Question

The message input to a delta modulator is $m\left(t\right)=\cos \left(1000\pi t\right)$ and the step size is $0.1V$. The minimum sampling frequency required to avoid slope overload distortion is _____ $kHz$.

• A. 31.42

Answer 1

The correct option is A 31.42
${\left|\frac{dm\left(t\right))}{dt}\right|}_{max}\le \frac{\Delta }{T_s}$

$1000\pi \le 0.1f_s$

$\frac{1000\pi }{0.1}\le f_s$

$f_s\ge 10\pi kHz$

$f_{s\left(min\right)}=10\pi kHz\approx 31.42kHz$