Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2017 / Paper 1 / 4 / a

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- Solution a

Solution

For the stated forward Fourier transform, the inverse has the opposite exponential sign and a factor

1/ (2 π)

:

f (t) = \frac{1}{2 π} \int_{- \infty}^{\infty} f (ω) e^{iω t} d ω .

This holds under the usual hypotheses for Fourier inversion, or in the sense of distributions when appropriate.

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