1. Characterize and fully analyze discrete-time signals in the time domain.
2. Analyze discrete-time systems in the time domain using difference equations and the impulse response. Categorize and evaluate FIR and IIR systems. Construct block diagram implementations of discrete-time systems.
3. Compute the z and Fourier transforms of discrete time functions and use them to analyze discrete-time signals and systems. Compute the transfer function, the frequency response, the impulse response and the output of systems.
4. Formulate the general digital filter design problem. Design and analyze digital filters and evaluate the various FIR and IIR filter design methods.
5. Evaluate the Discrete Fourier Transform (DFT) and Fast Fourier transform (FFT) of discrete-time signals. Illustrate their use in DSP applications.
6. Demonstrate skill and understanding in the use of MATLAB DSP tools for the analysis and design of discrete-time systems.

Introduction: Advantage of digital signal processing systems. Applications. Classification of signals and systems. Concepts of sampling and frequency in discrete time systems.

Discrete time signals and Systems: Signal operations. Properties. Useful signals. Correlation. Linearity, shift-invariance and causality of discrete time systems. Input output description of systems. Difference equation. Impulse response and convolution. Block diagram representations. Cascaded systems. Recursive and non-recursive realizations of systems.

The z-transform:  Properties. Rational z-transforms, poles and zeros, causality and stability. Location of poles and zeros and system behavior. Inverse z-transform and partial fraction expansion. Stability tests.

Frequency analysis of signals and systems: Fourier Transform of discrete time signals. Power density spectrum and cepstrum. Frequency response of discrete time systems. Magnitude and phase. Group delay. Ideal filters and their frequency response.

Discrete Fourier Transform: Properties and applications. Frequency analysis of signals using the DFT. Linear filtering based on the DFT. Fast Fourier Transform (FFT) algorithms and its applications.

Digital Filter Design and Implementation: Selected topics in the design and implementation of FIR and IIR digital filters.

• J. Proakis, D. Manolakis, Digital Signal Processing, Principles, Algorithms and Applications, 4th edition, Prentice Hall, 2007.

• A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, 2nd ed., Prentice Hall, 1999.
• V. Ingle, D. Manolakis, Digital Signal Processing Using Matlab, Prentice Hall, 2006.

The teaching of the course is lecture-based (3 hours per week) in a classroom, using a combination of traditional teaching with written notes on a white board and slide presentations using a projector for the presentation of the more complicated diagrams, graphs and MATLAB design tools. Students are assessed continuously and their knowledge is checked through tests, assignments and the final exam.

Lectures include the solution and discussion of example problems regarding the material presented. Relevant homework and assignments are given to the students for further study at their own. Due to the level and type of the course students are urged to participate in discussing the various topics and provide their opinion during problem-solving sessions. Lecture notes are compiled by students which serve to cover the main issues under consideration and serve as a guide for further reading. Students are also required to seriously use the textbook assigned to the course, in addition to other sources found either in the library or elsewhere in order to broaden their perspective on the various subjects presented in class and in the textbook. Additionally, they are expected to use DSP software tools for the analysis of signals and systems and the design and analysis of digital filters.