The course focuses on digital signals and systems covering the basic mathematical tools for their qualitative and quantitative characterization as well as their processing. In the first part of the course, the basic definitions related to discrete time signals are introduced together with the linear time invariant systems, the convolution operation, and Z transform in conjunction with its basic properties. Furthermore, the first part includes: the transfer function of a system, the bounded input and bounded output stability, the discrete time Fourier transform, the Nyquist sampling theorem, as well as the discrete Fourier transform with its properties, the cyclic convolution, and the fast Fourier transform. In the second part of the course, the well-known implementation schemes of transfer functions are introduced (direct forms, serial and parallel) together with the design principles of digital FIR filters, linear phase filters, the windowing approach, and the optimum filtering methodology. Additionally, the design of analog filters is studied (Butterworth, Chebychev, elliptic) and its principles are further used in the design of digital IIR filters. The methods of impulse invariance and bilinear transformation are investigated through representative examples. The theory and exercises of the course include representative application examples in the fields of sound and speech signals, images, and communication signals.