So the complex exponential Fourier series form an orthonormal basis for the space of functions. A periodic function can be represented with countably many elements from the basis, and an aperiodic function requires uncountably many elements.(adsbygoogle = window.adsbygoogle || []).push({});

Given a signal, we can find the coefficients of the exponentials in two ways:

1) Fourier transform

2) Inner product with that complex exponential

Though these two formulas are similar, they are not identical. So how could they both possibly give us the coefficient of a complex exponential?

Thanks!

BiP

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# Fourier transform vs Inner product

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