Question

The period signal shown in the figure below is sampled at a rate of 10 kHz and the samples are applied to a delta modulator system.



The minimum step-size of the delta modulator required to eliminate the slope-overload distortion is equal to ________mV.

• A. 2

Answer 1

The correct option is A 2
To eleminate slope-overload distortion,

$\frac{\Delta }{T_s}\ge {\left|\frac{dx\left(t\right)}{dt}\right|}_{max}$

${\left|\frac{dx\left(t\right)}{dt}\right|}_{max}=\left|\frac{10-0}{1-\left(1.5\right)}\right|=\frac{10}{0.5}=20V/sec$

$T_s=\frac{1}{f_s}={10}^{-4}sec$ $\because Giventhat{f}_s=10kHz$

So, $|\Delta |\ge T_s{\left|\frac{dx\left(t\right)}{dt}\right|}_{max}$

$\Delta \ge \left({10}^{-4}\right)\left(20\right)V$

${\Delta }_{min}=2mV$