Signals, Systems, and Communications
Signals, Systems, and Communications tests LTI analysis, Fourier and Laplace/Z transforms, sampling, modulation, and noise. You should move between time and frequency domains and check bandwidth and aliasing.
Core rules
- An LTI system is characterized by h(t) or H(f); output is convolution in time and multiplication in frequency.
- Sampling must exceed twice the highest signal frequency; a practical anti-alias filter leaves margin.
- A sampled tone above Nyquist folds to |f - kfs|.
- AM doubles bandwidth around the carrier; FM has wider bandwidth (Carson's rule).
- SNR in dB = 10 log10(Ps/Pn); voltage ratio uses 20 log10.
Worked example
A 1.2 kHz tone is sampled at 2 kHz. Nyquist is 1 kHz, so the tone aliases. The nearest multiple of fs is 2 kHz; the folded frequency is |1200 - 2000| = 800 Hz. The reconstructed sequence is indistinguishable from an 800 Hz tone, and no post-filter can recover the original. To avoid this, sample above 2.4 kHz and use an anti-alias filter with a transition band below 1 kHz.
Traps
Using fs ≥ 2fmax with no margin; confusing normalized frequency; applying 10 log10 to voltage; forgetting that convolution in time is multiplication in frequency; and assuming a real mixer output has only the sum frequency, not sum and difference.