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Abstract Dissonance
science forum Guru Wannabe

Joined: 29 Dec 2005
Posts: 201

Posted: Wed Jul 12, 2006 11:41 am    Post subject: Re: Fourier theory help

BTW, the sinc function I use is sinc(x) = sin(x)/x
Abstract Dissonance
science forum Guru Wannabe

Joined: 29 Dec 2005
Posts: 201

Posted: Wed Jul 12, 2006 11:22 am    Post subject: Fourier theory help

In that file at the very bottom I show 4 equations. The last 2 are suppose
to be the time dependent forms of the 2 before it.

Now, hat(s)_k should make sense as hat(s). hat(s)_k is just shifting the
function in the frequency domain by kO then "chopping" it off if its outside
[a, O].

Now I could have moved the pulse and left the function still but for
specific reasons I did it the other way. (notice when hat(s)_k is plugged
into hat(s) it reverts to this idea)

Anyways, now taking the inverse fourier transform of hat(s)_k one should
arrive at the second to last equation. This is because a product in the
frequency domain is a convolution in the time domain * sqrt(2*Pi). The
factors of exp(I*k*O*t) are because it represents a shift in the frequency
domain.

Applying the CIFT on hat(s) should give the last equation. I think this is
obvious too.

Now, the problem I have is when I go ahead and substitute s_k into the
equation for s I arrive at s = O*s. I'm somehow picking up a factor of O but
I cannot figure out where.

I've checked to make sure that the CIFT of the pulse is correct about a
dozen times(because it contains that factor of O that carries through).

I can't see if theres something I'm doing wrong and was hoping someone else
could. (I could define s(t) = 1/O sum(s_k) but that's cheating as it doesn't
follow from the CIFT of hat(s))

Thanks,
Jon

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