# Discrete-Time Systems

Discrete-time systems theory lays the foundation for digital signal processing algorithm development and design. This course first provides an introduction to discrete-time systems and then elucidates advanced topics in discrete-time signal processing. Topics include: (a) elementary digital signal processing (DSP): discrete-time signals and systems and their properties, z-Transform, frequency analysis, sampling and reconstruction, discrete Fourier transform; (b) multirate digital signal processing: decimation, interpolation, sampling rate conversion, digital filter banks; (c) linear Prediction and Optimum Linear Filters: linear prediction algorithms and properties, Wiener filters; and (d) adaptive filters: LMS algorithm, RLS algorithm.

### Learning Outcomes and Objectives

The notes and assignments on this resource page are intended to support learning of:

• advanced DSP problem solving skills
• rigorous thinking and creative visualization
• ability to overcome obstacles through ingenuity and resourcefulness

and encourage:

• an appreciation of the importance of advanced DSP for a broad class of engineering applications
• development of technical confidence
• a positive learning environment

### Text Book and Relevant Sections

These course resources make use of the following text:

John G. Proakis and Dimitris G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, 4th edition, 2007.

The following text book sections are covered.

• Chapter 1: 1.1, 1.2, 1.3, 1.4
• Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5
• Chapter 3: 3.1, 3.2, 3.3, 3.4, 3.5.5
• Chapter 4: 4.1, 4.2, 4.3, 4.4
• Chapter 5: 5.1, 5.2, 5.4, 5.5
• Chapter 6: 6.1, 6.2, 6.4, 6.5
• Chapter 7: 7.1, 7.2
• Chapter 8: 8.1
• Chapter 11: 11.1, 11.2, 11.3, 11.4, 11.5, 11.9, 11.10, 11.11
• Chapter 13: 13.1, 13.2, 13.3

### Problem Sets and Solutions

 Topic(s) Problem Set Questions Solutions Introduction to Discrete-Time Systems 1.2, 1.4, 1.6, 1.7, 2.2, 2.4, 2.5, 2.7 (a,g,j,k) PDF Discrete-Time Analysis and the z-Transform 2.13, 2.23, 3.6, 3.18(d), 3.23, 3.40 PDF Discrete-Time Frequency Domain Analysis 4.13, 4.16, 4.17,4.18,4.23, 5.4 (f,l), 5.11,5.65(a,c) PDF Sampling and Reconstruction 6.1, 6.10, 6.11, 6.13 PDF DFT and FFT 7.1, 7.3, 7.7, 7.13(a), 7.23(a,b,c,h), 7.28, 8.1, 8.3, 8.4, 8.7 PDF Sampling Rate Conversion 11.1, 11.2, 11.3, 11.4, 11.5 PDF Digital Filter Banks 11.9, 11.11, 11.12, 11.13, 11.15, 11.25, 11.29 PDF Adaptive Filtering 13.1, 13.2, 13.3, 13.12, 13.15 PDF

Note: Problem set solutions are courtesy of Julien Jainsky and Shoeb Mohammed who were former TAs for the course.