ECE 280/Spring 2010/Final

This is a list of the topics to be covered on the final exam for ECE 54 in the Spring, 2010 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
   • 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
9. Fourier Transform
   • 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
   • 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
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.
11. Amplitude Modulation and Demodulation
    • Know, understand, and be able to reproduce the basic block diagrams for Full AM (Fig. 5.3) and DSB-SC Modulation (Fig. 5.12 (a)).
    • 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 (Fig. 5.12 (b)).
    • 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.
12. Laplace Transforms
    • Understand that a 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
    • 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
    • Be able to set up equations for a circuit using Laplace Transform-based impedances and source representations

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. If you believe there are other equations that should be added, list them on the discussion page before 5PM on Wednesday, May 5th.

• Draft 1.0 (4/26/2010): Equation Sheet