Example 6.1
A digital television system has a source analogue
video signal with bandwidth extending from 0 Hz to 2 MHz. This signal is sampled at four
times the highest frequency using a 16-bit A/D converter. The resulting data signal is
sent over the air using a 16-QAM modulation format with a roll-off factor on the
pulse-shaping filters of a = 0.5.
What is the bandwidth occupied by the transmitted digital video signal?
Solution
The sampling rate for the A/D converter is 4 x 2 MHz
= 8 million samples per second. Each sample is encoded as a 16-bit word, resulting in a
bit rate of 16 x 8 million = 128 Mbps at the converter output.
A 16-QAM modulation format conveys four bits per
symbol, and because it is a bandpass format, this equates to a maximum bandwidth
efficiency of 4 bits/second/Hz for an ideal (a = 0) filter.
For a = 0.5, the bandwidth efficiency is reduced by a factor (1 + a) to 2.66 bits/second/Hz, and the bandwidth required
to support a data rate of 128 Mbps is 48 MHz.