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Determine the Fourier series expansion of the sawtooth waveform, shown below-3T -2T-T T2T 3T-1 1 x(t) t Solution: The signal is periodic with period 2T. Since the signal is odd we obtain x 0 =0. For n =0 x n = 1 2T T ?T x(t)e?j2?2 n T tdt = 1 2T T ?T t T e?j2? n 2T tdt = 1 2T2 T ?T te?j?n T tdt = 1 2T2 jT ?n te?j?n T t + T2 ?2n2 e?j?n T t T ?T = 1 2T2 jT2 ?n e?j?n... Determine the Fourier series expansion of the sawtooth waveform, shown below-3T -2T-T T2T 3T-1 1 x(t) t Solution: The signal is periodic with period 2T. Since the signal is odd we obtain x 0 =0. For n =0 x n = 1 2T T ?T x(t)e?j2?2 n T tdt = 1 2T T ?T t T e?j2? n 2T tdt = 1 2T2 T ?T te?j?n T tdt = 1 2T2 jT ?n te?j?n T t + T2 ?2n2 e?j?n T t T ?T = 1 2T2 jT2 ?n e?j?n

**Fourier Series and Boundary Value Problems**

[PPT] Document Database Online Site Fourier Series Practice Problems Solutions File Name: Fourier Series Practice Problems Solutions File Format: ePub, PDF, Kindle, AudioBook... Description : The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.

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## Fourier Series Problems With Solutions Pdf

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- Lecture 14: Half Range Fourier Series: even and odd functions (Compiled 4 August 2017) In this lecture we consider the Fourier Expansions for Even and Odd functions, which give rise to cosine and sine half range Fourier Expansions. If we are only given values of a function f(x) over half of the range [0;L], we can de ne two ?t extensions of f to the full range [L;L], which yield distinct
- Fourier Series and Boundary Value Problems, 8th Edition by James Brown and Ruel Churchill (9780078035975) Preview the textbook, purchase or get a FREE instructor-only desk copy.