(a) Minimum step size to avoid slope overloading.

(b) Signal-to-quantization noise ratio if speech is assumed to have nonuniform probability density function (PDF).

Solution:

For the DM system, if input signal $f(t)=b \cos \omega_m t$.

(a) Minimum step size to avoid slope overloading.

$\therefore\left|\frac{d f(t)}{d t}\right|_{\max }=b 2 \pi f_m$ if step size is used in DM system=a

$ \begin{aligned}\\ &\therefore f_s \geq \frac{2 \pi f_m}{a / b} \\\\ &\therefore a \geq \frac{2 …