Course Description:
This course starts with a discussion of the analysis and representation of discrete-time signals and systems, specifically discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Also, fast Fourier transform algorithm is discussed for efficient discrete Fourier transform computations. The second part of the course covers digital filter designs both finite impulse response and infinite impulse response filters.

Course Learning Outcomes:
CLO:1 Express discrete time signals and systems in time domain and frequency domain.
CLO:2 Analyze signals and systems in time and frequency domain.
CLO:3 Design digital filter and Multi-rate Signal Processing systems by applying discrete time systems by applying different digital signal processing techniques.

Course Contents:
1. Introduction-Three Lectures
• Signals, Systems, and Signal Processing
• Classification of Signals
• The concept of the frequency
• Analog-to-Digital and Digital-to-Analog Conversion

2. Discrete Time Signals and Systems-Five Lectures
• Discrete-time Signals
• Discrete-time Systems
• Analysis of Discrete-time Linear Time-Invariant Systems
• Discrete-time Systems described by Difference Equations
• Implementation of the Discrete-time Systems
• Correlation of Discrete-time Signals

3. The Z- and Fourier transform and its Application to the Analysis of LTI Systems-Three Lectures
• The z-transform
• Properties of the z-transform
• Rational z-transform
• Inverse z-transform
• Analysis of LTI Systems in the z-transform
• The one sided z-transform

4. Frequency Analysis of Signals-Three Lectures
• Frequency Analysis of Continuous –Time Signals
• Frequency Analysis of Discrete-Time Signals
• Frequency Domain and Time –Domain Signal Properties
• Properties of the Fourier transform for Discrete-Time Signals

5. Frequency-Domain Analysis of LTI Systems-Three Lectures
• Frequency -Domain Characteristics of LTI Systems
• Frequency response of LTI Systems
• Correlation Functions and Spectra at the Output of LTI Systems
• LTI Systems as Frequency-Selective Filters
• Inverse Systems and Deconvolution

6. Sampling and Reconstruction of Signals-Four Lectures
• Ideal Sampling and Reconstruction of Continuous –Time Signals
• Discrete Time Processing of the Continuous –Time Signals
• Analog-to-Digital and Digital-to-Analog Converters
• Sampling and Reconstruction of Continuous –Time Signals
• Oversampling A/D and D/A Converters

7. The Discrete-time Fourier transform-Four Lectures
• Frequency-Domain Sampling: The Discrete Fourier Transform
• Properties of the DFT
• Linear Filtering Methods Based on the DFT
• Frequency Analysis of Signals Using the DFT
• Efficient Computation of the DFT: Fast Fourier Transform Algorithms

8. Digital Filters Design-Four Lectures
• Design of FIR Filters
• Design of IIR Digital Filter
• Frequency Transformations

9. Multi-rate Signal Processing-Three Lectures
• Decimation by a Factor M
• Interpolation by a Factor L
• Sampling Rate Conversion by a Rational Factor M/L
• Application of the Multi-rate Signals Processing
• Digital Filter Banks