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> Volume 6, Issue 2
Preprint: Dithered Trigonometric Functions

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"Soltis James Dr." (soltis@server.uwindsor.ca) Guest

Posted: Wed Jan 22, 1997 8:31 am Subject: Preprint: Dithered Trigonometric Functions




#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 squarerlooking 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. 





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