This book offers a comprehensive treatment of modern signal processing theory and its main applications. Its unique perspective combines classic methods based on transforms and filter construction with analytical methods based on explicit signal models, and all algorithms and examples are illustrated with reproducible Matlab code. The first part of the book deals with classic non-parametric methods based on filters and transforms. A key here is the Discrete Fourier Transform and its relation to the continuous Fourier transform. Further, signals that can be described as stationary stochastic processes are treated, and common methods to estimate their covariance function and spectrum are described. This part ends with a description of different strategies for filtering of signals in the time and frequency domain. Typical application areas in this part are signal conditioning (noise attenuation) and spectral analysis. The second part describes parametric model-based methods. Different standard parametric models and their relation are surveyed, and methods to estimate the parameters in these models from measurements are presented. Related to this, one chapter describes adaptive filtering theory, where the goal is to estimate these parameters recursively in time for time-varying signal models. Important application areas here are prediction, signal conditioning and spectral analysis. Signal conditioning and prediction are also the key applications of the Wiener and Kalman filters, which are treated in separate chapters.