Information and Communication Systems
This domain tests how signals carry information: time- and frequency-domain representation, sampling and quantization, analog and digital modulation, noise, capacity limits, and basic error-control coding. Numerical items often combine decibels, bandwidth, and bit rate, so unit discipline matters as much as the formulas.
Core rules
- Fourier analysis decomposes a signal into sinusoids; bandwidth is the range of significant spectral components, not the highest clock rate.
- Nyquist sampling requires fs > 2B for a baseband signal of bandwidth B; sampling below that folds energy back as aliasing.
- Shannon–Hartley gives the error-free capacity upper bound over an AWGN channel: C = B log2(1 + S/N), with S/N as a linear power ratio.
- Nyquist signalling limits symbol rate: about 2B symbols/s in baseband and B symbols/s in a double-sideband passband channel. Bit rate = symbol rate × bits per symbol.
- Quantization: each additional bit improves SNR by about 6 dB for a uniformly loaded quantizer.
- Higher-order QAM raises spectral efficiency but requires higher SNR for the same BER.
Worked example
A 1 MHz passband channel has SNR = 20 dB. Convert: S/N = 10^(20/10) = 100. Shannon capacity C = 1,000,000 × log2(101) ≈ 1,000,000 × 6.66 = 6.66 Mbit/s. With ideal Nyquist signalling, the symbol rate is about 1 Msymbol/s; 16-QAM carries 4 bits/symbol, giving 4 Mbit/s, which is below the Shannon bound and therefore feasible in principle. Confusing the Nyquist symbol-rate limit with the Shannon capacity limit is the usual error.
Traps
- Using 20 log10 instead of 10 log10 for a power ratio.
- Inserting SNR in dB directly into Shannon's formula.
- Mixing bit rate and symbol rate, especially with multilevel modulation.
- Treating fs = 2B as sufficient when practical filters need oversampling.
- Adding dBm values as if they were ordinary powers.