Chapter 4: Signals and Systems for Communications

Learning Objectives

• Classify signals (energy vs. power, deterministic vs. random) and characterise LTI systems via impulse response and transfer function
• Compute Fourier transforms, apply Parseval's theorem, and relate bandwidth to time-domain properties
• State and apply the Nyquist--Shannon sampling theorem; identify aliasing and design anti-aliasing filters
• Convert between passband and complex baseband representations using the analytic signal and Hilbert transform
• Model the wireless channel as a linear time-variant (LTV) system with time-variant impulse response $h(t,\tau)$
• Compute output PSD of WSS processes through LTI systems and derive the matched filter as the SNR-optimal receiver