Consider the function f(x) = cos(2x) for -2pi < x ≤ 2pi and zero otherwise.A) Show that it meets the condition of having a Fourier transform.B) Find it's Fourier transform F(k).C) Demonstrate that F(0) = area under the curve of f(x).
Consider the function f(x) = cos(2x) for -2pi < x ≤ 2pi and zero otherwise.A) Show that it meets the condition of having a Fourier transform.B) Find it's Fourier transform F(k).C) Demonstrate that F(0) = area under the curve of f(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
Question
Consider the function f(x) = cos(2x) for -2pi < x ≤ 2pi and zero otherwise.
A) Show that it meets the condition of having a Fourier transform.
B) Find it's Fourier transform F(k).
C) Demonstrate that F(0) = area under the curve of f(x).
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