Digital communication and signal processing
Digital communication and signal processing
This domain tests sampling, quantization, Fourier processing, pulse shaping, equalization, and coding. Expect numerical questions on ADC resolution, FFT bins, ISI, and coding gain.
Core rules
- Nyquist requires fs>2fmax; practical systems oversample to relax the anti-alias filter. Aliasing folds high frequencies into the baseband.
- Full-scale sine SQNR is approximately 6.02n+1.76 dB for an n-bit ADC. Oversampling by factor K adds 10logK dB in quantization noise spread.
- An N-point FFT at sample rate fs has bin spacing fs/N. Windowing reduces leakage but widens the main lobe and lowers amplitude accuracy.
- Nyquist pulse shaping controls ISI; a matched filter maximizes SNR. Raised-cosine excess bandwidth alpha trades spectral efficiency against time-domain tail length.
- Coding (Hamming, convolutional, LDPC) adds redundancy for coding gain; interleaving spreads burst errors.
Worked example
A 12-bit ADC samples a full-scale sine. SQNR is approximately 6.02(12)+1.76=74.0 dB. If the same signal is oversampled by 4 and then low-pass filtered and decimated, quantization noise in the desired band improves by 10log4=6 dB, giving about 80 dB. The FFT of 1024 samples at fs=10 MHz has bin spacing 10 MHz/1024=9.77 kHz; this resolution is set by record length, not by the window.
Traps
Using fs=2fmax as sufficient in practice, applying the 6.02n formula to a non-full-scale or non-sine signal, and confusing FFT bin spacing with RBW. Also remember that cyclic-prefix overhead reduces throughput and that equalization cannot remove noise enhancement.