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Frequency Division Multiplexing (FDM)

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1. Concept of Multiplexing

Multiplexing is the technique of transmitting multiple simultaneous analog or digital signals over a single shared high-capacity physical data link.

• Multiplexer (MUX): Combines $n$ separate input channels into a single composite transmission stream.
• Demultiplexer (DEMUX): Separates the composite stream back into the original individual channels at the destination.

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2. Frequency Division Multiplexing (FDM) Principles

Frequency Division Multiplexing (FDM) is an analog multiplexing technique that is applicable when the physical link bandwidth (in Hz) is significantly greater than the combined bandwidths of the individual signals to be transmitted.

Modulation and Guard Bands:

• Each incoming baseband signal modulates a different high-frequency carrier signal ($f_{c1}, f_{c2}, f_{c3}, \dots$).
• The resulting modulated signals occupy distinct non-overlapping frequency bands along the spectrum.
• Guard Bands: Small unused frequency intervals placed between adjacent channels to prevent signals from overlapping and causing crosstalk.

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3. Mathematical Formula for Required Bandwidth

For $n$ channels where each channel requires bandwidth $B_{ch}$, separated by guard bands of bandwidth $B_{guard}$:

Solved Numerical Example:

• Problem: 5 voice channels, each with a bandwidth of $4\text{ kHz}$, are to be multiplexed onto a single transmission link using FDM. If each guard band is $500\text{ Hz}$ ($0.5\text{ kHz}$), calculate the minimum bandwidth of the link.
• Solution:

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4. Demultiplexing Process

At the receiver, the composite signal passes through a bank of Bandpass Filters (BPF):

Each filter extracts only the specific carrier frequency band assigned to that channel, and the demodulator shifts the signal back down to its original baseband frequencies.

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5. Applications, Advantages & Disadvantages

Real-World Applications:

1. AM & FM Radio Broadcasting: The air atmosphere is the shared medium; each radio station broadcasts on its own distinct carrier frequency (e.g., $98.3\text{ MHz}$, $104.0\text{ MHz}$).
2. Cable Television (CATV): Dozens of television channels are transmitted simultaneously over a single $75\text{ }\Omega$ coaxial cable.
3. First-Generation Cellular (1G AMPS) and ADSL telephone lines.

Advantages:

• Simple analog implementation; does not require complex digital framing or synchronization clocks.
• Supports continuous real-time transmission without buffering delay.

Disadvantages:

• Inefficient bandwidth utilization due to wasted guard bands.
• Susceptible to intermodulation distortion and analog noise amplification.
• Costly hardware (requires separate analog modulators and precision bandpass filters for every channel).

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