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I'm just searching for a generalized result here. Due to lack of note taking I am in a bind for this Fourier transform. The transform is....

[tex] \int_{-a/2}^{a/2} \cos (\frac{\pi x}{a}) e^{-j\beta s x} dx [/tex].

Of course, this is a general Fourier transform, although variables such as f and t are omitted as this is related to antennas.

Anyways, I figure that this is a product between a cosine function

[tex]cos(\pi x/a)[/tex]

and a unit rectangular pulse function between -a/2 and a/2. Of course, the Fourier modulation theorem states that we should have a transform of the form:

[tex] F(s) \sim sinc(0.5 a \beta s - \pi /a) + sinc(0.5 a \beta s + \pi /a) [/tex].

with scalar coefficients omitted for the sake of simplicity.

Anyways, I believe there to be an analytical expression for the sum of these Sinc functions, and it is allegedly a cosine function of certain parameters.

Anyways, the transform itself is complete from the general expression above, but the algebra is long winded to form it into another trig function.. Can anyone see a nice, glaring solution to this?

Cheers guys....

Brendan

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# Simple transform, wicked algebra.

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