EE 451
Homework Assignment 2
Due Sept. 11, 1996

In the following problems, be sure to normalize discretetime frequencies
so they are between pi and +pi.
 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?
 A signal x(t) = cos(2 pi 2000 t) is sampled at 6 kHz. What is the
discretetime frequency of x(n)?
 A signal x(t) = cos(2 pi 2000 t) is sampled at 1.5 kHz. What is the
discretetime frequency of x(n)?
 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).
 A discretetime 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?
 Problem 1.13 from Orfanidis. Plot the spectra in dB.
 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 f_{o}:
 a = 1, f_{o}=1.
 a = 2, f_{o}=1.
 a = 1, f_{o}=2.
 a = 2, f_{o}=2.
Discuss the effect of changing a and f_{o}.
Bill Rison,
<rison@ee.nmt.edu >