Practice Question on Computing the Fourier Series discrete-time signal

Obtain the Fourier series the DT signal

$ x[n] = \left\{ \begin{array}{ll} 1, & \text{ for } -5\leq n \leq 5,\\ 0, & \text{ for } 5< |n| \leq 10. \end{array} \right. \ $

x[n] periodic with period 20.

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Answer 1

Solution 1: ω_o = $ 2*\pi/T = 2*pi/20=\pi/10 $ a_o is the DC value of the AC signal and is therefore 1/2

a_k = $ 1/20 * \int_a^b \! x(t)*e^{-j*k*(\pi/10)*t}\,dx $ = $ e^{j*k*\pi/2}-e^{-j*k*\pi/2}/(2*\pi*j*k) = sin(k*\pi/2)/(k*\pi) $

=== Answer 2 === Write it here. === Answer 3 === Write it here. ---- Back to ECE301 Spring 2011 Prof. Boutin