Page 157 - Fundamentals of Communications Systems

Complex Baseband Representation of Bandpass Signals 4.33

The bandpass signal will be aperiodic if the two frequency are not integer
multiples of a common frequency. That implies that the two bandpass fre-
√
quencies must be irrational numbers. Choosing f c = 2 will produce an
aperiodic signal.

4.10 Miniprojects
Goal: To give exposure

■ to a small scope engineering design problem in communications.
■ to the dynamics of working with a team.
■ to the importance of engineering communication skills (in this case oral
presentations).

Presentation: The forum will be similar to a design review at a company
(only much shorter). The presentation will be of 5 minutes in length with an
overview of the given problem and solution. The presentation will be followed
by questions from the audience (your classmates and the professor). All team
members should be prepared to give the presentation.

4.10.1 Project 1
Project Goals: In engineering often in the course of system design or test
anomalous performance characteristics often arise. Your job as an engineer is to
use your knowledge of the theory to identify the causes of these characteristics
and correct them. Here is an example of such a case.
Get the Matlab file bpex1.m from the class web page. In this file the carrier
frequency was chosen as 7 kHz. If the carrier frequency is chosen as 8 kHz an
anomalous output is evident from the quadrature downconverter. This is most
(f ). Postulate a reason why this
easily seen in the output energy spectrum, G y z
behavior occurs.
Hint: It happens at 8 kHz but not at 7 kHz and Matlab is a sampled data
system. What problems might one have in sampled data system? Assume that
this upconverter and downconverter were products you were designing how
would you specify the performance characteristics such that a customer would
never see this anomalous behavior?

4.10.2 Project 2
Project Goals: Use the knowledge of the theory of bandpass signals to identify
unknown parameters of a bandpass signal.
A signal has a form
√ √
x c (t) = x I (t) 2 cos(2π f c t + θ) − x Q (t) 2 sin(2π f c t + θ) (4.67)