This course aims to introduce the basics of Digital Signal Processing using the mathematical tools presented in Signal and Systems courses. We review some of these tools with additional new concepts to go more deeply in analyzing digital systems. We present the basic digital networks used to implement discrete systems including the various structures of FIR and IIR digital filters. The effect of coefficients quantization and finite precision arithmetic on the performance of LTI systems is also presented. We also present the main methods used in digital filters design. A special interest is given to the interpretation of the DFT of sinusoidal signals to understand the limits of this tool in spectral analysis. We conclude by introducing the discrete cosine transform which is used in many applications as in JPEG image compression. Intended Learning Outcomes: - Describe discrete-time signals and its properties. - Describe discrete-time systems and its properties. - Apply Fourier Transform to analyze for discrete-time systems. - Understand the Sampling theorem and the quantization operation. - Review the Z-transform and its properties. - Apply the Z-transform to analyze discrete systems. - Describe the digital networks and main methods to implement discrete systems. - Understand the effect of coefficient quantization and finite precision arithmetic on the performance of discrete systems. - Identify design methods for FIR filters. - Identify design methods for IIR filters. - Apply the Discrete Fourier Transform to analyze discrete signals. - Apply the Cosine Transform and its main applications.