EC2410 Analysis of Signals and Systems

Analysis of digital and analog signals in the frequency domain; properties and applications of the discrete Fourier transform, the Fourier series, and the continuous Fourier transform; analysis of continuous systems using convolution and frequency domain methods; applications to sampling, windowing, and amplitude modulation and demodulation systems.

Prerequisite

MA1113 & ability to program in MATLAB or consent of instructor.

Lecture Hours

4

Lab Hours

1

Outcomes

1. Determine the effects of sampling a continuous-time signal and compute the power and energy of a continuous-time and/or discrete-time signal.
2. Evaluate the expected continuous-time expression for a signal by using the spectrum information of the discretized signal.
3. Compute the response of a LTI system by convolution and the response of a LTI system to a cosine signal excitation.
4. Characterize a LTI system in terms of its frequency response.
5. Compute the response of a LTI system by using FT properties and the Discrete Fourier Transform of a discrete time signal.
6. Analyze the contents of a basic discrete time signal from its frequency information.

Course Learning Outcomes

·       Given a continuous signal, determine the effects of sampling in time.

·       Be able to define the minimum sampling frequency to avoid aliasing when discretizing a continuous signal

·       Given a dynamic system, determine if it is Linear Time Invariant (LTI);

·       Given a LTI system, compute the response by convolution;

·       Given a periodic signal, determine its Fourier Series expansion;

·       Given a continuous time signal, compute its Fourier Transform;

·       Given a continuous time signal, compute the Fourier Transform using the tables and the properties;

·       Given a system, characterize it in terms of its frequency response;

·       Apply the properties of the Fourier Transform to basic modulation and demodulation problems;

·       Develop the ability to recognize and characterize simple discrete random processes in the time domain.

·       Learn to be able to fully characterize stationary discrete random processes from a second moment viewpoint in the time domain and frequency domains. Develop an understanding for Gaussian white noise for 1- and N-dimensional random vectors.

·       Learn to characterize random signals from a second moment viewpoint as they are processed through discrete linear systems. Also learn to characterize simple linear transformations for continuous signals in time and frequency domains.

·       Learn how to deal with uncertainty in estimated parameters via confidence intervals.