ELEC 2120 Summer 2013 Dr. Roppel

Final Exam Study Guide

Our Final Exam is on Tue. July 30 from 12:00 – 2:30 p.m.

The test will be closed book & notes, but for reference you may use two sides of paper with a maximum size of 8.5 x 11 inches each (both sides of one sheet, or one side each of two sheets). The reference sheet(s) must be hand-written by you. No computer printed or copied material is allowed. Your name must be on both sides of your reference sheet(s) at the top right. You must submit your reference sheet along with your test. It will be returned. I will also provide you with the tables of Fourier, DTFT, and Laplace transform pairs and properties.

Study strategy: Re-work HW problems, In-class exercises, and work through textbook examples in covered sections. Re-read covered sections.

Format: Combination of True / False, Multiple Choice, Short answer, brief discussion, and problem solving.

Sections covered: All sections in Chapters 1 and 2, and Chapt. 3 through 3.8.2.,

Chapt. 4: 1-3 Chapt. 5: 1-4, Chapt. 6: 1-6, Chapt. 8: 1-6

Skills required from Chapt. 1:

• Identify system properties including: linearity, causality, memory, time-variance, discrete-time vs. continuous-time.
• Identify signal properties including: Periodicity, time-shifting, continuous, piece-wise continuous, discrete.
• Write, draw, and describe the signals u(t), r(t), p(t), δ(t) in both continuous time and discrete time.
• Draw time-shifted signals, such as u(t-2).
• Sketch sinusoids, such as 3cos(2πt – π/4).
• Determine the period of a sinusoidal signal.
• Write and interpret MATLAB code for calculating and plotting signals in continuous and discrete time.

Skills required from Chapt. 2:

• Write the convolution representation of a system in both discrete-time ( Eq. 2.19) and continuous time (Eq. 2.73 or 2.74).
• Write and solve the differential equation for a first-order RC circuit.
• Perform a discrete convolution both graphically and mathematically
• Perform continuous-time convolution calculation for simple signals if h(t) is given.

Skills required from Chapt. 3:

• Calculate the trigonometric Fourier series coefficients a_k and b_k for a periodic signal.
• Calculate the cosine-with-phase coefficients A_k and θ_k for a periodic signal
• Calculate complex exponential coefficients c_k for a periodic signal.
• Sketch the line spectra for a periodic signal (magnitude and phase of c_k).
• Compute and sketch Fourier transform and inverse Fourier transform for simple signals.
• Be able to accurately sketch a sinc function and explain why it is important.
• Apply properties of the Fourier transform and Fourier transform pairs to simple signals.
• Apply the modulation property of the Fourier transform to compute and draw the magnitude spectrum for an AM signal, both DSB and DSBSC, given the spectrum of the baseband signal.

Skills required from Chapter 4:

• Calculate a DTFT (forward and inverse).
• Construct a DTFT plot with appropriate symmetry (even for magnitude, odd for phase).
• Calculate forward and inverse DFT.
• Construct a DFT stemplot with appropriate symmetry (even for magnitude, odd for phase).
• Identify the actual frequency associated with a given value of k on a DFT stem plot using f = k(SR/N).

Skills required from Chapter 5:

• Express the response of a system in the frequency domain (Eqn. 5.4, Eqn. 5.60)
• Analyze an RC circuit in the frequency domain using the Fourier transform (Example 5.2 and Example 5.5)
• Draw the magnitude response of ideal filters – LP, BP, HP, and notch (bandstop).
• Discuss and perform sampling and reconstruction (Section 5.4).
• Explain aliasing

Skills required from Chapter 6 :

• Solve an RLC circuit (or similar, e.g., RC, RL, LC) using the Laplace transform.
• Determine the forward or inverse Laplace transform by table lookup, and using partial fractions as necessary.
• Determine transfer functions for block diagrams consisting of series, parallel, and feedback connections.

Skills required from Chapter 8 :

• Determine the stability of a system
• Sketch a pole-zero plot for a given system
• Compute and sketch the step response of 1^st and 2^nd order systems
• Sketch the Bode magnitude and phase plots for a given transfer function
• Write the transfer function given a Bode magnitude sketch
• Convert from low pass to other filter types

Other skills:

Write or explain snippets of MATLAB code pertaining to the Fourier series, Fourier transform, and Laplace transform calculations that we have done for homework. For example, you should be able to write MATLAB statement(s) to:

• Produce a stem plot given an array to be plotted, with axis labels
• Create an array that is the combination of various unit-step functions
• Implement convolution
• Determine magnitude and phase of a complex number or array
• Produce a Bode plot
• Produce the step response of a system