Consider the periodic function defined within one period by the formula: y (x)=x + 1 -(x + 1)² if - 5x² (b)(i) Present the first four terms of the series plus the zero term in the explicit form. (ii) Find the Fourier spectrum 4 = √√²+ b² where a, and b, are the amplitudes of the cosine and sine Fourier harmonics respectively and plot it against n in the log-log scale.
Consider the periodic function defined within one period by the formula: y (x)=x + 1 -(x + 1)² if - 5x² (b)(i) Present the first four terms of the series plus the zero term in the explicit form. (ii) Find the Fourier spectrum 4 = √√²+ b² where a, and b, are the amplitudes of the cosine and sine Fourier harmonics respectively and plot it against n in the log-log scale.
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:Consider the periodic function defined within one period by the formula:
y(x)= x + 1 -(x + 1)²
if - Sx² +
(b)(i)
Present the first four terms of the series plus the zero term in the explicit form.
(ii)
Find the Fourier spectrum A = √√²+ b² where a, and b, are the amplitudes of the cosine
and sine Fourier harmonics respectively and plot it against n in the log-log scale.
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