ECE 280/Fall 2023/Test 2

This page lists the topics covered on the second test for ECE 280 Fall 2023. This will cover everything through Homework 8 and all lecture material ending just before the start of Bode Plots (for Dr. G's section). 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 different 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

Equation Sheet

See Ed

Specifically Not On The Test

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