ECE 280/Fall 2021/Test 1

DRAFT 9/25/21: This page lists the topics covered on the first test for ECE 280. The test will cover material through Homework 4 and Lecture 8. The tests will be different for the two lecture sections.

Test I Fall 2021 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 even part and odd part for any signal)
2. Independent and dependent variable transformations
   • Scaling, time shift, time scaling, time reversal
3. Elementary signals
   • 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)
4. Impulse and step response and their relationship to each other
5. Convolution
   • Using the integral
   • Using graphical convolution
   • Using convolution properties for elementary signals
6. System properties (from system equation, impulse response, or step response)
   • Memoryless
   • Causal
   • BIBO stable
   • Linear
   • Time Invariant
   • We will not ask about Invertible
7. Correlation
   • Autocorrelation, autocorrelation function, cross-correlation, cross-correlation function, measure of correlation

Previous Tests

Dr. G's previous tests for ECE 280 (and ECE 54/64) are at the Test Bank; note that in previous semesters a different version of the correlation function was used - that version is labeled $ \phi_{xy(t)} $ versus this semester's notation of $ r_{xy}(t) $.

$ \begin{align*} r_{xy}&=\int_{-\infty}^{\infty}x(\tau)\,y(t+\tau)\,d\tau=x(-t)*y(t)=x_m(t)*y(t) \\ \phi_{xy}&=\int_{-\infty}^{\infty}x(t+\tau)\,y(t)\,d\tau=x(t)*y(-t)=x(t)*y_{m}(t)=r_{xy}(-t)=r_{yx}(t) \end{align*} $

meaning the interpretation of the independent variable is different. For $ r_{xy}(t) $, the "t" is "How far to the left do I slide $ y $ for the area of the product of the signals to be $ r_{xy}(t) $?"; alternately, it could be interpreted as "How far to the right do I slide $ x $ for the area of the product of the signals to be equal to $ r_{xy}(t) $?"

Specifically Not On The Test

1. Maple
2. MATLAB
3. Python
4. Fourier Series