Objective

The course is designed for students to gain an understanding of random processes and the processing of discrete-time signal. Students have learnt basic concept in probability and statistics in ERG2012. In this course, they will first learn the concept of random variables and then random processes. As students have learned the processing of discrete-time aperiodic signal in ERG2030 Signals and systems, so in this course they will learn the processing of discrete-time periodic signal, in particular the Discrete Fourier Transform (DFT). Generally, abstract concept is first explained using concrete examples and then extended to the general case.

Syllabus

• Revision of probability Theory
• Random variables
• Random processes
• Revision of discrete-time aperidic signal processing
• Properties of LTI systems for discrete-time aperiodic signals
• Revision of signal processing
• Properties of LTI systems for discrete-time periodic signals

Learning Outcome

By the end of the course, students should be able to

• Understand the definitions of random variables and random processes and why they are needed.
• Know how to determine a probability density function of a random variable by reasoning or by experiments or from probability density functions of other random variables.
• Know how to estimate the normalized correlation coefficients of two random variables and determine if two random variables are independent.
• Understand what stationary random processes and ergodic random processes are, and why these concepts are needed.
• Understand what power spectral density and autocorrelation function are and their relationship.
• Understand what Gaussian random processes are and what white noises are.
• Understand the properties of continuous-time aperiodic signals, discrete-time periodic signals and discrete-time aperiodic signals, and why these representations are needed.
• Know how to compute the properties, which include the phase distortion, impulse response, frequency response, transient response and steady state response of a rational system function for discrete-time aperiodic signals and understand why these properties are needed.
• Know how to determine if such a rational system function is stable and causal.
• Know how to find the inverse of such a rational system function.
• Understand the definition and physical meaning of DFT.
• Know how to compute using a computer the DFT of a sequence which is a sample of a continuous-time waveform.  Understand what frequency components in the continuous-time waveform are represented by DFT coefficients.
• Know how to compute linear convolution by means of DFT.

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