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Why normalized filters Last question first, "Why $1/\sqrt2$": Because it makes the (Euclidean) norm of the filter $1$, so that the whole wavelet filter bank operation (if done right, that is, the decimated version) is orthogonal/isometric. It is a design choice, there is nothing wrong in staying with the integer values and correct the combined factor during ...

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The correlation is used to find the time shift between signsls while convolution represents system response to predefined input. Since the system response depends on previous input, rether then future input, the sign of the time distance is negative.

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The idea here is to build the problem in its Matrix Form. We have the filter $h$ which is represented by the matrix $H$ to represent Linear Convolution operation:  H = \begin{bmatrix} {h}_{1} & 0 & 0 & \ldots & & 0 \\ {h}_{2} & {h}_{1} & 0 & \ldots & & 0 \\ \vdots & & \ddots & & & \...

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staying faithful to the subject "removing window effect in freq domain via convolution" (despite the OP perhaps wanted to achieve something else or something similar), I feel to add my comment having personal experience with this specific topic. Often I have the necessity to remove a Hann window in frequency domain, working in a STFT framework which uses ...

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