Preprints: Physical wavelets and radar

[Gerald Kaiser (gkaiser@cs.uml.edu)]

Preprints: Physical wavelets and radar

Preprint: PHYSICAL WAVELETS AND RADAR:
A VARIATIONAL APPROACH TO REMOTE SENSING

To appear in IEEE Antennas and Propagation Magazine

Author: Gerald Kaiser, University of Massachusetts at Lowell


ABSTRACT: This is a tutorial paper in which the idea of radar
ambiguity functions is generalized to the context of "physical
wavelets." A time signal psi(t) is fed into a small transmitter
following an arbitrary (known) trajectory a(t) in space. The resulting
electromagnetic wavelet is reflected from an object following an
arbitrary (unknown) trajectory b(t), and the reflected wave is finally
received by an receiver following an arbitrary (known) trajectory
c(t). This results in a received time signal chi(t). The objective is
to estimate the unknown trajectory b(t) from a knowledge of the
transmitted signal psi(t), the received signal chi(t), and the known
trajectories a(t) and c(t) of the transmitter and the receiver. This
problem is solved by maximizing the AMBIGUITY FUNCTIONAL, which
generalizes the usual radar ambiguity functions (both wideband and
narrowband). When all three trajectories are assumed to be linear and
c(t)=a(t), so that the radar is monostatic, then the above ambiguity
functional reduces to the usual wideband ambiguity function, which is
just the wavelet transform of chi(t) with respect to psi(t) as the
basic wavelet. When psi(t) is assumed to be narrowband, this further
reduces to the narrowband ambiguity function, which is just the
windowed Fourier transform of the VIDEO SIGNAL of chi(t) with respect
to the basic window represented by the video signal of psi(t).