Signal Processing Explained: Systems, Analysis & Digital Communication Technologies

Abstract

Signal Processing Explained: Systems, Analysis & Digital Communication Technologies is a publication-grade Open Educational Resource (OER) module covering the mathematical foundations, discrete-time systems, spectral transforms, and digital filter architectures governing signal analysis across electrical and electronic engineering. Serving as an integral core module within the Electrical and Electronic Engineering curriculum on Prep4Uni.Online, this text bridges analog front-end conditioning and Nyquist-Shannon sampling with contemporary AI-era computational paradigms, neural operators, and edge digital signal processors. Key Features & Pedagogical Additions:• Theoretical Grounding & Contemporary Paradigms: Integrates classical continuous and discrete-time theory (Fourier transforms, z-transforms, Nyquist sampling, quantization noise, convolution, spectral windowing) with Physics-Informed Neural Networks (PINNs) solving acoustic Helmholtz wave equations for inverse tomography, Fourier Neural Operators (FNOs) for non-stationary spectrogram modeling, and Lie-group SO(3) Invariant Extended Kalman Filters (IEKF) for multi-axis sensor fusion.• Systems Engineering Architecture & Trade-Off Analysis: Structured comparison matrix contrasting Finite Impulse Response (FIR) against Infinite Impulse Response (IIR) filters, Fixed-Point (Q15/Q31) against Floating-Point arithmetic, Discrete Wavelet Transforms (DWT) against Short-Time Fourier Transforms (STFT), and Recursive Least Squares (RLS) against Least Mean Squares (LMS) adaptive filtering.• Worked Numerical Engineering Application: A complete, multi-step engineering calculation detailing an acoustic vibration monitoring chain—evaluating Nyquist oversampling margins, ADC quantization step sizes (V_LSB), theoretical 16-bit SQNR (98.08 dB), linear-phase FIR low-pass filter tap sizing via Bellanger's approximation, and a 204.8x computational speedup analysis comparing direct DFT against Radix-2 FFT algorithms.• Curricular Assessment & Analytical Inquiries: Contains 25 fully resolved foundational review questions, deep analytical design inquiries, and step-by-step numerical calculations spanning anti-aliasing cutoff frequencies, ADC quantization signal-to-noise ratios, Radix-2 FFT operation counts, FIR linear convolution output lengths, first-order discrete-time RC filter cutoff derivations, active notch filter decibel attenuations, and uncompressed audio bitrate compression ratios.