ECE 280/Spring 2024/Test 2

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