Translations:Illustrations of spectra/1/en

Let us now illustrate the spectra of different dipoles. We start with the unit spike: the coefficient 1 at time index 0. In terms of a two-length causal wavelet, the unit spike is (1, 0). The Fourier transform of (1, 0) is 1 for all $\omega$. Hence, the amplitude spectrum of the unit spike is equal to one for all frequencies or, in other words, the amplitude spectrum is white. If we write 1 = 1 + 0 i, we see that the phase-lag spectrum of the unit spike is $-{\rm {tan}}^{-1}\left({0/1}\right)$, which is zero for all $\omega$. In other words, the unit spike has the minimum-phase spectrum, which is equal to zero for all frequencies.