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ECEN 661  Modulation Theory
Homework #1
Assignment Date: 1/19/03
Due Date: 1/26/03
1. An audio signal
is FM modulated to produce
,
where
is the carrier frequency and
is the frequency deviation constant.
(a) Find the I and Q components of
.
(b) Find the real envelope and excess phase of
.
(c) Find the complex envelope of
.
2. An RLC bandpass filter has a transfer function given by
,
where
is the resonant frequency and
is the damping factor. Assuming that
so that the filter is narowband:
(a) Find the lowpass equivalent transfer function,
.
(b) Find the complex equivalent impulse response,
.
Hint:
It works out easiest if you take the “center” of the passband to be
which is
close to the resonant frequency of the circuit.
3. The PSD of a narrowband Gaussian noise pro
cess,
, is as shown in the figure at right.
(a) Find and sketch the PSD of the I and Q compo
nents of the narrowband noise process.
(b) Find and sketch the cross spectral density of the
I and Q components.
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 Spring '11
 Miller
 Frequency

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