Consider the periodic function defined within one period by the formula: P(x)=x+ / - (x+1)* if - SXS (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+b²where 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
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Consider the periodic function defined within one period by the formula:
1
P(x)=x+1-(x+) if
{(x) = x + ² = ( x + ² ) ²
/10
(ii)
sxs
(b)(i)
Present the first four terms of the series plus the zero term in the explicit form.
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.
Transcribed Image Text:Consider the periodic function defined within one period by the formula: 1 P(x)=x+1-(x+) if {(x) = x + ² = ( x + ² ) ² /10 (ii) sxs (b)(i) Present the first four terms of the series plus the zero term in the explicit form. 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.
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