Parseval’s Theorem
Using the Fourier Transform, Parseval’s theorem establishes a link between the energy of the time domain waveform and the energy of the spectrum: If \(x(t) \circ — \bullet X(j \omega)\), then \(\displaystyle \int_{-\infty}^{\infty}|x(t)|^2 d t=\frac{1}{2 \pi} \int_{-\infty}^{\infty}|X(j \omega)|^2 d \omega=\int_{-\infty}^{\infty}|X(f)|^2 d f\)
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