Monday, February 6. 2006
Understanding the Fourier transform
I borrowed the book “Fouriertransformation für Ingenieur- und Naturwissenschaften” by Klingen from the NuHAG library to use it as a help for understanding the (multidimensional) Fourier transform. Unfortunately, it seems to be on a rather applied/engineer level and only seems to contain one- and two-dimensional functions. We’ll see if it is useful to me.
Wednesday, February 1. 2006
d-dimensional Fourier transform
I know what the factor for
in the definition of the Fourier transform
means, if that factor is seen as a function in : If
is fixed, then the variation of
delivers the circle function, returning to the starting point for every
.
But what if ? Here,
has to be understood as the inner product
and the integral turns into the
-dimensional Lebesgue-integral, i.e., if
, this means
Now, what has to be understood by in higher dimensions?
Continue reading "d-dimensional Fourier transform"
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