Page 213 - Fundamentals of Communications Systems

Amplitude Modulation 6.35

(c) Determine the conditions on A such that envelope detection could be used
in the demodulation process with no distortion.
(d) Determine the MCPR of this modulation scheme as a function of A.

Problem 6.15. You need to test a VSB-AM system that your company has pur-
chased. The modulation scheme is DSB-AM followed by a bandpass filter, H c (f ).
The demodulator is exactly the same as DSB-AM when the phase offset, φ p ,is
known. The system does not work quite right and testing has led you to suspect
the filter H c (f ). After analysis and testing, you determine that the filter has
the following bandpass characteristic

⎧
⎪ 1 f c + 7500 ≤| f |≤ f c + 10000
⎪
⎪
⎪ 2 f c + 2500 ≤| f | < f c + 7500
⎪
⎪
⎪
⎨
4
H c (f ) = 3 f c ≤| f | < f c + 2500
⎪
⎪ 3
⎪
⎪ 4 f c − 2500 ≤| f | < f c
⎪
⎪
⎪
0 elsewhere
⎩
You will be using the system to transmit voice signals with a bandwidth of
5000 Hz.
(a) Compute H z (f ) = H I (f ) + jH Q (f ).
(b) What are the conditions on H I (f ) and H Q (f ) for f ∈ [−W, W] that will
produce a distortionless demodulator.
(c) Does the VSB system produce a distortionless output? That is, does ˆm(t) =
Km(t), where K is some constant?
(d) The filter above consists of five frequency segments with constant gain.
Because of cost restrictions, you can change the gain on only one of the
segments. Change one segment gain such that the system will produce a
distortionless output.
(e) What is the bandwidth efficiency of your resulting VSB system and the
resulting savings in transmission bandwidth over DSB-AM?
(f) What is the spectrum of the corresponding complex envelope equivalent,
H z (f ), of the improved filter?

Problem 6.16. This problem is concerned with double-sided band amplitude
modulation (DSB-AM) of the message signal given in Problem 5.1. Assume
a carrier frequency of f c = 200 Hz and a carrier amplitude of A c .

(a) Give the baseband, x z (t), and bandpass, x c (t), time waveforms for DSB-AM
for this message signal as a function of m(t).
(b) The bandpass signal is also periodic. What is the period? Give the Fourier
series representation for the bandpass signal