Translations:Phase rotation/30/en

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Because the carrier frequency lies to the right of the passband of the envelope spectrum, it follows that the shifted envelope spectrum vanishes for negative values of frequency . Hence, is the frequency spectrum of an analytic signal . The inverse Fourier transform of gives . The real part of is the modulated wavelet , and the imaginary part is the Hilbert transform of the modulated wavelet. We see that the envelope wavelet gives the instantaneous amplitude and that gives the instantaneous phase.