Question

a compact disc (cd) records audio signals digitally by means of a binary code. assume an audio signal bandwidth of 15 khz. (a) what is the nyquist rate? (b) if the nyquist samples are quantized into 65,536 levels (l

Answer 1

Therefore, the digital signal will use 16 bits to represent each sample.

How to solve this problem

a) The lowest sampling rate necessary to faithfully capture a signal without sacrificing information is known as the Nyquist rate. The Nyquist theorem is used to compute it, and it stipulates that the sampling rate must be at least twice the highest frequency in the signal.

The bandwidth of the audio transmission in this instance is 15 kHz. The Nyquist rate (Fs), as per the Nyquist theorem, can be computed as follows:

Fs=2× Maximum Frequency

Fs=2× 15,000Hz=30,000Hz

So, the Nyquist rate for this audio signal is 30,000 Hz.

b) The number of quantization levels determines the resolution of the digitized signal. If the Nyquist samples are quantized into 65,536 levels (which is equivalent to
`2^1^6` levels), this means that the quantization process divides the range of the signal into 65,536 steps.

The formula to calculate the number of bits (n) for quantization is given by:

`n=log _2` (Number of Quantization Levels

`n=log _2` (65,536)

n=16

This means that 16 bits are needed for quantization if the Nyquist samples are quantized into 65,536 levels.