Digital Signal Processing (DSP) is pervasive in our society, being an intrinsic component of all digital technology that is an essential part of modern life. This book presents the fundamentals of DSP in a concise and precise format. It starts with a review of the basics of discrete time signals and systems, with a focus on linear shift invariant systems. The book then goes on to review the Fourier and Z transform, along with the fundamentals of sampling and analog-to-digital (A/D) conversion—important basics for anyone searching for a clear link between DSP theory and practice. It also covers the covers the discrete Fourier transform (DFT) and the fast Fourier transform (FFT), along with digital filters design and implementation. A final chapter is dedicated to the analysis of some relevant DSP applications. The book will be useful to anyone with a background in engineering or science who needs to self-qualify on short notice, either to attend a technical meeting or to assume the management of a development team, for example. It will also be useful to someone who needs to learn enough to use a software tool for signal processing but who does not have the time to delve into the full theoretical details of the involved methods. In addition, this book can also be used as a textbook for an advanced undergraduate or graduate course in DSP with emphasis in problem solving.