Place: Room 621, GP South
Time: Tuesday 23rd August, 3:30 morning Tea. 4:00pm seminar

Title: Estimating Randomly Modulated Periodic Processes Generated from
Nonlinear Mechanisms
Speaker: Melvin J. Hinich

Abstract

Applied Research Laboratories of the University of Texas at Austin
There is always variation in the amplitude and phase of what is usually
called a periodic signal. The periodicity is really in the expected value of
the process from year to year. The variation is due to random effects that
disturb the basic periodicity. This "wobbly" periodic signal is called a
randomly modulated periodicity. Since a linear system can not generate a
stable periodic output the modulation pattern can be used to identify the
nature of the nonlinear data generating mechanism. In some applications the
modulation obscures the periodic pattern and a statistical test is required
to detect the underlying periodicity. I define the concept of a signal
coherence function of a modulated periodic signal and apply it to a variety
of practical signal processing problem areas. It is shown that the signal
coherence function can improve the detectability of this type of signal as
compared with the standard periodogram (spectrogram) methods. An artificial
data set was created to compare standard spectrogram analysis with the
signal coherence detector. The average pulse is reconstructed using the
signal coherence function. The FFT of the mean frame for the data is
computed, where the frame length is a multiple of the pulse length. The
amplitudes of the mean frame whose signal coherence is below a set threshold
are zeroed out. This complex vector is then transformed into the time domain
by an FFT operation. This reconstructed signal is called the coherent part
of the signal.

Bio
Professor Melvin Hinich principal research areas are in the fields of
Analytical Political Science, Time Series Analysis, Economics, and
Statistical Theory and Methods in Engineering and Science with particular
emphasis on Signal Processing. He has published widely in leading journals
in these fields as the following small sample indicates: Journal of the
American Statistical Association, Journal of Time Series Analysis, Annals of
Mathematical Statistics, Journal of Econometrics, Econometrica, Journal of
Economic Theory, Journal of the Acoustical Society of America,
Technometrics, IEEE Transactions on Signal Processing and Signal Processing.
Professor Hinich received his Ph.D in Statistics from Stanford University in
1963 and is currently Professor of Government and Economics at the
University of Texas at Austin and is also a Research Scientist in the
Applied Research Laboratories of the University of Texas. He has held
academic positions previously at Virginia Tech (Economics) and
Carnegie-Mellon University (Industrial Administration and Statistics). He
has also done consultancy work for Bell Laboratories, Columbia University's
Hudson Laboratories, the U.S. Navy, and a number of other organizations. He
is a Fellow of the American Statistical Association, the Institute of
Mathematical Statistics, and the Public Choice Society.