ECE 280/Spring 2017/Final

This is a list of the topics to be covered on the final exam for ECE 280 in the Spring, 2017 semester.

Coverage

1. Signal properties
   • Be able to identify whether a signal is even or odd, not periodic or periodic (and if periodic, the period), an energy or a power signal
2. Independent and dependent variable transformations
   • Be able to sketch signals which undergo the aforementioned transformations
3. Elementary signals
   • Be literate with the unit impulse and its integrals
4. System properties
   • Be able to identify whether a system is linear, time invariant, stable, memoryless, or causal given a relationship between an input signal and an output
   • Be able to determine whether a system is stable, memoryless, or causal given the impulse response or the transform of the impulse response or other information that could be used to find the impulse response or the transform of the impulse response
5. Convolution
   • Be able to set up convolution integrals for any two signals
   • Be able to solve the convolution integral for two signals composed of the unit step function and its integrals
   • Be able to solve the convolution integral for two signals if the integrand is no more complicated than a polynomial or an exponential
6. Impulse and step response
   • Understand and be able to use the relationships between the impulse response, the step response, and the transforms of each in various frequency domains
7. Correlation
   • Understand and be able to apply the notion that the process of solving a correlation through convolution generally means re-writing the second signal in the correlation in terms of right-sided signals so that the subordinate convolutions do not explode.
8. Fourier Series
   • 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
9. Fourier Transform
   • 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
   • Be able to use partial fraction expansion as an interim step of inverse Fourier Transforms
     • I will only give you FT having denominators of the form \(\Pi\left(j\omega+a_i\right)\) where all the \(a_i\) are real and unique.
   • Be able to determine a differential equation from a Fourier Transform-based transfer function
   • Be able to set up equations for a circuit using Fourier Transform-based impedances and source representations - these would necessarily be zero-state circuits.
10. Sampling and Reconstruction
    • Know, understand, and be able to reproduce the process of sampling with an impulse train of unit amplitude at a given sampling rate with sampling period \(T_S\).
    • Understand the necessity for a band-limited input signal and the relationship between the band-limit and the sampling rate required to make sure aliasing does not happen.
    • Be able to sketch the spectra for signals as they pass through block diagrams - to include filters as well as multiplication by periodic signals; be able to use these sketches to determine values or limits on values for samplers and reconstruction systems.
11. Amplitude Modulation and Demodulation
    • Know, understand, and be able to reproduce the basic block diagrams for Full AM and DSB-SC Modulation.
    • Know, understand, and be able to reproduce the circuit for envelope detection. You will not be required to determine values for the circuit elements.
    • Know, understand, and be able to reproduce the basic block diagram for a demodulator using coherent detection.
    • For Full AM and DSB-SC, and given system parameters and particular input signals, be able to sketch the frequency domain of transmitted and reconstructed signals.
    • If given a description of block diagram showing a system formed by a combination of filters, product oscillators, summation blocks, and multiplication blocks, be able to graphically and (if reasonable) analytically determine the frequency spectrum at each stage as a signal passes through the system.
12. Laplace Transforms
    • Understand that a Bilateral Laplace Transform is incomplete without its accompanying ROC or some statement that makes it possible to determine the correct ROC (i.e. "a causal signal..." or "a stable signal...")
    • Be able to determine Laplace and Inverse Laplace Transforms using the tables; for Inverses this also means being able to do partial fraction expansion, including for repeated roots.
    • Know how to identify when a MOAT will be useful and how to get the coefficients for it. Note: if I give you a problem with a MOAT, there will be no other roots involved.
    • Understand how the ROC relates to system stability and causality as well as signal sidedness
    • Be able to determine a differential equation from a Laplace Transform-based transfer function and vice versa
    • Be able to set up equations for a circuit using Unilateral Laplace Transform-based impedances and source representations (and solve if relatively simple)

Specifically Not on the Test

1. Maple
2. MATLAB
3. Items in lab that never appeared in homework

Equation Sheet

The following equation sheet will be provided with the exam: Equation Sheet