## EE 451

Homework Assignment 2
Due Sept. 11, 1996

1. In the following problems, be sure to normalize discrete-time frequencies so they are between -pi and +pi.
1. A periodic signal x(t) contains frequencies up to 1 kHz. At what rate must x(t) be sampled in order to reconstruct it unambigouusly?
2. A signal x(t) = cos(2 pi 2000 t) is sampled at 6 kHz. What is the discrete-time frequency of x(n)?
3. A signal x(t) = cos(2 pi 2000 t) is sampled at 1.5 kHz. What is the discrete-time frequency of x(n)?
4. A signal x(t) = sin(2 pi 100 t) is sampled at 1 kHz. Find another signal y(t) which, when sampled at 1 kHz, will have y(n) = x(n).
5. A discrete-time signal x(n) = cos(0.5 pi) + 2 cos(0.25 pi) is sent to an ideal reconstructor at a rate of 10 kHz. What is the output x(t) of the system?
2. Problem 1.13 from Orfanidis. Plot the spectra in dB.
3. Using the equation for |X(f)|2 from the above problem, plot x(t) and |X(f)|2 for the following values of a and fo:
1. a = 1, fo=1.
2. a = 2, fo=1.
3. a = 1, fo=2.
4. a = 2, fo=2.
Discuss the effect of changing a and fo.

Bill Rison, <rison@ee.nmt.edu >