Revision as of 05:20, 15 October 2010

Homework 7, ECE438, Fall 2010, Prof. Boutin

Due in class, Friday October 22, 2010.

The discussion page for this homework is here.

Question 1

Compute the discrete Fourier transform of the following discrete-time signals:

$ x_1[n]= e^{j \frac{2}{3} \pi n}; $

$ x_2[n]= e^{j \frac{2}{\sqrt{3}} \pi n}; $

$ x_3[n]= e^{j \frac{4}{3} \pi n}; $

$ x_4[n]= e^{j \frac{2}{1000} \pi n}; $

$ x_5[n]= e^{-j \frac{2}{1000} \pi n}; $

$ x_6[n]= \cos\left( \frac{2}{1000} \pi n\right) ; $

$ x_7[n]= \cos^2\left( \frac{2}{1000} \pi n\right) ; $.

$ x_8[n]= (-j)^n . $

How do your answers relate to the Fourier series coefficients of x[n]?

Question 2

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