## Q. 6.2

For a PCM system with a maximum audio input frequency of 4 kHz, determine the minimum sample rate and the alias frequency produced if a 5-kHz audio signal were allowed to enter the sample-and hold circuit.

## Verified Solution

Using Nyquist’s sampling theorem (Equation 1), we have
$f_{s} ≥ 2f_{a}$            (1)
therefore, $f_{s}$ ≥ 8 kHz

If a 5-kHz audio frequency entered the sample-and-hold circuit, the output spectrum shown in Figure 7 is produced. It can be seen that the 5-kHz signal produces an alias frequency of 3 kHz that has been introduced into the original audio spectrum.