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FDM bandwidth for 10 voice channels

Short answer

FDM is an analog technique where multiple signals modulate different carrier frequencies and share a link simultaneously in non-overlapping bands with guard bands. For 10 voice channels of 4 kHz and 500 Hz guard bands, required bandwidth = 10×4 kHz + 9×0.5 kHz = 44.5 kHz.

What is FDM? Assume a voice channel occupies a bandwidth of 4 kHz. We need to multiplex 10 voice channels with guard bands of 500 Hz using FDM. Calculate the required bandwidth.

FDM

Frequency division multiplexing (FDM) is an analog technique in which the bandwidth of a link is divided into several non-overlapping frequency bands. Each signal modulates a separate carrier frequency and occupies its own band, and all signals are transmitted simultaneously. Narrow guard bands separate adjacent channels to avoid interference. Band-pass filters at the receiver separate the channels.

Bandwidth calculation

Given: n = 10 channels, each 4 kHz; guard band = 500 Hz = 0.5 kHz. Guard bands are needed between adjacent channels, i.e. (n − 1) = 9 guard bands.

Total bandwidth = n × (channel BW) + (n − 1) × (guard BW) = 10 × 4 kHz + 9 × 0.5 kHz = 40 + 4.5 = 44.5 kHz

|ch1|g|ch2|g| ... |g|ch10|     10 channels + 9 guards

Answer: 44.5 kHz (if a guard band is also placed after the last channel, 10 guards give 45 kHz).

✓ Answer checked by Claude Sonnet 5.5

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