Translations:Phase rotation/27/en

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Let us illustrate the phase rotation of a wavelet. We will construct the wavelet in a special way. We start with a band-limited low-pass real symmetric frequency spectrum , which is called the envelope spectrum. The inverse Fourier transform of this envelope spectrum gives a real symmetric wavelet , which is called the envelope wavelet. Now we use the envelope wavelet to modulate a carrier signal. The carrier signal is the high-frequency sinusoidal signal . We assume that the carrier frequency is positive and lies above the pass-band of the envelope spectrum. The required signal is the modulated wavelet . The frequency spectrum of the modulated wavelet is