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(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?

(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?
Transcribed Image Text:(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?
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