Question

4 Voice signals, each with a bandwidth of 4 kHz, are to be transmitted through a baseband channel using time division multiplexing. If the signals are sampled at Nyquist rate and quantized with an 8-bit quantizer, then the theoretical minimum channel bandwidth required to transmit the multiplexed signal is used to

• A. 128 kHz
• B. 512 kHz
• C. 64 kHz
• D. 256 kHz

Answer 1

The correct option is A 128 kHz

Number of voice signals N = 4

Maximum frequency of each signal, $f_{m\left(max\right)}=4kHz$

Bits per sample, $n=8$

sampling rate of each voice signal, $f_s=2f_{m\left(max\right)}=8kHz$

Sampling rate of the multiplexed signal $f_{s\left(overall\right)}=N{f}_s=32kHz$

Overalll transmission rate, $R_b=n{f}_{s\left(overall\right)}=256kBps$

Theoretical minimum channel bandwidth required is,

$(BW{)}_{min}=\frac{R_b}{2}=128kHz$