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Re: Fourier transforms



Yes, in the context described by Brian (diffraction
slit is a rectangular pulse in 1 dim) both positive
and negative k have physical significance. But a
negative frequency w seems to be a mathematical
artifact.

I suppose this is somehow connected with our
inability to move backward in time; in space we
can really move in any desired direction. Our
mathematics does not care what x is; it can be time
or it can be a displacement. What else can it be?
Ludwik Kowalski

On Saturday, Oct 18, 2003, at 20:54 US/Pacific, Brian Whatcott wrote:

At 10:39 PM 10/18/2003, Ludwik, you wrote:

/// "how to interpret negative
frequencies?" In the context of my illustrations
(replying to Roger) negative w has no physical
meaning; it appears because our very powerful
mathematical machinery is not limited to one kind
of problems. Is such statement acceptable?

If one beam-expands a laser beam to illuminate a 35 mm slide
depicting vertical bars of constant spacing, a convex lens
placed after the slide shows the continuous Fourier transform
of the slide's spatial light intensities at the lens's focal plane
as light intensity versus spatial frequency on both sides of
the optical axis.
This demonstrates that the extension of a Fourier transform
on either side of an axis cannot be said to be a mathematical
artifact without physical significance.