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For a vector $\vec{u}\in\mathbb{R}^N$ let's denote $\pi_N\left(\vec{u}\right)$ the unique piecwise linear and $1$-periodic function matching the components of $\vec{u}$ on the discretization $x_k = \...

Summary: From discrete convolution theorem, it is understandable that we need 2N-1 point DFT of both sequences in order to avoid circular convolution. If we need to do deconvolution of a given ...

I often see a trick for calculating convolution of discrete data by a so-called Tabular method. There are a lot of Youtube videos and many Indian textbooks on Signal Processing [Books].1 Basically, ...

Consider the Cox-deBoor recursion formula for producing b-spline basis functions given a knot vector: $N_{i,0}(u)=1 $ if $u_i\leq u < u_{i+1}$ otherwise, $=0$ $N_{i,p}(u)=\frac{u-u_{i}}{u_{...

We are currently looking for a fast, i.e. subquadratic, algorithm for the following equation: $z_m = \sum_{i,j :\, (i \cdot j) = m} x_i \cdot y_j$. That is, we are given two finite input vectors $x$ ...