ECE445S Real-Time Digital Signal Processing Laboratory - Midterm #1

Prof. Brian L. Evans

While you are preparing for the midterm, please keep in mind the course objectives:

Having regular sleep, eating, exercise and downtime from until the midterm exam will be very helpful in allowing you to have full mental energy for the test.

You can download a zip file of the files on the Canvas site prior to the midterm #1 exam.

Midterm #1 will be an in-person exam on Wednesday, Mar. 21, 2025, from 10:30am to 11:45am, in ART 1.120 (seats 86):

The class average on midterm #1 has varied semester to semester. For the most recent in-person midterm #1 exams, the raw scores were 69.94 in fall 2021, 77.125 in spring 2022, 77.8 in spring 2023, and 73.2 in fall 2023.

Here are several example midterm #1 exams:

These and many other midterm #1 exams (mostly with solutions) are available in the course reader.

Midterm #1 Review Slides are available from Spring 2017. The review slides are not comprehensive, but instead contain a sampling of important topics.

The online supplement to the book DSP First has dozens of worked problems from the pre-requisite course on signals and systems. After selecting a chapter on the Homework menu at the top right of the page, all of the problems from that chapter will be visible. There is a Solution button for those with solutions.

For Midterm #1, you will be responsible for the following topics in lectures 0-6, homework 0-3, labs 1-3, and the accompanying readings, handouts, and discussions. Below, JSK is Johnson, Sethares & Klein's Software Receiver Design. I've also included sections for three signals and systems textbooks as well: O&W is Oppenheim and Willsky's Signals and Systems (2nd ed.) SP First is McClellan, Schafer and Yoder's Signal Processing First, and L&G is Lathi and Green's Linear Systems and Signals (3rd ed.).
Topic Lectures Lab JSK O&W SP First L&G Homework Problems Handouts
Introduction 0 1 Ch. 1
Bandwidth 1 3 Sec. 2.2 Sec. 4.3-4.4 Sec. 11-4 to 11-8 Sec. 6.3-1, 7.2, 7.3, 7.9 0.1, 0.2, 1.2, 1.3, 2.2, 2.3, 3.1, 3.2, 3.3 Introduction to Fourier Transforms and Pictorial dictionary of Fourier transforms (Canvas only)
Sinusoidal generation (oscillators) 1 2 Sec. 3.2 0.4
Upconversion and downconversion 1&4 Sec. 2.3-2.6, 3.6; Ch. 5; Sec. 6.1-6.4 Sec. 8.1-8.4 Sec. 11-8.2 Sec. 7.3, 7.7 0.1, 0.2, 0.3, 1.3, 3.2 Sinusoidal Amplitude Modulation Example and Summary
Communication system introduction 1 Ch. 1-2 Ch. 8 Sec. 7.7 0.2, 1.3, 3.2
Basic continuous-time signals 3 2 Sec. 2.10, 4.3 Sec. 1.3-1.4 Sec. 2-3, 2-5, 4-4 & 9-1 Sec. 1.4 0.1, 0.2, 0.3 Common Signals in Matlab
Continuous-time system properties 3 Sec. 1.6 Sec. 5-5 Sec. 1.7 0.2, 1.3 LTI System Properties, time invariance for an Ideal Delay and Integrator
Basic discrete-time signals 3 1 Sec. 1.3-1.4 Sec. 4-2.1 & 5-3.2 Sec. 3.3 0.1, 1.1, 1.2, 2.1 Common Signals in Matlab; Discrete-Time Periodicity; and Chirp Signals
Discrete-time system properties 3 2&3 Sec. 1.6 Sec. 9-4 Sec. 3.4-1 0.4, 1.1, 1.3, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3 LTI System Properties
Fundamental Theorem of Linear Systems for continuous-time systems 3&5 Sec. 3.5 Sec. 3.2 Sec. 10-1 Sec. 2.4-4 0.2 Fundamental Theorem of Linear Systems
Fundamental Theorem of Linear Systems for discrete-time systems 3&5 3 Sec. 3.5 Sec. 3.2 Sec. 6-1 Sec. 3.8-2 1.1, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3
Sampling theorem 4 2 Sec. 7.1 Sec. 4-1, 4-2 & 4-5 Sec. 8.1 0.1, 0.2, 0.3, 1.2, 1.3, 2.2, 3.2
Sampling and aliasing 4 2 Sec. 2.8, 3.4, 6.1 Sec. 7.3 an 7.4 Sec. 12-3 Sec. 8.2 0.1, 0.2, 0.3, 1.2, 1.3, 2.2, 3.2 Sampling the Unit Step Function
Bandpass sampling 4
Discrete-time to continuous-time conversion 4 2&3 Sec. 2.10 & 6.4 Sec. 7.2 Sec. 4-4 Sec. 8.2 1.2, 1.3, 2.2 (audio playback)
Continuous-time convolution 5 Sec. 4.4 and 4.5 Sec. 2.2 Sec. 9-6 and 9-7 Sec. 2.4 Convolution Example
Discrete-time convolution 5 3 Sec. 4.4 and 4.5 Sec. 2.1 Sec. 5-3.3 and 5-6 Sec. 3.8 1.3, 2.2, 3.1, 3.2 Convolution Example and Four ways to filter a signal
Z-transforms 5&6 3 App. A.4 and F Sec. 10.1-10.3, 10.5 Sec. 7-1 to 7-5 Sec. 5.1-5.2 0.4, 1.1 and 2.1
Transfer functions 5&6 3 Sec. 4.5 Sec. 10.7.3, 10.7.4 and 10.8 Sec. 8-3, 8-4 & 8-9 Sec. 5.3 0.4, 1.1, 2.1 Designing Averaging Filters and LTI Filters and Frequency Selectivity
Relationships between z and discrete-time Fourier transforms 5 3 App. F.2 Sec. 10.4 Sec. 7-6, 8-5, 8-6, and 8-10 Sec. 5.5 1.1, 2.1, 2.3, 3.1, 3.3
Discrete-time FIR filter design & implementation 5 3 Sec. 2.12, 3.3, 4.2 Sec. 10-9 Sec. 7-7 Sec. 5.4 1.3, 2.2, 3.1 Four ways to filter a signal and Designing Averaging Filters
Digital FIR filter analysis 5 3 Ch. 7 and App. G Sec. 7-7 to 7-9 1.1, 2.1 Designing Averaging Filters
Stability of discrete-time LTI systems 5&6 3 Sec. 10.7.2 Sec. 8-2.4, 8-4.2, and 8-8 Sec. 3.9 and 3.10 1.1, 2.1, 3.3 Bounded-Input Bounded-Output Stability
Discrete-time IIR filter design by pole-zero placement 6 Sec. 10.4 Sec. 8-9 and 8-10 Sec. 5.6 1.1(d), 2.1(d), 3.1 All-pass Filters
Classical discrete-time IIR filter design methods 6 3 Sec. 5.10 3.3 Elliptic IIR filter design
Implementing discrete-time IIR filters as cascades of biquads 6 3 Sec. 10-9 Sec. 8-9 Sec. 5.4 3.3 Parallel and Cascade Realizations of IIR Filters

Please review the following demonstrations:

  1. Pre-recorded in-class demonstrations from DSP First, 2nd ed.
  2. Other in-class demonstrations

You won't be responsible for any questions specific to the assembly language, instruction set architecture, or C programming on the STM32h735G-DK ARM board. However, you would be responsible for analyzing run-time complexity of algorithms without any specific processor in mind. Run-time complexity includes memory storage, memory read/write rates, and buffered input/output. It will be important to know about common data types used in signal processing algorithms, such as 8-bit/16-bit/32-bit two's complement integers as well as IEEE 32-bit/64-bit floating-point data formats. These issues were covered in lab as well as homework questions 2.3 and 3.3 and lecture 6 on IIR filtering.

Updated 03/09/25.