An introduction to the modeling and analysis of signals and systems. Topics include convolution, Fourier series, Fourier transforms, bandwidth, basic filter design, modulation techniques, random variables and random processes and spectral density.

 COURSE STRUCTURE

The first part of the course will cover linear systems and deterministic signals. Topics will include convolution, Fourier analysis, and communications-related topics. The remainder of the course will be dedicated to probability, random variables, and random processes.

Homework 15% (no late HWs accepted, may drop lowest one and includes MATLAB assignments if given).

Test #1: 18% (CLOSED BOOK).

Test #2: 21% (CLOSED BOOK).

Test #3: 21% (CLOSED BOOK).

Final Exam: 25% (CLOSED BOOK).

1. Classify systems based on properties of their input-output relationship.
2. Analyze and synthesize signals using the definitions and properties of the Fourier series and Fourier transform.
3. Apply convolution, Fourier series, and Fourier transform methods to determine the output of linear time-invariant systems.
4. Analyze and design simple modulation systems and filters.
5. Define a random experiment; its outcomes, events, and probability distribution.
6. Apply independence of events, conditional probability, and Bayes rule to random experiments.
7. Calculate the probability of an event given the cumulative distribution function or probability density function of its random variable.
8. Determine the mean, variance, and standard deviation of a random variable.
9. Determine the autocorrelation and power spectral density of a random signal.
10. Characterize LTI system response to random signal.

Students model and analyze signals and systems using MATLAB.

ZTF 1: Definition and identification of signal types. Define singularity functions and their properties. Energy and power signals

ZTF 2: Definition and identification of system types. Convolution integral. Impulse response of linear systems.

ZTF3: Fourier series representation of signals.

ZTF 4: Define the Fourier transform and inverse Fourier transform. Properties of the Fourier transform. Frequency response of a linear system. Communications applications of the Fourier transform.

ZTF: Basics of probability.

P 1: Total probability and Bayes' theorem.

P 2: Random variables and distribution and density functions.

P 2: Conditional probability.

P 3: Definitions of various statistics of a random variable. Functions of random variables.

P 4: Joint density and distribution functions. Conditional density and distribution functions.

P 5: Functions of multiple random variables.

P 6: Random processes.

P 6: Autocorrelation function for a random process. Crosscorrelation.

P 7 & 8: Power spectral density functions and applications.