Question

The samples of a sinusoidal message signal $m\left(t\right)=2cos\left(200t\right)V$ are applied to a delta modulator, whose step size is 1 V. THe minimum sampling rate required to eliminate the slope-overload distortion, for the given message signal is ______ samples/s.

• A. 400

Answer 1

The correct option is A 400
The condition required to eliminate the slope-overload distortion is,

$\frac{\Delta }{T_s}\ge {\left|\begin{array}{c}\frac{dm\left(t\right)}{dt}\end{array}\right|}_{max}{\left|\begin{array}{c}\frac{dm\left(t\right)}{dt}\end{array}\right|}_{max}={\left|\begin{array}{c}400sin\left(200t\right)\end{array}\right|}_{max}=400V/sSo,{\Delta }_{f_s}\ge 400V/s{f}_s\ge \frac{400}{\Delta }=400\text{samples/s}\because \Delta =1VSo,f_{s\left(min\right)}=400samples/s$