Conference rusure::math

1384.0. "Suggestions for MAPLE package" by SMAUG::ABBASI () Fri Feb 08 1991 12:38

 This is posted in MAPLE and MATH confreneces.

Folks,

 Maple developers are currently working on a Fourier analysis package
 (fourier series and fourier transforms), and I've been talking to the 
 developers, Here is what features that have currently implemented in this
 package which will be part of their next release of MAPLE.
 
 They will also be happy to take suggestions from us about any features
 that we would like to see in this new package that they might have
 missed, and they will try to add that feature into the package.

 So If some of you out their have a wish-list of what they want out of
 a fourier transform package, please post it here or mail to me, and I'll make
 sure the Maple developers get your reply.
 
 Please indicate in your reply if you would like me to forward the reply
 to MAPLE or not.

 This is what they have already in it.

Thank You.
/Naser
------------------------------------------------------------------------
 
Fourier transforms are part of the integral transforms package (inttrans).
To use this, one should type with(inttrans).
 
It takes advantage of certain reduction formulas, of which, fourier 
series can fairly easily be obtained.  Functions that it knows about are
the Heaviside, Sign, Exp, Fourier (ie the fourier transform of a fourier
transform), Convolute, Even, Odd, Integration, Conjugate, Summation, Evaluate,
Rectangular, Dirac, III (Comb function), and a few others.
 
The reduction formulas are based on operator commutivity.  Complex 
exponentials (linear in the FT variable), sines, and cosines result
in the "frequency modulation" of the same integral without them.  
Hence there is an evaluate function that may appear.  This can be suppressed
by using the regular three argument function call.  The alternative is
the following 4 argument function call:
 
	fourier(expr,t,w,[_full_reduce]);
 
Integer and symbolic exponent polynomials reduce to derivatives in
the frequency domain -- ie, outside of the integral.
 
Remaining to be added, is a way to specify a periodic function, one that 
is well defined over an interval and periodic indefinitely.  The comb function
is one just like this, but because it is special, it is listed as is.
 
With all of this in mind, the fourier series is:
 
	F(n) 
 
	== evaluate(fourier(expr,t,w,[_full_reduce]),w=n*w0)
 
As to bodi plots, these are in the works.  Instead of having to convert
the general function to a linear representation (by taking the logarithms
of the respective parts), effort (by someone else) is being put into allowing
for logarithmic and semilogarithmic axis.  It remains to be 
seen if the standard bodi magnitude and phase approximations are 
implemented (if possible) in such a command.
 
If you can think of any functions that I have left out (oops, derivative was
left off of the list), then please forward it to me.  I would be more
than happy to install this.
 
Hans Ziemann
Maple 
Symbolic Computation Group
University of Waterloo