|Semester||Semester 5 – Fall|
The course focuses on the basic techniques for processing discrete-time signals, constituting one of the core elective courses in the department specialization area of signals, communications, and networks. In summary, it covers the following topics:
- Review of the theory of discrete-time signals and systems with emphasis on the analysis of linear, time-invariant systems using the discrete-time Fourier and Z transforms.
- Sampling of continuous-time signals, their reconstruction from their samples, and discrete-time processing of continuous-time systems.
- Sampling rate changes using discrete-time processing, multi-rate signal processing, and filter-banks.
- Transform analysis of linear time-invariant systems, minimum-phase systems, and linear systems with generalized linear phase.
- Structures for discrete-time system implementation.
- Infinite impulse response filter design by means of the impulse invariance method or the bilinear transform.
- Finite impulse response filter design by windowing.
- The discrete Fourier transform, algorithms for its fast computation, and circular convolution.
- Fourier analysis of signals using the discrete Fourier transform, including windowing, the time-dependent Fourier transform, signal spectrogram and periodogram, as well as signal reconstruction by overlap-add.
- Basic computational tools in Matlab corresponding to the above.
This course introduces students to the basic concepts and algorithms employed in the processing of discrete-time signals, while also providing numerous examples to allow student familiarization with them, as well as practical computational tools within the Matlab software framework, further demonstrating these.
Students successfully completing this class will have mastered the main concepts, algorithms, and tools in digital signal processing. For example, they will be able to:
- Perform signal sampling and reconstruction operations employing appropriate parameters and functions.
- Process continuous-time systems in the discrete-time domain and vice-versa.
- Change the sampling rate of discrete-time signals, while avoiding aliasing effects.
- Compute the frequency response of linear time-invariant discrete-time systems, perform minimum-phase / all-pass system decomposition, and describe linear-phase systems.
- Implement discrete-time systems using various structures.
- Design finite and infinite impulse response filters using various techniques.
- Understand the significance of the discrete Fourier transform and its fast implementation.
- Perform discrete-time signal analysis in the frequency domain employing the windowing method and the time-dependent Fourier transform, as well as signal reconstruction by overlap-add.
- Compute signal spectrogram and periodogram.
- Implement programs in Matlab to perform aforementioned tasks.