Answer Happy

Let f be the triangle wave function defined by f(x)=π−∣x∣ for −π

Posted: Thu Jul 14, 2022 3:48 pm

by answerhappygod

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Let f be the triangle wave function defined by f(x)=π−∣x∣ for −π<x≤π, and extended to be 2π-periodic on the real number line. Find the Fourier series of this function in complex exponential form. You should verify the Fourier coefficients of f are: f^​(n)=⎩⎨⎧​π/202/(πn2)​ if n=0 if n=0 and even  if n is odd ​ Problem 2 Rewrite the Fourier series in Problem 1 as a cosine series. Hint: Use the Euler formula cosx=2eix+e−ix​ This should match the solution of Problem 1 in the Week 2 Homework.