Communications
Amplitude and angle modulation, noise, digital modulation, and the information theory that bounds all of it.
About this subject
Communications covers how information is carried over a channel: amplitude and angle modulation, sampling and pulse modulation, digital modulation schemes, noise, and information theory - entropy, channel capacity and coding.
The subject mixes power bookkeeping (how much of an AM signal's power is in its sidebands), bandwidth rules of thumb (Carson's rule), and logarithms (entropy and capacity). Keeping track of linear ratios versus decibels is the most important single habit.
Solved questions
Each question is a practice problem written for this portal at GATE standard. Try it first, then open the full derivation, and read the note on the idea behind it.
- NAT Total transmitted power of an AM signal at 50 percent modulation Amplitude modulation · 2 marks
- NAT FM transmission bandwidth by Carson rule Angle modulation · 1 mark
- NAT Shannon capacity of a 3 kHz channel at 30 dB SNR Information theory · 2 marks
- NAT Entropy of a four-symbol discrete memoryless source Information theory · 1 mark
Key formulas
The results these questions lean on most. Know what each symbol means, and when each one applies.
| What | Formula |
|---|---|
| AM total power | $P_t = P_c\,(1 + \mu^2/2)$ |
| AM power efficiency | $\eta = \mu^2 / (2 + \mu^2)$ |
| Carson's rule | $B_T \approx 2(\Delta f + f_m)$ |
| FM modulation index | $\beta = \Delta f / f_m$ |
| Shannon capacity | $C = B\log_2(1 + S/N)$, with $S/N$ as a power ratio |
| Decibels to ratio | $S/N = 10^{\,\text{dB}/10}$ |
| Entropy | $H = -\sum p_i \log_2 p_i$ bits per symbol; at most $\log_2 M$ for $M$ symbols |
How to prepare
- Convert every decibel figure to a linear ratio before putting it into a formula.
- Learn where each factor of two comes from in AM power, rather than memorising the formula.
- Check entropy answers against the maximum $\log_2 M$ - a larger value is always wrong.
- Know which bandwidth rules are exact and which are approximations.
Common traps
Each of these costs marks every year. The questions above are built to catch them.
- Using decibels directly inside Shannon's logarithm.
- Writing $P_c(1 + \mu^2)$ for AM power.
- Answering $2\Delta f$ for FM bandwidth.
- Assuming a four-symbol source always has 2 bits of entropy.