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   -> Volume 4, Issue 6


Software: Wavelet Signal Processing Workstation (MATLAB Demo)
 
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Anthony Teolis (tonyt@drsews.nrl.navy.mil)
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PostPosted: Tue Dec 03, 2002 1:19 pm    
Subject: Software: Wavelet Signal Processing Workstation (MATLAB Demo)
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Software: Wavelet Signal Processing Workstation (MATLAB Demo)

We have made the following wavelet signal processing software
available to the wavelet community.


Wavelet Signal Processing Workstation Version 0.1D (MATLAB Demo)

(c) Copyright 1995
AIMS, Inc.
6110 Executive Blvd., Suite 850
Rockville, MD 20852-3904

Inquiries, comments, and/or bug reports may be sent to:

tonyt@dr_sews.nrl.navy.mil


Introduction:

This document explains the functionality of a DEMO version of
an interactive software tool for the analysis of 1 and 2 dimensional
signals using continuous and discrete wavelet transformations.

The software runs in MATLAB versions 4.0 and later.

Downloading:

The demo version m-files (decommented) are available via
guest login or ftp to dr_sews.nrl.navy.mil. The guest password is
"WSPW_demo". A compressed and tar-ed version "WSPW_demo.tar.Z"
is located in the guest home directory.


Background:

The WSPW is built on a hierarchy of user levels which consist of
(i) Graphical User Interface,
(ii) Workstation Module,
(iii) MATLAB, and
(iv) C-code.
Users may choose to operate at any one of these levels although the
contribution of this software is at levels (i) and (ii). The main
trade-off associated with user operation level is between flexibility
in functionality (or speed) and ease of use. At the highest level,
the Graphical User Interface, the user is constrained by the functionality
of the interface. On the Workstation Module level users may construct
their own user interfaces, while the MATLAB and C-code levels are
conventional MATLAB.

In this demo distribution the user is effectively restricted to operate on
the Graphical User Interface level.


Functionality:

The WSPW Demo supports the ``continuous" Fourier and the
``continuous" and discrete wavelet analyses of a predefined set of
1 and 2 dimensional signals.

On startup the WSPW 0.1D Signal Loader window is spawned. This
window consists of three main user interface panels which hold graphical
controls which direct processing actions. The three panels are (from
bottom to top) Load panel, Transform panel, and the Data Type panel.
Each is explained below:

Data Type Panel

The Data Type panel is used to specify either ``sig" (1D)
or ``image" (2D) processing. Selection of one or the other effects
the other choices in the other user interface panels.


Transform Panel

The Transform panel is used to specify a transformation
to apply to a loaded signal. Possible transforms include the
``sfft" (continuous Fourier transform), ``cwt", (continuous
wavelet transform), and ``fwt" (fast wavelet transform) for
1D signals and just the `fwt2" (two dimensional fast wavelet
transform) for image data. Auxiliary windows are spawned by
the selection of any of the wavelet type transforms. The two
possible types of interface windows spawned are either the ``Discrete
Wavelet Interface" or the ``Parameteric Bandlimited (PBL) Wavelet
Interface". These interfaces are described below.

The ``alpha" parameter is generic transform parameter.
For the sfft it is unused, and for the cwt and fwt(2), its
value is interpreted as a frequency upshift and scale limit
respectively. For the cwt the signal to be transformed is first
upshifted by the quantity ``alpha" along the frequency axis
before the wavelet transform is computed. For the fwt or fwt2
alpha is used to specify the number of scales to compute.

Depressing the ``Xform" button causes the specified
transform to be computed on the loaded data.


Load Panel

The Load panel is used to select and load a signal
from a predefined menu of signals. The user may also specify
a level at which to add noise to the clean signal. Depressing
the Load button causes the specified signal with the specified
noise to be loaded (actually synthesized) and displayed in the
body of the Loader window. The noise is additive Gaussian noise
with zero mean and standard deviation given by the noise parameter.
(SNRs are roughly 10 log10(std)).

All of the 1 dimensional (1D) signals in the ``File(s)"
menu are analytic, i.e., the have Fourier transforms which
vanish for negative frequencies, and therefore are complex signals.
Once a 1D signal is loaded its real part and magnitude are
displayed in separate graphs in the Loader window. Processing
can now be performed on the loaded signal.



Wavelet Interfaces:

Discrete Wavelet Interface

The discrete wavelet interface is minimal in that it
allows only the specification of Daubechies type wavelets of
orders 1 through 9. A single menu and button comprise the
interface panel. Depressing the button ``Daub" causes the
Daubechies high and low pass filter coefficients as well
as the wavelet and scaling functions to be computed and
displayed.


Parametric Band Limited (PBL) Wavelet Interface

The PBL wavelet interface allows the specification of
a parameterized family of analyzing wavelets and a corresponding
filter bank. Analyzing wavelets are specified directly in the
frequency domain by three parameters: order, bandwidth (BW), and
center frequency (CF). Filter banks are generated by two additional
parameters: number of filters Nf and a dilation constant a0>1. The
bank has filters with impulse responses

{ D_(a0^k) g }, k = 1,2, ..., Nf,

where D_s is the L^2 dilation by s operator defined as

(D_s g)(t) = s^(1/2) g(s t).

Depressing the ``Wavelet" button causes the specified wavelet
to be computed and displayed in time and frequency.
Depressing the ``Bank" button cause the specified wavelet to
be computed and displayed in time and frequency (just as the
``Wavelet" button does) and additionally computes and displays
the magnitude Frequency transfer functions for the entire
filter bank and the total filter bank support function G where

G = sum_{k=1}^Nf | (D_(a0^k) g)^ |^2.

This function is directly related to the inversion properties
of the transform.
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