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ft_conv and WPPM_ft_conv
rowlesmr #1
Member since Oct 2011 · 146 posts
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Subject: ft_conv and WPPM_ft_conv
I'm starting to look into some Fourier transform things for some peak shape things, and have a couple of (initial) questions  about how it works in Topas.

Is FT_K=0 taken to be at the peak position?

Looking at the Gaussian and Lorentzian examples in test_examples\ft:
X-space        -> G=(2 Sqrt(Ln(2)/Pi)/w) Exp(-4 Ln(2) (X/w)^2) goes to
FT_K-space   -> Gt = Exp(-(Pi w k)^2/(4 Ln(2)))

If I do the same transformation in Maple, I get a slightly different expression
k-space          -> Gt = Exp(-(w k)^2/(16 Ln(2)))

which can be taken care of if (Topas k) = 2 Pi (Maple k). Is this correct? Tech ref is unclear on this.

X-space        -> L=(2/(Pi w)) / (1+4(X/w)^2) goes to
FT_K-space   -> Lt = Exp(-Pi w k)

If I do the same transformation in Maple, I get a slightly different expression
k-space          -> Gt = Exp(-(1/2) w k) Heaviside(k) + Exp((1/2) w k) Heaviside(-k)

where Heaviside(k) is a piecewise function =0, k < 0, =1 k>0, undef k=0.

Plotting the Topas FT_K-space function over k = -5..5 gives a single exponential, whereas the Maple version gives back-to-back exponentials.

How are convolutions defined in Topas in this instance? If I wanted to write down the fourier transform function, which is correct?

WPPM_ft_conv is said to be done on data interpolated to s-space.

How is s-space defined? is it Sin(Th)/Lam? or some other definition?


I think that's all for now.

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