Heuristic Derivation of the Classical Fourier Transform
In the previous chapters, we developed some useful tools for dealing with periodic functions on the real line. The question now is whether we can extend the basic concepts already developed and obtain comparable tools for dealing with nonperiodic functions on the real line. Obviously, the answer is yes (otherwise, this would be a much shorter text), and, judging from the above title, this must be the chapter where that extension is done.
What we will actually derive here (with limited concern for rigor) are the two integral formulas on which the Fourier transforms are based, along with a fundamental relation between these two formulas. The basic idea behind the derivation is straightforward. ...
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