ECEN 661  Modulation Theory
Homework #4
Assignment Date: 2/13/08
Due Date: 2/20/08
1. (Text 4.34, 4th edition) The information sequence
is a
sequence of iid random variables, each taking values
with
equal probabilities. This sequence is to be transmitted at base
band by a biphase coding scheme, described by
.
where
is shown in the figure.
(a) Find the PSD of
.
(b) Assume that it is desirable to have a zero in the PSD at
. To this end, we use a pre
coding scheme by introducing
, where
is some constant, and then transmit the
sequence using the same pulse shape. Is it possible to choose
to produce a frequency null
at
? If yes, what are the appropriate values and the resulting power spectrum?
(c) Now assume we want to have zeros at all multiples of
. Is it possible to have
these zeros with an appropriate choice of
in the previous part? If not, then what kind of precod
ing do you suggest to result in the desired nulls?
2. (Text 5.6, 4th edition) Consider the lowpass equivalent (complex valued) signal
,
, with energy
.
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 Spring '08
 Miller
 Signal Processing, Bandpass filter, AWGN, 08 g

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