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It's a spurious artifact due to not referencing your phase generation to the center of your data window, and not doing an fftshift before the fft to place your phase reference point at fft input index 0. e.g. For varying frequencies, either you have to know, generate, or want the phase at location T/2 of your continuous sinusoid. The phase result of an ...

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There is a huge gap between the formalism and construction for the continuous wavelet analysis (Mexican hat or Morlet wavelet, the latter being only approximate or complex Gaussian wavelet) and the discrete wavelet transforms (DWT). Let us make a long story short. Continuous wavelet transforms (CWT) hinge on a continuous wavelet $\psi$, for which for any (...

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Without more details, when a signal is properly recorded at $F_n$ Hz, one is entitled to expect that all information below the half of it, namely $F_n/2$ Hz, can be recovered, somehow. This is an application of the classical Shannon Sampling Theorem. Twice the maximum frequency is sufficient to sample a signal... in theory. The question says: max frequency ...

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