Question

A message signal, which is bandlimited to 15kHz, is sampled at a rate 40% higher than the Nyquist rate and quantized by a 8-bit uniform quantizer. The theoritical minimum channel bandwidth required to tranmit the resultant binary data with proper signal shaping is _____kHz.

• A. 168

Answer 1

The correct option is A 168
$f_{m\left(max\right)}=15kHz$
Sampling rate , $f_s=1.40\times 2f_{m\left(max\right)}=1.40\times 30=42kHz$
Bits per sample, $n=8$
Bit rate, $R_b=n{f}_s=8\times 42=336kbps$
Minimum channel bandwidth required is,
$(BW{)}_{min}=\frac{R_b}{2}=\frac{336}{2}kHz=168kHz$