This book covers the fundamental concepts of digital signal processing (DSP), introducing discrete-time signals, the z-transform, frequency analysis, discrete and fast Fourier transforms, digital filters, FIR, and statistical DSP. With applications ranging from engineering to telecommunications and medical imaging, this text focuses on representing signals with mathematical models and processing them using discrete-time systems. Understanding DSP is crucial for professionals in various fields as it allows for effective signal representation and manipulation. The book starts with an introduction to DSP and a review of discrete-time signals and systems, followed by a detailed exploration of the z-transform and frequency analysis using DTFT. It further delves into discrete Fourier transforms, fast Fourier transform algorithms, and the implementation of discrete-time systems. The journey continues with in-depth discussions on digital filters, including the design and analysis of infinite impulse response (IIR) and finite impulse response (FIR) filters. The book also covers statistical digital signal processing, multirate DSP, and applications in speech and radar. Through a variety of exercises and a comprehensive glossary, readers will gain a solid understanding of DSP fundamentals and applications.