ECE 280/Fall 2024/Test 1

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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