ELEC 320, Fall 2004
Prof. Rich Kozick
Date Assigned: Wednesday, November 17, 2004
Date Due: Monday, November 29, 2004
- Exam 3
will be on Friday, November 19, 2004.
The exam topics are the Fourier series and the Fourier transform.
I will provide you with the formulas for the Fourier series and
tables of Fourier transform pairs and properties.
Please continue to study Section 5.1 on the sampling theorem.
You may also want to browse sections 5.2 and 5.3 on the DFT and FFT
(we discussed these in Lab 7).
For the week of November 29,
please begin reading Chapter 6 on the Laplace transform.
Sections 6.1 and 6.2 describe the forward and inverse Laplace transform
operations. Sections 6.3 and 6.4 describe the application of the Laplace
transform to solving differential equations and circuits (ZSR and ZIR!).
Since you have done this in MATH 212 and ELEC 225-226,
we will mention it only briefly in this course.
The concept of the transfer function of an LTIC system,
H(s), is very important.
If you have notes on the Laplace transform from previous
courses (MATH 212 and ELEC 225-226), you might want to find and
review those notes.
This might make some enjoyable reading over Thanksgiving break.
Lab Design Project:
We will work on your projects on November 22-23 and 29-30, and then you
will present your results on December 6-7.
Please see the
on the course web page for more details.
Please answer the following question related to the fast
Fourier transform (FFT).
Refer to Lab 7
for notes on how to perform the FFT with MATLAB.
You are given a data file
that can be downloaded from the Web version of this assignment at
The file contains discrete-time data that was obtained by
sampling a continuous-time signal at the rate of
300 samples per second.
The data can be loaded into MATLAB with
load sig1.dat -ascii
after which a variable named sig1 will be available.
(The MATLAB command whos gives you a listing of
all variables defined in the MATLAB workspace.)
Suppose it is known that either two or four distinct sine
waves are present in the data.
Explain your reasoning.
How many sine waves do you think are present in the data, two or four?
What are their frequencies, in hertz?
- Is there a difference in amplitude among the sine wave components?
If so, which frequency component(s) have the largest amplitude?
Please solve Problem 5.1-4
in the Lathi text on the zero-order hold digital-to-analog
(D/A) conversion system.
Answer the following additional question related to the
zero-order hold D/A converter.
Assume that the analog signal f(t) is band-limited to B Hz,
and that the sampling rate Fs = (1/T) = 2B samples/sec.
What should be the frequency response of the "reconstruction filter"
that is applied to the output of the system in Figure P5.1-4
so that the result is identical to the original analog signal, f(t)?
Specify a formula for the frequency response, and also sketch
the magnitude and phase of the frequency response.