ECE 280/Fall 2023/Test 1
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This page lists the topics covered on the first test for Dr. Gustafson's section of ECE 280. The test will cover material through Homework 4 and convolution. The tests will be different for the two lecture sections.
Test I Fall 2023 Coverage
- 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)
- Independent and dependent variable transformations
- Scaling, time shift, time scaling, time reversal
- Given transformations make a sketch; given a sketch, determine the transformations
- 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
- 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
- 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!
- 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
- Discrete-difference equation solutions
- Differential equation solutions
- Correlation
- Fourier Series
- Maple
- MATLAB
- Python
Previous Tests
Dr. G's previous tests for ECE 280 (and ECE 54/64) are at the Test Bank.