University of Kansas Electrical Engineering & Computer Science

EECS 361 - Signals and System Analysis

Announcements

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• No class October 2, 2025

• In-class review of concepts to be covered and additional time for questions for Test 1 Tuesday, October 7, 2025

• Open review Tuesday, October 7, 5:30-6:50 PM in LEEP2 2425

• Test 1 Thursday, October 9, 2025

• Test 1 Covers Homework 1-7

• Mathematical Formulas to be provided on Tests and Final

• Equations to Know Not provided on Test 1

• Practice Test 1

• Test 1 Topics (Also see Concepts noted on each homework problem)

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Course Information:

• EECS 361 Class Syllabus
• EECS 361 Talking Points
• Required Text:
  • Required: zyBooks: NI Engineering Signals and Systems (2e) - Interactive Edition (The zyBook is based on: Signals and Systems: Theory and Applications, Ulaby and Yagle, Michigan Publishing, 2018 https://services.publishing.umich.edu/publications/ee/ Companion Website: http://ss2.eecs.umich.edu)
  • Process to get the zyBooks: NI Engineering Signals and Systems (2e) - Interactive Edition
    1) Go to learn.zybooks.com and create an account.
    2) Be sure to use your “official” KU e-mail address, NOT a gmail or other e-mail address.
    3) Type/paste the class zyBook code for this class KUEECS361FrostFall2025 into the box that appears.
    4) Subscribe
  • Steps you can see how many points each Participation Activity is worth
• Homework
  • Grader: Fatima Alshaikhli, e-mail: fatima.al-shaikhli@ku.edu
  • Homework Formatting Rules
  • Plots and graphs on homework must be generated by a computer tool (see EECS 361 Class Syllabus)
  • Homework must be submitted by email as a pdf file.
    • e-mail homework to  Fatima Alshaikhl at e-mail: fatima.al-shaikhli@ku.edu
    • Must use subject line LastName_361_Homework#, e.g., Frost_361_Homework5 . 
    • Must use file nameLastName_361_Homework#.pdf, e.g., Frost_361_Homework5.pdf .
    • Homework is due at 5:00 pm on the due date.
• Changes announced in class and this class web site supersede these written instructions.

Homework

Quick Reference to useful information:

• Mathematical Formulas to be provided on Tests and Final
• Fourier Transform Table to be provided on Tests and Final
• Equations to Know
• Sinc Excel
• Sinc cdf
• Sinc Web page calculator
• Fourier Transform Table in frequency, f
• Polar to Rectangular Online Calculator
• Convolution property of Fourier Transforms
• Application of Fourier Transfrom Properties
• Duality Property
• Plotting Functions in MatLab using fplot
  • Example - 1: Plot rect function
  • Example - 2 Plot of product of two functions
  • Example - 3 Plot piecewise function
  • Example - 4 FFT Plot
• Creating stem plots in MatLab

On-Line Resources:

• Signals, Systems, and Signal Processing: A Computational Approach by Mariusz Jankowski, 2024, an ebook in Mathematica
• Signals, Systems and Signal Processing an Interactive Course, duration 7 h 30 min covers many of the same topics as this course. From Wolfram U.
• Signals and Systems (On-line Class from MIT)
  • Alan Oppenheim. RES.6-007 Signals and Systems. Spring 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
• DSP First
• Digital Signal Processing
  • Alan Oppenheim. RES.6-008 Digital Signal Processing. Spring 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
• Signals and Systems Tutorial
• Signals and Systems videos (Not free, there as a cost for these and I have not vetted them)

Supporting links and interactive tools, and visualizations to reinforce signals and systems concepts

• Download Wolfram CDF Player (links to most of the interactive tools given below are in the Instructor notes in class zybook)
  • Introduction
    • Draft Network Performance (M/M/1, M/M/1/K, and Erlang-B, Erlang-C)
    • Voice Example-Quantizing
    • Voice Example-Frequency Content
    • Voice Signal as sum of Cosines
    • Waveforms and Spectrograms
    • Audio Spectrogram
    • Removal of Tone Interference from the ITU female Voice Signal
    • Removal of Tone Interference from the Communications from Apollo 11 Moon Landing
    • Removal of Speech Signal from an Oboe Signal Using an FFT threshold filter
    • Removal of Speech Signal from a Two Tone Signal Using two BPFs
    • Image Compression using Fourier Transform
    • Examples of Complex Division
    • Web Software Defined Radio (SDR)
  • Operations on Signals
  • Types of Signals
  • Pulse Width
  • Example of time shifting and changing the width of continuous time signals
  • Example of flipping and time shifting continuous time signals
  • Representation of Generalized Periodic Signals
  • Two sided Spectral Plots of Cosines
  • Continuous and Discrete Cosine
  • Complex numbers and phasor diagrams
  • Animation of Positive & Negative Frequency Rotating Phasors
  • Time Delay and Phase Shift for Cosine
  • Comb Function
  • Examples of Stem Plots
  • Operations on Discrete Singals and Discrete Signals Sinusoidal
  • Example of flipping and time shifting discrete time signals
  • Discrete Time BIBO Examples
  • Rotating Phasors
  • Definition of Linear System
  • Phasor Model for RC Filter Electronic Circuit
  • Examples of non-linear devices
  • Impulse response & convolution
  • Application of impulse/step response along with linearity and time invariance
  • Fun With Convolution, Linear Time-Invariant Systems, and the Allen Fieldhouse
  • Approximation for impulse function
  • Convolution with a Rectangular Pulse
  • Interactive plot shows how a short pulse can be used to measure the impulse response.
  • Example of Analytical Calculation of a Convolution
  • Step-by-Step Graphical Convolution Example 1
  • Step-by-Step Graphical Convolution Example 2
  • Approximate Impulse Response
  • Impluse and Step Response for RC filter
  • Demonstration of Cascaded Systems
  • Discrete time differentiator
  • Discrete-Time Convolution
  • Convolution Sum
  • Analytical Calculation of the Discrete Convolution
  • Multiple Convolution of rectangular pulses (cascaded systems)
  • Power and Energy
  • Examples of Energy and Power of Signals
  • Power in Periodic Pulse Trains
  • Power in Sum of Cosines
  • Parseval's Theorem for Energy Signals and % Energy in Band
  • System Responses and Analog Filters
  • Multipath Channel Response
  • Example of linear, constant-coefficient, differential equation
  • Measuring the System Response of a Low Pass Filter
  • Measuring the System Response of a High Pass Filter
  • Example of Low Pass Filter
  • Measuring the System Response of Band Pass Filter to a Cosine Input
  • Response of Low-Pass RC (RC=1)Filter to Periodic Waveforms
  • Filter on Triangle Waveform
  • Rise Time Examples
  • Response of Second Order System with Frequency Response
  • Transfer Function for Series RLC circuit
  • Demonstration of the Importance Phase
  • Demonstration of Pulse Width-Bandwidth Tradeoff
  • Ideal Bandpass Filter-Impulse response and Transfer Function
  • Examples of Analog Filters
  • Fourier Series
  • Introduction to Fourier Analysis
  • Orthogonality Definition and Examples
  • Fourier Series Example
  • Development of Fourier Series for Periodic Pulse Train
  • Fourier Series for Three Periodic Functions
  • Fourier Series of Simple Functions
  • Fourier Series of Five Signals
  • Fourier Series Coefficients of a Rectangular Pulse Signal
  • Example of Periodic Extension of a Function
  • Gibbs Phenomenon for Pulse Train
  • Gibbs Phenomenon three pulses shapes
  • Power in Periodic Signals and Parseval's Theorem
  • Bandpass Filtering of a Periodic Pulse Train
  • Power Supply Analysis
  • Spectrum at the output of a nonlinearity
  • Fourier Transform
  • FCC Spectrum Mask for 8-VSB
  • Rectangular Pulse and Its Fourier Transform
  • Fourier Transform Pairs
  • Fourier Transform of Periodic Signals
  • Fourier Transform of an Infinite Impulse Train
  • Fourier Series coefficients from the Fourier Transform
  • Duality
  • Continous Time Fourier Series from Continous Time Fourier Transform-Example
  • Energy and Parseval's Theorem
  • Definition of Bandwidth with Examples
  • Time-bandwidth Product
  • Fourier Transform Applied to RC Circuit
  • Fourier Optics - 2-d Fourier Transform
  • Double Sideband Large Carrier Modulation
  • Superhetrodyne Receiver
  • Frequency Division Multiplexing
  • Example of Aliasing with Realistic Signal
  • Flat-top Sampling
  • Analog to Digital Conversion-Quantization and Pulse Code Modulation (PCM)
  • Example of Bandpass Sampling
  • Distortion
  • Harmonic Distortion
  • DFT
  • DFT Development
  • Example 6.17.1 DFT of Periodic Sinusoid
  • Picket Fence Effect in the DFT
  • Spectral Leakage in the DFT
  • Example of Hanning Window to Reduce Spectral Leakage
  • Comparison of Rectangular and Triangular Windows
  • Example of Convolution using DFT/IDTF
  • Equivalence of Linear and Circular Convolutions
  • Comparison of rect and Blackman Windows
  • Discrete Fourier Transform of a Two-Tone Signal with Different Windows Functions
  • Discrete Fourier Transform with control of maximum frequency of a Two-Tone Signal with Different Windows Functions
  • Demonstration of DFT is the z-transform X(z) evaluated on the unit circle sampled at regular intervals
  • Inverse Filtering Using the DFT
  • Inverse Filtering Using the DFT Allen Fieldhouse Audio
  • Removal of Speech Signal from an Oboe Signal Using an FFT threshold filter
  • Spectral leakage and the Discrete-Time Fourier Transform (DTFT) and the DFT
  • DTFT and Inverse DTFT
  • DFT of a Chirp Signal
  • Spectogram
  • Z-Transform and Digital Filtering
    • Direct II realization of the ARMA difference equation
    • Inverse z-Transform in MATLAB
    • Relating the Fourier Transform of a Sampled Signal to the z-Transform
    • Poles and Zeros
    • Distance between a point in the z-plane and unit circle
    • z-transform of a causal, finite-length signal
    • z-transform of digital pulse
    • H[z] and locations of Poles and Zeros
    • Block Diagram of Second Order Filter
    • Relating Different Descriptions of LTI Discrete Systems
    • 3-D plots of z-transform of Discrete Time Signals
    • Time Domain Filter Output to Sampled Cosine Input
    • Transfer Function Analysis by Manipulation of Poles and Zeros
    • Inverse z-transform by Polynomial Long Division
    • Z-plane to Frequency Response
    • Convolution of finite discrete signals using polynomial multiply
    • Complex z-Plane Plot and Frequency Response for System with 2 Poles
    • Complex z-Plane Plot and Frequency Response for System with 2 Complex Poles and 2 Comples Zeros
    • Complex z-plane and Frequency Response for a system with 2 Complex Zeros and two poles at z=0
    • Design of First and Second Order Digital Filters
    • 3-D plots of transfer function and frequency response for a 10 point equal weighed moving average.
    • Notch Filter: Speech Signal with One Tone Interferer
    • Notch Filter: Speech Signal with Two Tone Interferers
    • Removal of Speech Signal from a Two Tone Signal Using two BPFs
    • Removal of Periodic Interference with a Comb Filter
    • Linear phase FIR 5 tap LP filter with a 3dB bandwidth of 400 Hz with a same rate of 2000 samples/sec
    • Design a first order LPF with specified 3dB bandwidth
    • FIR filter design by solving a linear system of equations.
    • FIR filter design by frequency sampling the DTFT
    • Comparison of FIR and IIR filter designs
    • FIR filter designs based on first and second order IIR Filter specifications, including computational requirements
    • Digital IIR Filter Design Showing Poles and Zeros
    • Infinite Impulse Response (IIR) Digital Low-Pass Filter Design by Butterworth Method
    • Tools to Analyze and Design Discrete Time Linear Filters
    • Image Devonvolution
    • Example of Bilinear transformation
    • Analysis of discrete time feedback system
    • Closed Loop Tracking System

    Control Systems with Examples

Related on-line material

Comb Function

Other Special Functions

Tacoma Narrows Bridge Collapse

Fun With Convolution, Linear Time-Invariant Systems, and the Allen Fieldhouse

SIGSALY: The Forgotten High-Security Communications System That Helped Win WWII

National Security Agency publication-Sigsaly - The Start of the Digital Revolution

Academic Integrity and Plagiarism

The department, school and university have very strict guidelines regarding academic misconduct. Obviously, copying is not allowed on exams. Students are expected to submit their own work on individual homework and projects. Lending or borrowing all or part of a simulation model or program from another student is not allowed. Students ARE allowed to borrow and modify any code on this class web site in their projects. Instances of cheating will result in a referral to the department chairman and the dean of engineering.
All sources in your written work (project reports) must be properly referenced; if you use a source from the literature or the idea of another for your work you must reference it. If you quote or copy a block of text, it must be cited and included in quotation marks (if a sentence or less in length) or in block quote style (if more than a sentence in length). If you paraphrase text (reword a phrase, sentence, or paragraph), you must also quote or blockquote followed by “[paraphrased]” in addition to proper citation. Figures taken from other sources must be referenced.

The USC academic integrity quiz is also useful reading. If you have any doubt, talk to me – inexperience in past writing or coming from an environment where plagiarism was permitted will not be an acceptable excuse for academic misconduct.

I recommend that you take intermediate notes from which you write your own words. I strongly recommend that you not write in one window while displaying the work of others in another window; this is asking for trouble. “Unintentional” paraphrasing is also not an acceptable excuse for academic misconduct.

Modified with permission from James P.G. Sterbenz http://www.ittc.ku.edu/~jpgs/courses/eecs800/ and John Gauch http://www.ittc.ku.edu/~jgauch/teaching/258.f03/syllabus.html

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Use of EdTech services

• Professors and instructors at the KU School of Engineering are aware that some students are actively posting homework, laboratory, and exam questions and responses to EdTech services (e.g., Chegg) even during exam time frames.
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  Keep in mind that when a person signs up to participate by either uploading, and/or downloading, and/or using posted material from these sites, the “terms of service” that are agreed to do not protect the person when KU and/or the School of Engineering decide to conduct investigations related to academic misconduct (e.g., plagiarism and/or cheating).
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  In fact, EdTech services, like Chegg, retain contact information of students who use their services and will release that information, which is traceable, upon request. Using these services constitutes academic misconduct, which is not tolerated in the School of Engineering. It violates Article 3r, Section 6 of its Rules & Regulations, and may lead to grades of F in compromised course(s), transcript citations of academic misconduct, and expulsion from the University of Kansas.
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  If unsure about assignments, it is important that students use the allowable available resources, such as instructor office hours, graduate teaching assistants, and/or tutoring. The School of Engineering wants students to be successful; cheating is not the way to attain that success.

• Changes announced in class and the class web site supersede these written instructions.
• Student with disabilities or special needs should see me immediately for accommodations.

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Use of smartphones, tablets, and laptops in class.

Smartphones, tablets, and laptops may only be used in direct support of class activities.

Texting, general web browsing, checking of e-mail is NOT permitted during class

Video and audio recording of the EECS 361 class lectures is strictly  prohibited.

Author