Question

A message signal, which is band-limited to 20 kHz is sampled with Nyquist rate and quantized by a 3-bit uniform quantizer. The theoretical minimum channel bandwidth required to transmit the resultant data with proper signal shaping is equal to_______kHz.

• A. 60

Answer 1

The correct option is A 60
Given that, $f_{m\left(max\right)}=20kHz$

Bits per sample, $n=3$

Sampling rate, $f_s=2f_{m\left(max\right)}=40kHz$
Bit rate, $R_b=n{f}_s=120kbps$

Minimum channel bandwidth required is,

$(BW{)}_{min}=\frac{R_b}{2}=60kHz$