Communication Systems (Analog and Digital)
Communication Systems (Analog and Digital) tests modulation, bandwidth, noise performance, sampling and digital link budgets. Questions often ask for one number plus a reason.
Core rules
- AM: s(t)=Ac[1+m cos ωmt]cos ωct; m≤1 avoids overmodulation. Bandwidth = 2fm. Sideband power fraction = m²/(2+m²).
- FM: Carson's rule B ≈ 2(Δf + fm); modulation index β = Δf/fm. FM trades bandwidth for SNR.
- Nyquist: fs ≥ 2fmax; PCM bit rate = n fs. Quantisation SNR for a full-scale sinusoid ≈ 6.02n + 1.76 dB.
- Matched filter maximises SNR at sampling; BER for BPSK/QPSK is Q(sqrt(2Eb/N0)).
- Shannon capacity C = B log2(1+S/N); it is an upper bound, not a modulation scheme.
- Coherent detection needs carrier recovery; non-coherent detection is simpler but costs about 3 dB.
Worked example
A voice signal is sampled at 8 kHz and quantised to 8 bits. Bit rate = 8000×8 = 64 kbit/s. Quantisation SNR ≈ 6.02×8 + 1.76 = 49.9 dB for a full-scale sinusoid. If the signal occupies only half the full-scale range, SNR falls by 6 dB to about 43.9 dB. This is why companding is used in telephony: it preserves small-signal resolution.
Traps
- Using 2fm for FM bandwidth instead of Carson's rule.
- Forgetting the 1.76 dB term or applying the formula to a non-sinusoidal signal.
- Confusing Eb/N0 with SNR without accounting for bandwidth.
- Sampling at exactly Nyquist with non-ideal filters.
- Assuming Shannon capacity is achievable with any simple scheme.