ECE 280/Summer 2018/Test 2

This page lists the topics covered on the second test for ECE 280 Summer 2017.

Test II Summer 2018 Coverage

1. Everything on Test 1
2. 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
3. Fourier Transform (Continuous Time and Discrete 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 set up integrals or summations to determine \(x[n]\) or \(X(e^{j\omega})\) for signals that have Discrete Time 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 or DTFT having denominators of the form \(\Pi\left(1-\alpha e^{-j\omega}\right)\)
4. 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.
5. Communication Systems
   • 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 reasonably) analytically determine the frequency spectrum at each stage as a signal passes through the system.

Equation Sheet

The following equation sheet will be provided with the test. Equation Sheet

Specifically Not On The Test

1. Maple
2. MATLAB
3. Laplace Transforms