ECE 280/Spring 2024/Test 2

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This page lists the topics covered on the second test for ECE 280 Spring 2024. This will cover everything through Homework 8 and all lecture material ending just before the start of Bode Plots. There are sample tests for Dr. G at Test Bank.

Test II Coverage

  1. Everything on Test 1
  2. Correlation - note that in previous semesters different versions of the correlation function may be used - the two possibilities are:
    \(\begin{align*}\phi_{xy}&=\int_{-\infty}^{\infty}x(t+\tau)\,y(t)\,d\tau=x(t)*y(-t)=x(t)*y_{m}(t)=r_{xy}(-t)=r_{yx}(t)\\r_{xy}&=\int_{-\infty}^{\infty}x(\tau)\,y(t+\tau)\,d\tau=x(-t)*y(t)=x_m(t)*y(t)=\phi_{xy}(-t)=\phi_{yx}(t)\end{align*}\)
    meaning the interpretation of the independent variable is different. For $$\phi_{xy}(t)$$, the "t" is "How far to the right do I slide $$y$$ for the area of the product of the signals to be $$\phi_{xy}(t)$$?"; alternately, it could be interpreted as "How far to the left do I slide $$x$$ for the area of the product of the signals to be equal to $$\phi_{xy}(t)$$?" For Fall 2023 for Dr. G's section, $$\phi_{xy}$$ will be used exclusively.
  3. Linear constant-coefficient discrete difference equations
  4. Fourier Series (Continuous Time only)
    • Know the synthesis and analysis equations
    • Be able to set up integrals or summations to determine \(x(t)\) or \(X[k]\) for periodic signals
    • Know how to find the actual Fourier Series coefficients for periodic signals made up of cos and sin
    • Be able to use the Fourier Series and Fourier Series Property tables
  5. Fourier Transform (Continuous Time)
    • Know the synthesis and analysis equations
    • Be able to set up integrals or summations to determine \(x(t)\) or \(X(j\omega)\) for signals that have Fourier Transforms
    • Be able to use the Fourier Transform and Fourier Transform Property tables, including figuring out necessary adjustments to make things work for the tables
    • Be able to use partial fraction expansion for inverse Fourier Transforms
    • Be able to use Fourier Transforms to find zero-state solutions to differential equations
    • Be able to find a transfer function, step response, and impulse response from a differential equation
    • Be able to find a differential equation from a transfer function, step response, or impulse response

Equation Sheet

See Canvas

Specifically Not On The Test

  1. Maple
  2. MATLAB
  3. Sampling and reconstruction
  4. Communication systems
  5. Laplace Transforms