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The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.

28 votes

Fourier vs Laplace transforms

Here is a heuristic point of view from engineering considerations. I must confess I do not fully know the mathematical reasons. Suppose you want to consider $f(t)$, a function of time, $t$. Imagine t …
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14 votes
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Why sin and cos in the Fourier Series?

$1$. Mathematical reason. There is one reason which makes the basis of complex exponentials look very natural, and the reason is from complex analysis. Let $f(z)$ be a complex analytic function in th …
Anweshi's user avatar
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5 votes
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Complete formulas book for Communication System engineer

I would suggest "Handbook of Formulas and Tables for Signal Processing", by Alexander D. Poularikas. This link should help you. This is the amazon link.
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Calculating fourier transform at any frequency

Here is one answer from the electrical engineering(or, image processing) point of view. However this answer much non-mathematical and more for practical illustration. Since this is a non-mathematical …