Consider the periodic function f(t) with fundamental interval −π ≤ t ≤ π that is defined by: f (t) = {−t − π for −π ≤ t < 0, {−π for 0 ≤ t < π, f (t + 2π) = f (t). a. Sketch the graph of the function f for −3π ≤ t ≤ 3π, and hence state whether the function is even, odd, or neither even nor odd. b. Calculate the Fourier series for f(t) and hence show that the first few terms are: F(t) = (-3/4)π - (2/π) cos (t) - (2/9π) cos (3t) - sin (t) + (1/2) sin (2t) - (1/3) sin (3t)
Consider the periodic function f(t) with fundamental interval −π ≤ t ≤ π that is defined by: f (t) = {−t − π for −π ≤ t < 0, {−π for 0 ≤ t < π, f (t + 2π) = f (t). a. Sketch the graph of the function f for −3π ≤ t ≤ 3π, and hence state whether the function is even, odd, or neither even nor odd. b. Calculate the Fourier series for f(t) and hence show that the first few terms are: F(t) = (-3/4)π - (2/π) cos (t) - (2/9π) cos (3t) - sin (t) + (1/2) sin (2t) - (1/3) sin (3t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the periodic function f(t) with fundamental interval −π ≤ t ≤ π that is defined by:
f (t) = {−t − π for −π ≤ t < 0,
{−π for 0 ≤ t < π,
f (t + 2π) = f (t).
a. Sketch the graph of the function f for −3π ≤ t ≤ 3π, and hence state whether the function is even, odd, or neither even nor odd.
b. Calculate the Fourier series for f(t) and hence show that the first few
terms are:
F(t) = (-3/4)π - (2/π) cos (t) - (2/9π) cos (3t) - sin (t) + (1/2) sin (2t) - (1/3) sin (3t).
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