Question

A uniform quantizer is used to quantize a random message signal, whose amplitude is uniformly distributed in the range [-a, a]. If the maximum allowed quantization error is 0.1% of the peak value of the message signal, then the minimum number of bits per sample required by the quantizer will be equal to __________.

• A. 10

Answer 1

The correct option is A 10
For a uniform quantizer, the maximum quantization error is $\frac{\Delta }{2}$.

So, $\frac{\Delta }{2}\le \frac{0.1}{100}\left(a\right):$ where, $\Delta =stepsize$

$\Delta \le \frac{a}{500}$

$\frac{2a}{2^n}\le \frac{a}{500}$

$\because$ $\Delta =\frac{a-(-a)}{L}=\frac{2a}{2^n}$

Where L = Number of quantization levels and n = number of bits per sample.

So, from equation (i), $2^n\ge 1000$

$n\ge 10$ $\because ncanbeanintegeronly$

$n_{min}=10$