Question

Six analog information signals each band-limited to 4 kHz, are required to be time-division multiplexed and transmitted by a TDM system. The minimum transmission bandwidth and the signalling rate of the PAM/TDM channel are respectively.
1. 24 kHz and 48 kbps
2. 24 kHz and 8 kbps
3. 48 kHz and 48 kbps
4. 48 kHz and 16 kbps
5.

Answer 1

Correct Answer - Option 1 : 24 kHz and 48 kbps

Explanation:

The bit rate for a PAM/TDM system is given by

Rb = nfs

Where

Rb = Bit rate/Signaling rate

n = number of bits in the encoder

fs = sampling frequency

From Nyquist criteria

fs = 2fm

Where fm = message signal frequency

Minimum transmission Bandwidth (B.W.) = nfm ----(1)

Rb = nfs ----(2)

Given:

f_m = 4 kHz

n = 6

Minimum transmission Bandwidth (B.W.) is given by equation (1)

B.W. = 6 × 4 = 24 kHz

f_s = 2 × 4 = 8 kHz

Signaling rate is given by equation (2):

R_b = 6 × 8 = 48 kHz