## 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.