Intereting Posts

Convergent series whose Cauchy product diverges
Is there another kind of two-dimensional geometry?
What is wrong with treating $\dfrac {dy}{dx}$ as a fraction?
solving third-order nonlinear ordinary differential equation
How to reparametrize curves in terms of arc length when arc-length evaluation cannot be computed analytically
Quotient Objects in $\mathsf{Grp}$
How to prove the sum of combination is equal to $2^n – 1$
Strange Recurrence: What is it asymptotic to?
$\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$
Why is a statement “vacuously true” if the hypothesis is false, or not satisfied?
Matrix exponential Differentiation
Erf squared approximation
For what values does this method converge on the Lambert W function?
N white and black balls and N boxes Probability
Are the functions $\sin^n(x)$ linearly independent?

Continuing from this rather silly trivial question factoring real valued filters into shorter complex ones, hoping this won’t be as trivial.

If we modify it a bit:

$$z_0 = e^{2\pi i / 8}$$

and

$$\left(z_0^{[3k,2k]} * z_0^{[3k,-2k]}\right)$$

will for $k \in \{2,3,4\}$:

$$k=2 \rightarrow \left[\begin{array}{ccc}

-1&2i&1

\end{array}\right]$$

derivative in real part

$$k=3 \rightarrow \left[\begin{array}{ccc}

i&0&1

\end{array}\right]$$

captures displacements by -1 and 1 position. E.g. both “lazy” filters.

$$k=4 \rightarrow \left[\begin{array}{ccc}

1&-2&1

\end{array}\right]$$

which is a second derivative approximation.

- $R/Ra$ is an injective module over itself
- Isomorphisms between $\mathbb C$ and field $\mathbb K$
- Locally compact nonarchimedian fields
- Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
- Intersection maximal ideals of a polynomial ring
- What elements in a tensor algebra are invertible?

Theses ones I found by trial and error. I guess what I am asking for is systematic ways to find filters which are easy to build “on the fly”, cheap to calculate, and which capture previously known important features.

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- Adapting a proof on elements of order 2: from finite groups to infinite groups
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- Explaining the product of two ideals
- Does commutativity imply Associativity?
- Suppose G has order 4, but contains no element of order 4. A) prove that no element of G has order 3.?
- How far can we go with group isomorphisms?

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