We know that the law of conservation of energy dictates that the energy carried by a waveform in the time domain must equal the energy contained in its power spectrum in the frequency domain. How would i go about showing analytically this law holds for a Gaussian waveform: $e^{-a(x-b)^2}$ and its Fourier Transform. I think I need to use Placherel's theorem but I'm not sure how to start the proof.
2026-04-07 17:36:09.1775583369
Need help with Placherel's Theorem
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