I have a large class of fourier transform integrals that I would like to solve, approximate, or just get some insight into how they work. They take the form:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int exp(j*θ(x))exp(-j*ω*x)dx[/itex]

with the restriction that θ(x) is real.

Now this general class is very hard, but perhaps someone has some insight to it...?

Let's consider a specific example which is of interest to me:

[itex]\int exp(j*cos(x))exp(-j*ω*x)dx[/itex]

So it's the fourier transform of a sinusoidally-rotating rotating exponential...anybody have any clues how to solve or get a functional approximation for the result?

Anyways, just thought I'd post here and see if anyone has encountered similar problems.

This is being used to compute the near-to-far-field transformation of a special kind of holograms.

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# Solving or approximating a special class of fourier transforms

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