Transforms feel arbitrary until you see what they measure. This book keeps the instrument in view.
Signal processing is often taught as a sequence of mathematical procedures, with the meaning of each transform left implicit. This book reverses that order. You begin by classifying signals and systems, then build convolution by hand in both continuous and discrete time, and decompose responses into zero-input and zero-state parts. Fourier series and transforms arrive as answers to real questions about frequency content, with line spectra, energy relations and the Gibbs phenomenon explained rather than asserted.
You then take sampling seriously: Nyquist limits, aliasing you can see, reconstruction and anti-alias filtering. Discrete chapters cover the discrete Fourier transform with windowing and leakage, fast algorithms, the z-transform, and FIR and IIR filter design with finite word length effects. Closing chapters handle noise, power spectral density and modulation. Throughout, the emphasis stays on what each tool measures and when it applies, so that the mathematics remains connected to the signals on the wire.
What you will learn
• Classify signals and systems, and test linearity, time invariance, causality and stability
• Build convolution by hand in continuous and discrete time, and interpret impulse responses
• Solve differential and difference equations, separating zero-input and zero-state responses
• Read Fourier series and transforms as frequency-content measurements, including line spectra, energy relations and the Gibbs phenomenon
• Apply the Laplace transform to system analysis and stability
• Handle sampling correctly: Nyquist limits, visible aliasing, reconstruction and anti-alias filtering
• Use the discrete Fourier transform with windowing and leakage control, and apply fast algorithms
• Work with the z-transform, and design FIR and IIR filters with finite word length effects in view
• Analyze random signals, noise, power spectral density and modulation in practical settings
For electrical engineering students and practising engineers working with sampled data, this book provides a coherent path from signal classification to filter design and noise analysis. If you need to understand not only how to compute a transform but what it tells you about a real signal, this treatment keeps the instrument in view from the first chapter to the last.