Re: simple trigonometric expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg73147] Re: simple trigonometric expression*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sun, 4 Feb 2007 08:15:33 -0500 (EST)*References*: <epv3ev$8j7$1@smc.vnet.net><eq1ifg$2tp$1@smc.vnet.net>

Ok Don, It is much better now! Thanks a lot! Best Regards Dimitris Don Taylor <dont at agora.rdrop.com> wrote: Certainly. The fourier transform takes a relatively arbitrary periodic function and returns an equivalent function which is a sum of Sin and Cos for integer multiples of 2pi. Thus, even if the function is very complicated, just by finding the period of the function, usually by inspection it is possible to know what to give the fourier transform for a period. The result will be c0,c1,s2,c2,s2,c3,s3,... where the function c0*Cos[0*2*Pi]+c1*Cos[1*2*Pi]+s1*Sin[1*2*Pi]+c2*Cos[2*2*Pi]+s2*Sin... As long as the trig expression only has Sin and Cos and powers and sums of those, or can be put in that form, it does not matter whether there are multiple angles of these or powers of these, the method finds the unique trig expression that is the fourier transform of this. If there are Tan or Cot or Csc or Sec terms then this method does not really give satisfactory results, but otherwise it can handle very large multiples of angles and many different combinations of angles and often simplify such expressions by a great deal. I hope this helps don