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In the area of systems and signals, the Fourier series is commonly represented in the form of a sum of complex exponentials, as follows kmax x(t) = Σ (akejkwot) k=-kmax However, in other areas of electrical engineering, e.g. power electronics, the Fourier series is usually presented in the form of a trigonometric sum, as follows x(t) = kmaz 1 = a + acos(kwot) + bÅsen (kwot) k=1 a) Derive the expression to estimate the values of ao, ak and bk from the trigonometric sum expression (hint: multiply by the cosine or sine function and integrate over the period). b) Another alternative way of representing is the compact trigonometric form, given by the expression ∞ f(t) = a + ΣA, cos(nwot - On), n=1 FIND THE VALUE OF AN IN TERMS OF THE COEFFICIENTS AK AND BK ESTIMATED FROM THE TRIGONOMETRIC SUM EXPRESSION AND EXPLAIN STEP-BY-STEP.

In the area of systems and signals, the Fourier series is commonly represented in the form of a sum of complex exponentials, as follows kmax x(t) = Σ (akejkwot) k=-kmax However, in other areas of electrical engineering, e.g. power electronics, the Fourier series is usually presented in the form of a trigonometric sum, as follows x(t) = kmaz 1 = a + acos(kwot) + bÅsen (kwot) k=1 a) Derive the expression to estimate the values of ao, ak and bk from the trigonometric sum expression (hint: multiply by the cosine or sine function and integrate over the period). b) Another alternative way of representing is the compact trigonometric form, given by the expression ∞ f(t) = a + ΣA, cos(nwot - On), n=1 FIND THE VALUE OF AN IN TERMS OF THE COEFFICIENTS AK AND BK ESTIMATED FROM THE TRIGONOMETRIC SUM EXPRESSION AND EXPLAIN STEP-BY-STEP.

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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In the area of systems and signals, the Fourier series is commonly represented in the form of a sum of complex exponentials, as follows kmax x(t) = Σ (akejkwot) k=-kmax However, in other areas of electrical engineering, e.g. power electronics, the Fourier series is usually presented in the form of a trigonometric sum, as follows x(t) = kmaz 1 = a + acos(kwot) + bÅsen (kwot) k=1 a) Derive the expression to estimate the values of ao, ak and bk from the trigonometric sum expression (hint: multiply by the cosine or sine function and integrate over the period). b) Another alternative way of representing is the compact trigonometric form, given by the expression ∞ f(t) = a + ΣA, cos(nwot - On), n=1 FIND THE VALUE OF AN IN TERMS OF THE COEFFICIENTS AK AND BK ESTIMATED FROM THE TRIGONOMETRIC SUM EXPRESSION AND EXPLAIN STEP-BY-STEP.
Transcribed Image Text:In the area of systems and signals, the Fourier series is commonly represented in the form of a sum of complex exponentials, as follows kmax x(t) = Σ (akejkwot) k=-kmax However, in other areas of electrical engineering, e.g. power electronics, the Fourier series is usually presented in the form of a trigonometric sum, as follows x(t) = kmaz 1 = a + acos(kwot) + bÅsen (kwot) k=1 a) Derive the expression to estimate the values of ao, ak and bk from the trigonometric sum expression (hint: multiply by the cosine or sine function and integrate over the period). b) Another alternative way of representing is the compact trigonometric form, given by the expression ∞ f(t) = a + ΣA, cos(nwot - On), n=1 FIND THE VALUE OF AN IN TERMS OF THE COEFFICIENTS AK AND BK ESTIMATED FROM THE TRIGONOMETRIC SUM EXPRESSION AND EXPLAIN STEP-BY-STEP.
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