http://wearcam.org/ece431/lab5/lab5.htm
<h1>Lab5: The Fast Fourier Transform and a
    Wearable Personal Safety Device with a Radar Vision system for
    detecting crime before it happens</h1>

<quote>
We have seen Mary Baker Eddy with one eye!
</quote>
<br>
---cryptic sentence inserted into commercial short-wave broadcast to inform
British Royal Radar Establishment of the invention of the T/R (Transmit/Receive)
switch allowing a single radar antenna to be used for both transmitting and receiving
(having seen the Christian Science building with just one antenna).
<p>
In class, we learned how to implement the Discrete Fourier Transform (DFT),
and how to compute it efficiently using Decimation In Time (DIT) and
Decimation In Frequency (DIF), etc..  We also learned about windows,
and, in particular, we learned about sliding windows where the window
moves through time to show a varying spectral information.
<p>
This approach to Fourier analysis is called "Time Frequency" (TF)
analysis, which will form the basis of this lab.
<p>
Various matlab (or octave) scripts and data files are provided for you,
in this lab5 directory.  See for example, READMEscripts and
READMEdata from the lab5 directory.

<h1>Introduction</h1>
You may wish to
<a href=intro.htm>read this introduction,
http://wearcam.org/ece431/lab5/intro.htm,
if you'd like to learn more about
the Personal Safety Device (PSD) that generated the datasets,
and have some additional background for answering the questions,</a>
or you can also proceed directly to the lab5 directory and give a try
at the questions below, perhaps referring to the above introduction after
you've tried the various scripts, etc.:

<p>
BE SURE TO START MATLAB (or octave which is the free matlab-like system)
FROM THE lab5 DIRECTORY, SO THE MATLABPATH (or equiv. octave path) IS
SET TO INCLUDE THE CURRENT WORKING DIRECTORY, startup.m, etc..

<h1>Questions</h1>
First run tests.m to get a sense of some examples of some of the datasets.
Also see READMEdata.
The tests.m file will load in these datasets which are used for some
of the runs below:
<p>
Plot tfhandtv for uncalibrated pickpocket (e.g. zc) and compare to zccal.
See READMEscripts for an explanation of tfhandtv and other scripts.
You can generate these plots automatically by simply running showcal.m
which will also show you a real versus imaginary plot of the radar data.
<p>
Problem 1: Explain the physical and intuitive meaning of the difference
between positive and negative frequencies.  What is negative frequency?
<p>
Problem 2:
Notice that the uncalibrated radar data causes mirroring in the f=0 axis
(e.g. an inability to distinguish positive from negative frequencies).
Comment on why the calibration procedure (e.g. calibrateradar.m) mitigates
this problem.
<p>
Problem 3:
Look at the car3 data (possibly modify showcal.m for this purpose) and
propose a possible explanation for why the car3 data appears to be partially
reflected in the frequency=0 axis even after running calibrateradar.m on it.
<p>
Problem 4:
Suggest how you might use the spectral analysis (Fast Fourier Transform)
information obtained from tfhandtv.m to see whether or not a given situation
may be dangerous.  Describe the characteristics of possible dangerous
situations as seen through the eye of the radar.  Make particular reference
to Fourier analysis.
<p>
Problem 5:
An engineer starts a company to manufacture a hands-free cursor pointing
device to replace the mice usually used on a computer.
The device can either be placed on a desktop (or below the desk
since it can see through wood) to sense the user's hand,
or it may be worn on the front of the body so it can sense hand
position while the user is mobile.
Suggest how you might use a miniature radar as a pointing device.
Engineer A decides to spin the radar around in the radome and obtain
a radar image of a user's hand, and select the brightest pixel in the
image as the position of the hand.
Engineer B decides to use a single pixel of the radar image, and use
phase for one axis of the pointer, and magnitude for another.
Which engineer would you rather be?
If you paid attention in class on Nov. 10th, this should be very easy to
answer.
<p>
BONUS PROBLEM: The above problems are sufficient for obtaining a 100% grade
on this lab, if done well.  However, if you like, you may attempt this
optional bonus problem: Compute the chirplet transforms of some of the
datasets.  Note that this takes a long time to compute.  Use the script ff.m
and explain what this script does, and what is meant by Frequency Frequency
(FF) analysis.  Explain why the Chirplet transform is particularly well suited
to the analysis of radar data, and its benefits over and beyond Fourier
analysis.
Not necessary for this lab, but perhaps of additional interest,
is a <a href=http://wearcam.org/chirplet/vi91/index.htm>
short paper</a> on time frequency analysis.
<p>
You will hopefully soon be out in industry, or in graduate school.
You must learn how to think independently and to solve problems
creatively.  Hopefully this lab has been enjoyable.
<hr>
If you are interested in learning more about the chirplet transform
and radar vision, you can also download a recent
<a href=/icassp01.ps.gz>draft of a paper on chirplet based radar vision</a>.
<hr>