For the listed functions A) through D), do the following: • Plot the function f(x) and its magnitude |f(x)]. Compute the Fourier transform of f(x): g(k) = 1 /27 Le f(x) e-ikix dat (1) • Compute and plot the magnitude |g(k)| as a function of k. • For each function and its transform, think about (but do not compute!) Parseval's Theorem: [*_ \g(k) ³²dk = f*_ \ƒ(x)|²dx Based on your drawings of the function and its Fourier transform, which side of Parseval's theorem would be easier to compute? A) f(x) = e-|x|

For the listed functions A) through D), do the following: • Plot the function f(x) and its magnitude |f(x)]. Compute the Fourier transform of f(x): g(k) = 1 /27 Le f(x) e-ikix dat (1) • Compute and plot the magnitude |g(k)| as a function of k. • For each function and its transform, think about (but do not compute!) Parseval's Theorem: [_ \g(k) ³²dk = f_ \ƒ(x)|²dx Based on your drawings of the function and its Fourier transform, which side of Parseval's theorem would be easier to compute? A) f(x) = e-|x|

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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