From my undergraduate textbook: Circuits, Signals, and Systems by Siebert, p 453(adsbygoogle = window.adsbygoogle || []).push({});

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Consider the two principal waveform representations schemes ...

[tex]

x(t) = \int x(\tau)\delta(t - \tau)d\tau

[/tex]

[tex]

x(t) = \int X(f)e^{j2\pi f t}df

[/tex]

If we consider the set of delayed impulses as determining one set of orthogonal vectors and the set of complex exponentials as determining another set, then [itex] x(\tau) d\tau [/itex] and [itex] X(f) df [/itex] are the components of [itex] x(t) [/itex] along the corresponding coordinates. The frequency-domain representations of [itex] x(t) [/itex] thus amounts to picking a coordinate system that isrotatedfrom the time-domain coordinate system. And Parseval's Theorem

[tex]

\int x^2 (t) dt = \int |X(f)|^2 df

[/tex]

is just a statement of the fact that the length of a vector is independent of the coordinate system in which it is described

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Is this true? If so, then it should be possible to the find the axis of rotation, right? How does one go about that? Does the question make sense?

Thanks

Roy

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# Is a fourier transform a rotoation?

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