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MathGroup Archive 2007

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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




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