Beginning from the first principles, readers will learn how signals are acquired, represented, analyzed and transformed by digital computers. Specific attention is given to digital sampling, discrete Fourier analysis and linear filtering in the time and frequency domains. All concepts are introduced practically and theoretically, combining intuitive illustrations, mathematical derivations and software implementations written in the Python programming language. Practical exercises are included at the end of each chapter to test reader knowledge. Written in a clear and accessible style, is particularly aimed at students and general readers interested in audio and digital signal processing, but who may not have extensive mathematical or engineering training.