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.