## Example 7.1

#### A broadcast audio source signal contains frequencies in the range from 50 Hz to 18 kHz. What is the minimum sampling rate required for an A/D converter in order to ensure that there will be no aliasing? What is a practical sampling rate to choose for this application?

#### If by accident a high frequency tone at 30 kHz is added into the audio source, at what frequency will this signal appear in the sampled waveform if the sampling rate is set at 40000 samples per second?

### Solution

#### The Nyquist sampling rate for perfect signal reconstruction (no aliasing) must be twice the highest frequency component of a baseband signal, that is, 2 x 18 kHz = 36000 samples per second. This sampling rate assumes that a 'brick-wall' low pass filter can be used to remove alias components. In practice, a sampling rate of 44100 samples per second is commonly used in the HiFi industry as the standard sampling rate for high quality audio signals with frequencies up to 20 kHz.
If a sampling rate of 40000 samples per second is used to digitize a tone with a frequency of 30 kHz, the sampling process will produce a difference frequency component at (40000 – 30000) = 10000 Hz, which falls well within the half Nyquist bandwidth of 20 kHz for a 40 kHz sampled system. It would thus appear that a 10 kHz tone had been applied at the input to the A/D converter.

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