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   -> Volume 3, Issue 13


Preprints: Preprints from Air Force Institute of Technology
 
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"Bruce W. Suter"
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PostPosted: Mon Dec 02, 2002 1:19 pm    
Subject: Preprints: Preprints from Air Force Institute of Technology
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Preprints: Preprints from Air Force Institute of Technology

OBTAINING PREPRINTS from Air Force Institute of Technology (AFIT)

1.0 Obtaining Preprints from AFIT

Preprints are available by anonymous FTP from the AFIT computer
"archive.afit.af.mil". You must have Internet access. Papers are
in the subdirectory "pub/wavelets".

2.0 Instructions Comments

ftp archive.afit.af.mil Numerical address 129.92.1.66
anonymous This is your special id
YOURNAME@YOURSCHOOL Send your real id as your password
cd pub/wavelets Directory with wavelet preprints
binary Ensures Integrity of Downloading File
get {file} Downloads file
quit Closes the connection


3.0 Printing Received Files on UNIX Machines

The instructions below are for UNIX machines. Single documents and
papers with only a few simple diagrams are stored as compressed postscript or
ASCII LaTex files.


Problems?

Make sure your computer disk has enough space to unpack the file
you downloaded.
See your local computer expert.
E-mail a description of your troubles to bsuter@afit.af.mil
[Bruce Suter] or xxia@afit.af.mil [Xiang-Gen Xia].

The files that can be retrived are listed below:

TI: Multirate: A New Computational Paradigm
AU: John R. O'Hair and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted for Publication in June 1994
AB: In this paper, a new multirate paradigm is introduced. Multirate is shown to
be a powerful divide and conquer methodology capable of being applied to the
entire field of Numerical Linear Algebra. Multirate can be successfully
applied to vector-vector, matrix-vector and matrix-matrix operations. These
operations form the foundation of such software suites as LAPACK. Since
LAPACK is dependent upon BLAS, and BLAS is, in turn, depends upon these
three operations, it can be seen that multirate can be applied to problems
encountered throughout the field of Numerical Linear Algebra. As examples
of practical Numerical Linear Algebra problems (which happen to be
encountered in signal processing), the new paradigm for multirate is applied
to two common algorithms: the FFT and the DHT. The application of multirate
to these algorithms lead to the generation of easily implemented parallel
algorithms. In the case of the FFT, multirate provides an alternate means of
generating the Four Step FFT reported by Van Loan for use in MIMD shared
memory architectures. The multirate DHT, on the other hand, provides a new
algorithm that makes use of shortened DHT, DCT-II and DST-II transforms run
in parallel for much faster execution times. Thus, multirate can be applied
to traditionally sequential algorithms to improve their performance.
MA: archive.afit.af.mil
FN: Paradigm.ps.Z
TL: Compressed Postscript

TI: The Zak Transform and Decimated Time-Frequency Distributions
AU: John R. O'Hair and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted for Publication in December 1993
AB: In this paper, the interrelationship between the Zak transform and the
Generalized Discrete Time-Frequency Distribution (GDTFD) is examined.
Starting with the discrete Zak transform, its definition is broadened to
include arbitrary windows creating the Windowed Zak Transform (WZT). The
WZT is then combined with the spectrogram. It is demonstrated that the
spectrogram based upon the WZT, called the Zak-Spectrogram (ZS), is a
generalization of the standard spectrogram. Next, building upon the idea of
the weighted spectrogram, the weighted ZS is used to produce a new class of
GDTFD, called the Decimated GDTFD (D-GDTFD). The Decimated GDTFD is similar
to the GDTFD except it trades bandwidth for computational speed and requires
significantly less storage in order to be implemented. The reduction in
discrete bandwidth is from 2 x pi for the GDTFD to ( 2 x pi )/m for the
D-GDTFD. An important attribute of the D-GDTFD is that it requires
significantly less storage than the GDTFD. The D-GDTFD requires only 1/m^2
of the storage of the GDTFD. An example using the Binomial distribution is
given to illustrate the connection between the D-GDTFD and the GDTFD.
Throughout the paper, examples of multirate systems are given which could be
used to implement the building blocks of the D-GDTFD. This makes the D-GDTFD
practical to implement using slower and less expensive elements.
MA: archive.afit.af.mil
FN: Zak.ps.Z
TL: Compressed Postscript

TI: Multirate Time-Frequency Distributions
AU: John R. O'Hair and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted for Publication in May 1994
AB: Two new fast Generalized Discrete Time-Frequency Distribution (GDTFD)
algorithms are presented. The algorithms make use of multirate as a
computational paradigm to impose the divide and conquer methodology on the
GDTFD. The first new algorithm is based upon the inner product formulation
of the GDTFD which allows it to calculate the frequency content of a signal
for particular instances of time. The second algorithm is based upon the
outer product formulation of the GDTFD and as such is a block method
calculating multiple instants of time simultaneously. The first method is
computationally less expensive when calculating selected columns of a GDTFD
while the second method is computationally less expensive when calculating
every column of a GDTFD. Parallel implementations of the new algorithms
provide over an order of magnitude increase in throughput over the fastest
existing algorithm which was developed by Cunningham and Williams.
MA: archive.afit.af.mil
FN: MRTFD.ps.Z
TL: Compressed Postscript

TI: Kernel Design Techniques for Alias-Free Time-Frequency Distributions
AU: John R. O'Hair and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted for Publication in July 1993
AB: This paper presents three methods to deal with the problem of aliasing in
Discrete Time-Frequency Distributions. The work reported here is based upon
the Alias-Free Generalized Discrete-Time Time-Frequency Distribution
(AF-GDTFD) introduced by J. Jeong and W.J. Williams. As such, these methods
do not require the analytic form of the signal in order to avoid aliasing.
We consider the case for kernels designed and implemented in the ambiguity
plane paying special attention to kernels for which continuous time-lag
forms of the kernel does not exist or is difficult and impractical to
calculate. These new methods allow for the calculation AF-GDTFD in
O(N^2 log N) vice the O(N^3) operations of the previous published method
and for a broader class of kernels. This work provides a consistent
theoretic and practical basis for the calculation of a truly alias-free
Wigner distribution. We demonstrate the use of the new formulations on the
Butterworth, Binomial and Wigner distributions.
MA: archive.afit.af.mil
FN: Kernel.ps.Z
TL: Compressed Postscript

TI: A Family of Two Dimensional Nonseparable Malvar Wavelets
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in Jan. 1994
AB: Malvar wavelets or lapped orthogonal transform (LOT) has been
recognized as a useful tool in eliminating blocking effects in
transform coding. Recently, it has been also extended to more
general forms, which enable one to construct an orthonormal basis
from arbitrary local orthonormal bases on different intervals.
In this paper, we study two dimensional cases and construct
nonseparable Malvar wavelets, which is potentially important in
multidimensional signal analysis. With nonseparable Malvar wavelets,
we then construct nonseparable Lemari'{e}-Meyer wavelets which are
band-limited. We also present several numerical examples.
FN: nonsep.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: A Systematic Method for the Construction of Time-Varying FIR
Multirate Filter Banks with Perfect Reconstruction
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in Feb. 1994
AB: In this paper, we present a theory to construct time-varying FIR
multirate filter banks with perfect reconstruction (PR) property
by using arbitrary FIR multirate PR filter banks in different time
intervals. We construct proper window functions cooperating with
the even and odd extensions of filters at the boundaries of the
intervals. We present conditions on such window functions for the
perfect reconstruction property of the global filter banks in the
construction, which are independent of local filter banks. From this
theory, one is able to use discrete wavelet transforms with different
bases, discrete cosine transform and any other transforms on different
time intervals in overlapped transforms with PR property. The theory
can be applied to both infinite and finite length signals and moreover
the blocking effects in the transitions between neighboring filter banks
have been taken into account. Numerical examples using discrete cosine
transform and discrete wavelet transform in two different time intervals
of different length are presented to illustrate the theory.
FN: tvfb.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: FIR Paraunitary Filter Banks Given Several Analysis Filters:
Factorizations and Constructions
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in March 1994
AB: FIR paraunitary filter banks have been extensively studied and
well-understood recently. In this paper, we address the following
problem: How to characterize and construct an FIR paranunitary
filter bank when its several analysis filters are given in priori.
To study this problem is not only important in orthogonal M-band
wavelets with certain regularity where we need to construct wavelet
filters when a scaling filter with certain regularity is found in
priori, but also important in the design of multirate filter banks
where we have already had several desired analysis filters. This
paper presents a solution to the above problem and a method to
construct all possible FIR paraunitary filter banks in terms of a
McMillan degree when several analysis filters are given.
FN: gsaf.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: On Necessary and Sufficient Conditions for Perfect Reconstruction
Multidimensional Delay Chain Systems
AU: Xiang-Gen Xia, Bruce W. Suter and Mark E. Oxley
IN: Air Force Institute of Technology
ST: Submitted in March 1994
AB: In this paper, we present necessary and sufficient conditions for
a perfect reconstruction (PR) multidimensional (MD) delay chain
system. With these results, one is able to systematically check if
a D-dimensional delay chain system with a D x D sampling matrix
M and a D x D delay matrix L has PR property in a simpler way than
before, where the matrix modulo operations are avoided. Moreover,
given a D x D sampling matrix M, in many cases one can determine
all possible D x D delay matrices L so that the delay chain systems
with the sampling matrix M have PR property. Several examples are
provided. We also present a method to generate D x D sampling and
delay matrices M and L such that their corresponding MD delay chain
systems are PR.
FN: mdchain.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: Improved Backus-Gilbert Method for Signal Reconstruction with a
Wavelet Model
AU: Xiang-Gen Xia, C.-C. Jay Kuo and Bruce W. Suter
IN: Air Force Institute of Technology
ST: SPIE Proceedings, Orlando, Florida, April 1994
AB: In this article, we first introduce scale-time limited signal
spaces with continuous wavelet transform and present some properties
of these signals. We then generalize the Backus-Gilbert (BG) method
for moment problems so that the BG method is applicable to scale-time
limited signals and meanwhile the property of the scale-time limitedness
is utilized.
FN: bg.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: On the Householder Transform in C^m
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: To appear in Digital Signal Processing
AB: In this paper, we show the necessary part of the Householder
transform in C^m developed by Venkaiah, Krishna and Paulraj.
FN: house.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: A Construction of Two Dimensional Perfect Reconstruction
Spatial-Varying FIR Filter Banks With Overlaps
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in June 1994
AB: Because of the nonstationarity of signals, such as, speech
and images, time-varying filter banks have been recently
discussed for one dimensional signals. To build multidimensional
spatial-varying filter banks, a trivial way is to use tensor
product of time-varying filter banks, i.e., separable spatial-
varying filter banks. However, nonseparable filter banks for
multidimensional signals are desired in many applications, such as,
subband coding. In this paper, we present a systematic method to
construct two dimensional spatial-varying filter banks with perfect
reconstruction property from arbitrary given two dimensional
separable or nonseparable local perfect reconstruction FIR filter
banks on different rectangular regions, where overlaps between
neighboring regions are allowed to eliminate the blocking effects.
In particular, nonseparable discrete wavelet transforms are studied.
A numerical example is given to illustrate the theory.
FN: svfb.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: Malvar Wavelets with Asymmetrically Overlapped Windows
AU: Xiang-Gen Xia, Bruce W. Suter and Mark E. Oxley
IN: Air Force Institute of Technology
ST: Submitted in April 1994
AB: Malvar wavelets (or lapped orthogonal transforms) with symmetric
overlaps have been recently studied extensively. In this paper,
we consider Malvar wavelets with asymmetric overlaps in both
continuous-time and discrete-time cases. We present conditions
on window functions in continuous-time case so that Malvar wavelets
can be constructed from different local bases. However, in
discrete-time case, we show that Malvar wavelets are impossible
unless the overlaps are symmetric. Numerical examples are presented
to illustrate the theory.
FN: asym.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: Multirate Filter Banks with Block Sampling
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in April 1994
AB: In this paper, we study general vector filter banks where the input
signals and transfer functions in conventional multirate filter
banks are replaced by vector signals and transfer matrices,
respectively. We show that multirate filter banks with block
sampling and linear time invariant transfer functions studied by
Khansari and Leon-Garcia are special vector filter banks where the
transfer matrices are pseudo-circulant. We present some fundamental
properties for the basic building blocks, such as, Noble identities,
interchangeability of down/up sampling, polyphase representations
of $M$-channel vector filter banks and multirate filter banks with
block sampling. We then present necessary and sufficient conditions
for the alias free property, FIR systems with FIR inverses,
paraunitariness and lattice structures for paraunitary vector filter
banks. We also present a necessary and sufficient condition for
paraunitary multirate filter banks with block sampling. As an
application of the theory, we present all possible perfect
reconstruction delay chain systems with block sampling. We show
some examples which are not paraunitary for conventional multirate
filter banks but are paraunitary for multirate filter banks with
proper block sampling. In this paper, we also present a connection
between vector filter banks and vector transforms, which have
applications in image coding.
FN: block.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript

TI: Construction of Malvar Wavelets on Hexagons
AU: Xiang-Gen Xia and Bruce W. Suter
IN: Air Force Institute of Technology
ST: Submitted in August 1994
AB: In this paper, we construct two dimensional continuous (smooth)
Malvar wavelets defined on a hexagon $A$, which constitute
an orthonormal basis of $L^2(A)$. The method can be generalized
to many hexagons.
FN: hex.ps.Z
MA: archive.afit.af.mil
TL: Compressed Postscript
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