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Assume we have some real-valued x(t). Then we know from class that x(t) can be expressed in the sine-cosine form of the Fourier Series as: x(t) = ao +2B₁, cos(wkt) - Σ2Ck sin(wkt) +Σ -₂0₂ k=1 k=1 There also exists the amplitude-phase form of the Fourier Series for a real-valued x(t): x(t) = = ao + 8 k=1 2Ak cos(wkt + 0k) aki Find expressions for the amplitude Ak and the phase shift 0 in terms of bk.

Assume we have some real-valued x(t). Then we know from class that x(t) can be expressed in the sine-cosine form of the Fourier Series as: x(t) = ao +2B₁, cos(wkt) - Σ2Ck sin(wkt) +Σ -₂0₂ k=1 k=1 There also exists the amplitude-phase form of the Fourier Series for a real-valued x(t): x(t) = = ao + 8 k=1 2Ak cos(wkt + 0k) aki Find expressions for the amplitude Ak and the phase shift 0 in terms of bk.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Assume we have some real-valued x(t). Then we know from class that x(t) can be expressed in the sine-cosine form of the Fourier Series as: ∞ x(t) = ao +2B₁ cos(wkt) - Σ2Ck sin(wkt) k=1 k=1 ∞ There also exists the amplitude-phase form of the Fourier Series for a real-valued x(t): x(t) = ao + 2Ak cos(wkt + 0k) k=1 Find expressions for the amplitude Ak and the phase shift 0 in terms of ak, bk.
Transcribed Image Text:Assume we have some real-valued x(t). Then we know from class that x(t) can be expressed in the sine-cosine form of the Fourier Series as: ∞ x(t) = ao +2B₁ cos(wkt) - Σ2Ck sin(wkt) k=1 k=1 ∞ There also exists the amplitude-phase form of the Fourier Series for a real-valued x(t): x(t) = ao + 2Ak cos(wkt + 0k) k=1 Find expressions for the amplitude Ak and the phase shift 0 in terms of ak, bk.
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