ECE 280/Fall 2024/Test 1

This page lists the topics covered on the first test of ECE 280. The test will cover material through Homework 4 and convolution.

Test I Coverage

1. Signal properties
   • Aperiodic or periodic (and if periodic, what is the period?)
   • Energy (and if so, the total energy), power (and if so, the average power), or neither
   • Even or odd (and regardless, be able to find/sketch the even part and odd part for any signal)
2. Independent and dependent variable transformations
   • Scaling, time shift, time scaling, time reversal
   • Given transformations make a sketch; given a sketch, determine the transformations
3. Elementary signals
   • Exponentials
   • Impulse function $$\delta(t)$$ and its first four integrals ($$u(t)$$, $$r(t)$$, $$q(t)$$, and $$c(t)$$)
   • Quickly write a formula for piecewise functions made up of straight lines (i.e. accumulations of value and slope changes)
   • Impulse function $$\delta[n]$$ and unit step $$u[n]$$ for discrete signals
4. Impulse and step response and their relationship to each other
   • Remember that the response to a series of scaled and shifted impulses is a series of similarly scaled and shifted impulse responses
   • Also remember that the response to a series of scaled and shifted step functions is a series of similarly scaled and shifted step responses
   • The response to anything more complicated than that will require convolution
5. Convolution (continuous and discrete)
   • Meaning and use
   • Calculating using the integral/sum
   • Calculating using graphical convolution
   • Calculating using convolution properties for elementary signals - i.e. Speed Convolution!
6. System properties (from system equation, impulse response $$h(t)$$ or $$h[n]$$, or step response $$s_r(t)$$ or $$s_r[n]$$)
   • Memoryless (note: if memoryless, then definitely also causal)
   • Causal (note: if non-causal, then definitely not memoryless either)
   • BIBO stable
   • Linear (automatic yes if impulse or step response is given)
   • Time Invariant (automatic yes if impulse or step response is given)
   • We will not ask about Invertible

Not covered on test 1

1. Discrete-difference equation solutions
2. Differential equation solutions
3. Correlation
4. Fourier Series
5. Maple
6. MATLAB
7. Python