ECE 315 - Signal Processing Methods



Lectures: Prof. Marco F. Duarte, Marcus Hall 215I,
Office Hours: Tuesday 10:30-11:30am, Wednesday 11:15am-12:15pm, Thursday 1:30-2:30pm (or by e-mail appointment)

Teaching Assistant:
Mohammad Khosravi, Office Hours: Thursday 6:30-8:30pm via Zoom


Lectures: 10:10am-11:00am Monday, Wednesday, Friday at 124 Hasbrouck Laboratory


This course focuses on the study of discrete-time signals and linear discrete-time systems. It constitutes the basic theory behind a further study of digital communication theory and systems, digital control theory and systems, digital signal and image processing, networking, and almost all disciplines of electrical engineering. Upon successful completion of this course you should be able to:

  1. model continuous-time random processes as inputs and outputs of linear and time-invariant systems;

  2. identify discrete-time signals and systems and their properties,

  3. compute and apply the z-transform for purposes of system analysis and filter design;

  4. compute and apply the discrete-time Fourier transform, the discrete-time Fourier series, and the discrete Fourier transform for purposes of discrete-time system analysis and digital filter design.


ECE 213: Continuous-Time Signals and Systems.

ECE 214: Probability and Statistics.


We will use two textbooks that are available online for download at no cost and in physical version at low cost:

  1. Signals and Systems: Theory and Applications” by F. Ulaby and A. Yagle (can be purchased for ~$70).

  2. Introduction to Probability, Statistics, and Random Processes” by H. Pishro-Nik (can be purchased for ~$30).

  3. H. Hsu, “Signals and Systems,” Schaum’s Outline Series, McGraw Hill, 2010: provides a significant number of examples and exercises for exam preparation at a low cost.


Week 1: Review of basic concepts in probability. Random processes. Mean and correlation functions.

Week 2: Wide-sense stationarity. Gaussian processes. Power Spectral Density.

Week 3: Noise models. White noise. Noise in electronic systems.

Week 4: Discrete-time signals; review of basic signals, signal operations and properties.

Week 5: Discrete-time system properties. Difference equation representations. Impulse response, convolution.

Week 6: Z Transform. Properties and inversion. Partial fraction expansions.

Week 7: Analysis of discrete-time systems in the z transform domain.

Week 8: Filter design and stability. Frequency response.

Week 9: Fourier Series representations of periodic discrete-time signals. Discrete-Time Fourier Transform.

Week 10: Discrete Fourier Transform and its application to discrete periodic signals. Fast Fourier Transform.

Week 11: Z Transform-domain system analysis: filter classifications, causality. Deconvolution, dereverberation.

Week 12: Windowing. Spectrograms. FIR and IIR Filter Design. Downsampling, upsampling, and interpolation.

Week 13: Discrete-time random processes; applications in communication and signal processing systems.