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Convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.

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Wavelet computation with filter bank - differing results

Convolution is defined as $$ \left[\tilde{H} * a_{j+1}\right](2k) := \sum_{n=0}^{3} \tilde{h}_na_{j+1,2k-n} $$ and uses a periodically extended signal. For $\tilde{G}$ it is defined likewise. … Regarding the other two, I came up with the idea that my convolution might be wrong, and I tested two other "modes" of PyWavelets, namely zero-padding (zpd) and periodic-padding (ppd). …
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