Question

The samples of sinusoidal message signal $m\left(t\right)=cos\left(2\pi f_{m}t\right)V$ are applied to a delta modulator, whose step size is 2V. The minimum sampling rate required to eliminate the slope-overload distortion is approximately.

• A. $3.14f_m$
• B. $2f_m$
• C. $f_m$
• D. $f_m$

Answer 1

The correct option is A $3.14f_m$

The condition required to eliminate the slope-overload distortion is,
$\frac{\Delta }{T_s}\ge |\frac{dm\left(t\right)}{dt}{|}_{max}=|2\pi fmsin\left(2\pi fmt\right){|}_{max}$
$2f_s\ge 2\pi f_m$
$f_s\ge \pi fm\approx 3.14fm$
$f_{s\left(min\right)}=3.14fm$