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"flawed" means wrong. The sampling theorem is valid. Period. For anything.

You simply do not understand that any non-periodic signal can be constructed of a set of periodic functions.

Sine waves (cosine, complex exponential) are ONE such set of periodic functions.

ANY signal, periodic or not, can be constructed of a set of complex exponentials, which is the same as saying "sine wave including both amplitude and phase" ditto cosine.

You can also construct any signal out of a set of square waves. (Walsh-Hadamard basis, Haar basis)

You can construct any signal out of a set of unit impulses. (We call that the "time domain")

You can construct any signal out of a set of orthonormal white noise vectors. (Look into "spread spectrum" methods.)

Polynomial remainders. (in Rabiner and Gold, look up "number-theoretic transforms")

...

There are literally an infinite set of such families of basis vectors and functions. Some are periodic, some are not. Periodicity is completely irrelevant here.

Back to the questions at prophead, you simply do not understand what A A' = I means, do you?

It means that a set of complex exponentials (that's what Fourier analysis uses) span the space of complex signals. "span" is neither ambiguous or undefined, and means just what it sounds like.

Algebra of functions. Linear algebra. Fourier Analysis. Get thee to Morrison's "Fourier Analysis".



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