Use the fourier series analysis integral to compute

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Reference no: EM13218198

1)Consider a periodic function x(t) with fundamental period T0, where a single period is specified by

x(t) = cos*((pi)/(2*T0)) for -T0/2 <= t <= T0/2

(a) Draw a labeled sketch of x(t) over a few periods: be careful, make sure you follow the exact definition of x(t)

(b) Compute DC coefficient a0:

(c) Use the Fourier series analysis integral to compute the coefficients ak for the periodic function x(t) for all k. Show that the answer can be simplified to

(2*sqrt(2)*(-1)^k)/(pi*(1-16*k^2))

2) Consider the periodic function x(t) with period T0 defined as follows:

x(t) = 1 if t is in interval [-T0/4 , To/4)
0 if t is in interval [-T0/4 , T0/4) union [T0/4 , T0/2)

(a) Find the Fourier series representation of x(t).

(b) Define y(t) = 2*x*(t - T0/2). Sketch the waveform of y(t), and find the Fourier series representation of y(t) without evaluating any integral.

Reference no: EM13218198

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