The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 6, Issue 2


Preprint: Dithered Trigonometric Functions
 
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
"Soltis James Dr." (soltis@server.uwindsor.ca)
Guest





PostPosted: Wed Jan 22, 1997 8:31 am    
Subject: Preprint: Dithered Trigonometric Functions
Reply with quote

#10 Preprint: Dithered Trigonometric Functions

By making use of the Jacobian elliptic functions
one can generate a whole new class of basis functions
with properties of interest in signal processing as
regards transform processing.
The prescription is to replace 2*pi in the
digital Fourier (and related DCT,DST,etc.) with 4*K in the
relevant equations , where K is the elliptic integral
of the 1st kind.Also the standard sine and cosine should
be replaced by the Jacobian sn and cn functions.Unlike
the standard case , many versions of any transform exist
since the SHAPES of sn and cn differ (unlike sin and cos).
Thus , for example, one can have(symbolically)
W =cn+sn(K+)+i*(sn+cn(K+))
There are many variations on this theme.e.g,
W=cn+i*sn
The resulting transform(s) matrices are of interest,
with due regard to aliasing issues ,however of special interest
the inversion of this matrix leads to BASIS functions which mimic the
standard trig functions with fuzzy or dithered behavior.
There are many versions of the transform , since unlike
sin and cos the waveshapes of Jacobian sn and cn differ.
For example, shifting the sn function by K (see above) in
its argument offers squarer-looking cosine waves.
A special attribute is that the Jacobian elliptic
functions offer a 'built in' stretching parameter so that
their utility extends beyond the standard trig functions.
Obviously, in standard WAVELET work , one can replace the
presence of trig functions with this arena of work.
Please contact me at emailing soltis@server.uwindsor.ca
for any details, including MATLAB programs.
All times are GMT + 1 Hour
Page 1 of 1

 
Jump to: 
 


disclaimer - webmaster@wavelet.org
Powered by phpBB

This page was created in 0.026419 seconds : 18 queries executed : GZIP compression disabled