FDM Bandwidth for 10 Voice Channels: 25-Comp-B5 Computer Communications, December 2014, Q3

Question 3: FDM Bandwidth for 10 Voice Channels (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Ten voice channels, each occupying 5 kHz of bandwidth, to be frequency-division multiplexed with a 500 Hz guard band separating each pair of adjacent channels.

Given data
Quantity	Value
Bandwidth per voice channel	5 kHz
Number of channels, $n$	10
Guard band width	500 Hz = 0.5 kHz

Find. (a) the spectrum allocation diagram; (b) the total bandwidth the FDM link requires.

Fig. Q3(a) — spectrum allocation for 10 FDM voice channels with 500 Hz guard bands between adjacent channels.

Approach. Sum the ten channel bandwidths, then add one guard band for every pair of adjacent channels — $n$ channels placed side by side in frequency need $(n-1)$ internal guard bands, since nothing lies beyond the two outer edges of the composite spectrum that needs protecting.

Total channel bandwidth. $$n \times BW_{ch} = 10 \times 5\ \text{kHz} = 50\ \text{kHz}.$$
Number of guard bands needed. One guard band sits between each pair of adjacent channels, so $n$ channels need $$n - 1 = 10 - 1 = 9\ \text{guard bands}.$$
Total guard-band bandwidth. $$9 \times 0.5\ \text{kHz} = 4.5\ \text{kHz}.$$
Required total bandwidth. $$BW_{total} = 50\ \text{kHz} + 4.5\ \text{kHz} = \boxed{54.5\ \text{kHz}}.$$

Final results — Question 3
Quantity	Result
Bandwidth per channel	5 kHz
Number of channels	10
Number of guard bands	9
Total guard-band bandwidth	4.5 kHz
Required total bandwidth	54.5 kHz

Topic: Frequency-Division Multiplexing (FDM) bandwidth budgeting.

Key relations: $BW_{total} = n \cdot BW_{ch} + (n-1) \cdot BW_{guard}$.

Why this works: FDM places each channel's modulated spectrum in its own frequency slot; a guard band is a deliberately unused sliver of spectrum inserted between adjacent slots so that a real (non-ideal) bandpass filter's roll-off skirt cannot let one channel's energy leak into its neighbour. There is nothing beyond the outermost channels that needs protecting the same way, so only the $(n-1)$ internal boundaries require a guard band.

Common pitfall: using $n$ guard bands instead of $(n-1)$ (effectively double-counting, or placing one at each outer edge where none is needed), or forgetting guard bands altogether and reporting only the 50 kHz channel total.

Source: Stallings, Data and Computer Communications, 10th ed., Ch.8 (Multiplexing) §8.1 (Frequency-Division Multiplexing).

Question 3 of 7: FDM Bandwidth for 10 Voice Channels

Question 3: FDM Bandwidth for 10 Voice Channels (20 marks)