love
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Could just request the absolute value. This worked fine for me:

WolframAlpha["abs of fourier transform Dawson(sqrt(t)theta(t))"]

It even showed a plot.

The second issue probably comes down to having a parameter that W|A balks on. Using specific numbers seems to work fine. The Wolfram Language can handle the general parameter case using the Assumptions option.

FourierTransform[DawsonF[Sqrt[at]]HeavisideTheta[t], t, w, Assumptions -> a > 0]

(* Out[132]= (Sqrt[a] (I w + Abs[w]))/(4 (a - I w) Abs[w]^(3/2)) *)

General remark: Posting specific examples makes it easier for others to do diagnoses and provide relevant responses. This post had such an example and that of course is quite helpful.
POSTED BY: Daniel Lichtblau
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