Generation of discrete-time signals through the sampling process and their spectral representation. Mathematical representation and properties of digital signal processing (DSP) systems. Typical DSP systems, e.g., digital filters and applications. The ztransform and its relation to the Laurent series. Evaluation of the inverse z transform using complex series and contour integrals. Application of the z transform for representation and analysis of DSP systems. The processing of continuous time signals using DSP systems. The discrete-Fourier transform and the use of fast Fourier transforms for its evaluation. Introduction to the design of DSP systems.

Learning Outcomes

1. Understand linearity, time invariance and convolution

2. Explain relation between continuous- and discrete-time Fourier transform

3. Understand z-transform and its use in solving problems

4. Evaluate forward and inverse z and Fourier transforms for discrete signals

5. Demonstrate competency in working with both time- and frequency-domain representations of discrete-time sampled signals

6. Design a discrete-time filtering algorithm based on given requirements

7. Use MATLAB effectively for analysis and design of sampled digital signals

8. Explain significance of sampling theorem and use it in the context of discrete-time processing of continuous-time signals

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