Understanding Signal Processing with MATLAB: Introduction to Frequency Analysis and Filters

Finally, a signal processing textbook where every equation runs as code.Understanding Signal Processing with MATLAB bridges the gap between textbook formulas and working implementations. If you have ever stared at a convolution formula and thought “I understand this”—only to find yourself lost the moment you open MATLAB—this book is for you.The Core Philosophy: Signals Are VectorsA discrete-time signal is just a column of numbers. A filter is just a matrix. Convolution is just matrix-times-vector. Once you see signal processing through this lens, everything clicks. This book builds that intuition systematically, from Chapter 1 to the final capstone project.Every concept follows the same loop: equation → MATLAB code → figure → numerical verification. Hand-coded implementations are checked against built-in functions like fft and conv, and the error norm is printed so you can judge correctness for yourself.What You Will Learn

• Sampling and quantization — Build the time axis from scratch. See aliasing in your own plots, not just as a theorem.
• Complex exponentials and phase — Geometric intuition for rotation and projection that underpins all frequency analysis.
• LTI systems and convolution — Implement convolution as a Toeplitz matrix–vector product.
• Frequency response and DTFT — Compute frequency responses by hand, then verify against the FFT.
• DFT and FFT — Build the DFT matrix from its definition. Confirm Parseval’s theorem numerically.
• Windows and PSD — Explore the main-lobe/sidelobe tradeoff. Build a Welch-style PSD estimator.
• STFT and spectrograms — Implement the Short-Time Fourier Transform. Understand the time–frequency tradeoff.
• Z-transform and IIR filters — Plot poles and zeros. Design resonators and notch filters.
• FIR filter design — Design filters using the window method. Evaluate ripple and attenuation. Complete a capstone project extracting a frequency band from a noisy signal.

No Toolboxes RequiredEvery algorithm runs on a base MATLAB installation—no Signal Processing Toolbox needed. When you build each function yourself and verify it against the built-in equivalent, you understand what every line does. The companion GitHub repository provides 30 reusable functions and 10 chapter scripts, all executable with a single “Run All.”Who This Book Is For

• Undergraduate students taking a first course in digital signal processing
• Self-learners who know the theory but struggle to translate formulas into code
• Engineers who want to move beyond black-box toolbox calls

Prerequisites: Basic MATLAB skills (arrays, plotting, functions), complex numbers, and vectors. Linear algebra and probability are introduced as needed—no prior coursework required.Companion Code: All scripts and functions are freely available at github.com/isobe-tech/MATLAB-signal-processing-book