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A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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Actually the redundancy perfectly explains why the adjoint property is not verified. The reconstruction operator is not orthogonal anymore and therefore the inverse is not necessarily its adjoint. Yo …
answered Mar 7 by Zaccharie Ramzi
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I recently stumbled upon a bothering fact when using the pywavelet library in Python. When we use the default "symmetric" padding, the inverse wavelet transform is not the adjoint of the wavelet … transform (and it's not the mathematical inverse of the wavelet transform, "only in one direction"). However, if you use the "zero" padding the adjoint property is verified (not the inverse property …
asked Mar 6 by Zaccharie Ramzi
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reconstruction. So I was wondering whether for discrete wavelet transform this redundancy was needed theoretically or if it was an implementation choice. This person at pywt seems to think it is theoretical but I wanted to know why. …
asked Mar 7 by Zaccharie Ramzi