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Student Support Forum: 'Fast Transforms' topicStudent Support Forum > General > Archives > "Fast Transforms"

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Ernesto Estevez Rams
08/25/99 7:53pm

Hello there,

I was trying to implement the fast cosine transform and the fast sine transform in mathematica. I tried the usual way of extending the data in a even and a odd manner and then doing a fast fourier transform using Fourier[]. It did not work. The output in each case was a mixture of real and imaginary parts and not a completelly real or a pure imaginary output.

I then looked more closely to the Fourier function. I generated an odd data list making a table out of a sine function.

dat=Table[Sin[x],{x, 0, 10 Pi, 10 Pi/256}]

then

Fourier[dat]

The output should had been pure imaginary. It was not. The output ressembled the delta function behavior in frecuency 1 and -1 but it had complex numbers with real and imaginary parts in it. The analytical function FourierTransform[] gives the correct Pi I (Delta[1+w]+Delta[-1+w]), yet in the FFT implementation it seems to be some numerical precision error. I increased the data to the interval {0, 100 Pi}and increased the number of points to 1000. Still the output contained non neglible mixed complex number.

Going back to my original problem. I want to implement the Fast cosine transform and the fast sine transform. I am expecting that when I apply this function to my data set I get as an output a transform data which represents a real valued physical data. Any hints on how to do it?

Thanks in advance
Ernesto




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