Release Notes for Wavelets Version 8.1 (November 2008)


Wavelets Version 8.1 contains an updated version of Wavelets
Version 1.0.

This file contains the following information:

SUPPORTED PLATFORMS AND SYSTEM REQUIREMENTS 
ENHANCEMENTS 
NOTES AND KNOWN ISSUES
RUNNING Wavelets
USER'S GUIDE PDF
CONTACT INFORMATION FOR FEEDBACK


SUPPORTED PLATFORMS AND SYSTEM REQUIREMENTS

Wavelets Version 8.1 requires TIBCO Spotfire S+ 8.1 or later on
Windows, Solaris, or Linux platforms.

See the Spotfire S+ 8.1 Release Notes for information about operating
system and system configuration requirements.

In addition to the Spotfire S+ requirements, you must have at least
15MB of free disk space for the typical installation on Windows.


ENHANCEMENTS

The new methodology implemented in Wavelets 8.1 stems almost entirely
from Don Percivals book entitled, Wavelet Methods for Time Series
Analysis, co-authored by Andrew Walden and published by Cambridge
University Press in 2001. In addition, some functionality was provided
by Derek Stanfords team (consisting of Alan Gibbs and Keith Davidson).
A summary of the relevant new methodology is as follows:

1. New wavelet transforms

Specifically, these transforms are DWT, MODWT, DWPT, MODWPT. These
differ from those in Wavelets 1.x in that (1) they are based on
convolution style filtering, (2) they only use periodic boundary
conditions (making them energy conservative and usable for wavelet
variance estimation), and (3) they are designed so that the boundary
coefficients (those subject to circular filter operations) are easily
identifiable, making them useful for certain wavelet-based statistics.
We also have implemented the Dual Tree Wavelet Transform (DTWT) in both
1-D and 2-D. The DTWT has the advantage of being approximately
shift-invariant without only a two-fold degeneracy. The corresponding
multi-resolution decompositions and approximations are also coded in
Wavelets 8.1.

2. Wavelet variance-covariance estimators

If you integrate (over frequency) the spectral density function (SDF),
you obtain the variance. The wavelet variance is a regularization of
the SDF in that it represents the variance of the process on a
scale-by-scale basis (each scale is associated with a particular octave
band of frequencies). Both biased and unbiased versions of the MODWT
and DWT variance estimators have been implemented.

3. Fractionally Differenced (FD) Process parameter estimators

If the SDF follows a power law, then it is known as a colored noise
process (e.g., white noise, pink or 1/f noise, random walk or red
noise, etc.).  The level of the SDF and the log-log slope (alpha) of
the SDF are the two parameters that govern the model. Many real-world
processes exhibit colored noise behavior, whose alpha fluctuates as a
function of time. Of all the power law models, the so-called FD model
is the best (no restriction on alpha, no continuity problems at pink
noise border, simple mathematical model). In Wavelets, we have
implemented wavelet-based estimators of FD model parameters, ranging
from instantaneous to block estimators. We also have two types:
weighted least squares and maximum likelihood estimators. This
technology has been used successfully on the analysis of aerothermal
turbulence data. But it may also have a place in the finance community,
where (possibly short term) SDF power law behavior exists.

NOTES AND KNOWN ISSUES

cpt.2d: The function cpt.2d fails in certain circumstances. In particular, 
the example in the help file fails:

   xx <- phone-mean(phone) 
   par(mfrow=c(1,2)) 
   image(xx) 
   bb2 <- crystal.names("block.dct.2d", 2) 
   cc2 <- cpt.2d(xx, crystal.names=bb2, taper="poly2") 

with the following error message:

   Problem in cpt.2d(xx, crystal.names = bb2, taper = "poly2"): Object "rdict" 
   not found


RUNNING Wavelets

From within Spotfire S+, at the command line, enter:

> module(wavelets)

In Spotfire S+ for Windows, you can also load Wavelets by choosing File >
Load Module > wavelets from the menus.


USER's GUIDE PDF

The Wavelets 2 User's Guide is available in pdf form. The file is called 
Wavelets2.pdf, and you can locate it in your SHOME/modules/wavelets directory.


CONTACT INFORMATION FOR FEEDBACK

Please feel free to contact us with questions or feedback about this
release. Send all questions and general comments to:

	http://spotfire.tibco.com/support

We are very interested in receiving your comments and suggestions for
improving Wavelets.
