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]?
