International Conference on Antenna Theory and Techniques, 2013, Odessa, Ukraine pp. 408-411
WAVELET ANALYSIS OF SIGNALS IN PROBLEM
OF SHORT RANGE RADIOLOCATION
L. A. Varyanitza-Roshchupkina and G. P. Pochanin
Usikov Institute of Radiophysics and Electronics of NAS of Ukraine, Kharkiv,
Ukraine
E-mail: vrla@ire.kharkov.ua, gpp@ire.kharkov.ua
Abstract
The results of simulation of cylindrical pulsed EM wave diffraction on a cylindri-
cal subsurface object have been presented. The structure of signals received at the ob-
servation point has been analyzed. The possibility of separation of signal components
corresponding to reflections from discontinuities of the region of space under consid-
eration has been investigated. For this reason the corresponding wavelet spectra have
been constructed and analyzed on the basis of atomic wavelet functions.
Keywords: Diffraction, cylindrical waves, subsurface radar, GPR, signal processing,
wavelet, wavelet spectrum, atomic function.
1. INTRODUCTION
Problems of short range UWB radiolocation are char-
acterized by small mutual distances between a trans-
mitting antenna, a receiving antenna and subsurface
objects of research that are comparable to the space
duration of a sounding pulse. As a consequence, the
EM waves, coming directly from the source and been
reflected and diffracted by different space heterogene-
ities, arrive at the observation point with a relatively
small time shift. The result of interference of these
waves is the EM oscillation, wherein it’s impossible
to separate individual components of the EM process,
and the received signal processing is necessary for
finding components, which characterize the reflection
of unknown objects.
The classical Fourier transform is a very useful
mathematical instrument for analyzing and synthesiz-
ing signals, but sometimes it is not enough effective
for complex signal processing. Spectral analysis of the
real signal has to be done both in frequency and in
time domain. The advantages of such an analysis are
obvious. To perform this analysis the basic functions
that allow to detect both the frequency and time char-
acteristics of analyzed signal are required. In other
words, do the basic functions have to have certain
properties called frequency - temporal locality. Such
functions are called wavelets [1, 2]. One of the most
popular tools of wavelet analysis at present is atomic
function [3, 4]. These wavelets will be used in this
paper to analyze the time and amplitude distributions
obtained by solving the problem of diffraction of a
cylindrical pulsed EM waves on subsurface cylindri-
cal object.
2. PROBLEM STATEMENT
Let the upper half-space 0 :
0
y Q Q have the
dielectric properties of vacuum. Let the lower half-
space 0 :
y Q be a union of two disjoint regions
P Q Q
1
, one of which Q
1
is a homogeneous
dielectric and the second one
P:
2 2 2
) ( ) ( r b y a x is a cylindrical region that
can be dielectric or metal (Fig. 1).
A cylindrical E–polarized pulsed wave, the source
of which is an endless linear radiator S, which axis is
located at a height of y = h
1
above the media interface
and is parallel to the axis z, falls on a plane media
interface y = 0.
The current amplitude is changed in time by the
Gaussian pulse formula:
2
/ ) ( 2 ln 4
0
5 . 0 0
) (
T t t e
e J t J
(1)
where
0
J is an amplitude ratio; t
0
is a center of pulse
symmetry; T
0.5
is an excitation pulse duration at the
half amplitude level.
Fig. 1. Geometry of the problem:
0
Q – vacuum;
1
Q – dielectric, P – metal; S – source; R –
observation point.
978-1-4799-2897-2/13/$31.00 ©2013 IEEE