Give the value of the term a₁ in Cartesian representation. αι = Give the formula for the even indices (n even). Note The formula for the even indices should contain only real quantities. F(n) = Compute the coefficients for f(t), i.e., F(n) for n = −4, −2, —1, 0, 1, 2, 4. Write the formula for approximation using these terms using a constant and three cosines with phase. f(t) ≈
Give the value of the term a₁ in Cartesian representation. αι = Give the formula for the even indices (n even). Note The formula for the even indices should contain only real quantities. F(n) = Compute the coefficients for f(t), i.e., F(n) for n = −4, −2, —1, 0, 1, 2, 4. Write the formula for approximation using these terms using a constant and three cosines with phase. f(t) ≈
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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Transcribed Image Text:Give the value of the term a₁ in Cartesian representation.
αι
=
Give the formula for the even indices (n even). Note The formula for the even indices should contain only real
quantities.
F(n) =
Compute the coefficients for f(t), i.e., F(n) for n = –4, −2, –1, 0, 1, 2, 4. Write the formula for approximation
using these terms using a constant and three cosines with phase.
f(t) ~
Transcribed Image Text:Consider the periodic function with period 0.00714285714285714 given by
f(t) = { sin (2140t)
0
if 0 ≤ t < 0.00357142857142857
if 0.00357142857142857 ≤ t < 0.00714285714285714.
The Fourier Series of this signal has an interesting form. The coefficients are zero for all odd indices, except n = ±1.
So we'll ask you for the value of a₁ (the value for a_1 is the conjugagte) and the formula for the even indices, an for
n even, i.e., n = 0, 2, 4, 6...
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