PSfrag replacements
PROBLEM:
Consider the signal
x(t) = [10 cos(3000πt − π/6)]2 .
(a) Express the signal x(t) as a sum of complex exponential components. Do this by using the
jθ
− jθ
relationship cos θ = e +e
to convert the cosine term into complex exponentials and then
2
expand the squared expression.
(b) What frequencies (in Hz) are present in this signal?
(c) For each frequency identified in part (b), give the complex amplitude of the corresponding
complex exponential component. Make a table of your analysis with frequency in one column
and complex amplitude in a second column.
(d) Use your spectrum information to express x(t) in the form x(t) = A + B cos(ω 0 t + φ).
McClellan, Schafer and Yoder, Signal Processing First, ISBN 0-13-065562-7.
c 2003 Pearson Education, Inc.
Prentice Hall, Upper Saddle River, NJ 07458. SOLUTION
McClellan, Schafer, and Yoder, Signal Processing First, ISBN 0-13-065562-7.
Prentice Hall, Upper Saddle River, NJ 07458. © 2003 Pearson Education, Inc.