Homework #1 Due Monday January 22, 2018
PDF file Homework #2 Due Monday February 12, 2018
PDF file Homework #3 Due Monday March 5, 2018
PDF file Final Project Report Due 5pm Friday, March 23, 2018
Please use a word processing system to write your report (LaTeX strongly recommended).
You should not write more than 10 pages.
Submit your pdf file of your report to me via email.
The best possible scenario is to write a report on a project you yourself
come up with. Examples are:
Description of your Ph.D. research projects where you plan to use
the tools you learned (or will learn) in this course.
A survey of some particular area of applications of the ideas learned (or
to be learned) in this course, e.g., image compression, denoising,
interpolation, fast algorithms, numerical analysis, statistics, etc.
If you have difficulty specifying your project,
I would suggest that you do one of the following possible projects.
Regardless of which project you choose, I would recommend to use
either:
If you are male, then ask a female student (not necessarily in this class)
to get her voice recording of the same words as you recorded.
If you are female, get voices of a male student.
Apply the Windowed Fourier Transform to these voice recordings to compute
the spectrograms.
Interpret the results. Can you identify male voices and female voices
by looking at the spectrograms?
Repeat the same experiments using the Continuous Wavelet Transform and
the scalograms. Which are easier to interpret the voices, spectrograms or
scalograms?
Describe your further thoughts for recognizing male/female voices.
Instead of male/female voice signals, you can use any two classes of
signals that show different time-frequency characteristics. Examples include:
comparison of historical records of some stock prices of two companies or
market indices of two countries, or seismograms (seismic signals) caused by
earthquakes vs those by nuclear explosions, to name a few.
Apply the synchrosqueezed wavelet transform to your favorite data you
prepared above, and plot the time-frequency plane figure of your data.
Apply more conventional windowed Fourier transform and continuous wavelet
transform to your data, and plot the time-frequency plane and time-scale plane
figures generated by these transforms, respectively.
Interpret these time-frequency/time-scale plane figures, analyze your data
on these time-frequency/time-scale planes, and discuss what you have found out
about your data, and discuss pros and cons of each of these three transforms.
Apply the generalized Morse wavelet transform with various different parameters (β, γ) to your favorite data you prepared above, plot the
time-frequency plane figure of your data.
Interpret these time-frequency plane figures, analyze your data
on these time-frequency planes, and discuss what you have found out
about your data, and discuss which parameter pair (β, γ) gives you the best result in terms of data interpretation.
Expand your favorite data you prepared above into the Gaussian Basis with
a particular parameter ζ, plot the magnitude of the expansion coefficients in the nonincreasing order. Then do the same for different values of ζ and compare the results. In particular, examine the relationship between the speed of the decay of the magnitude of the coefficients and the parameter ζ.
Repeat the above experiments for a different signal and check your previous explanation and conclusion on the relationship between the coefficient decay speed and ζ still hold or not.