Intereting Posts

shortest path to Tychonoff?
Products and Stone-Čech compactification
Inverting the Cantor pairing function
Set of Finite Measure: Uncountable disjoint subsets of non-zero measure
Algorithms for Symbolic Manipulation
Right triangle on an ellipse, find the area
Topology and Arithmetic Progressions
When is a notion of convergence induced by a topology?
Motivation for different mathematics foundations
Can I bring the variable of integration inside the integral?
Least Upper Bound Property $\implies$ Complete
Enumerations of the rationals with summable gaps $(q_i-q_{i-1})^2$
What are the issues in modern set theory?
Why is the localization at a prime ideal a local ring?
Show that image of $res$ lies in $H^n(H,A)^{G/H}$

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.

- An example about finitely cogenerated modules
- Zero image of an element in the direct limit of modules
- Definition of semi-ring homomorphism
- Can you always find a surjective endomorphism of groups such that it is not injective?
- if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.
- $gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$

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.

- Normal Subgroup Counterexample
- When do equations represent the same curve?
- How to prove that the converse of Lagrange's theorem is not true?
- Points and maximal ideals in polynomial rings
- About group multiplication table
- How to show convolution of an $L^p$ function and a Schwartz function is a Schwartz function
- Characterizing Dense Subgroups of the Reals
- Determining the structure of the quotient ring $\mathbb{Z}/(x^2+3,p)$
- What are some real-world uses of Octonions?
- Degree of field extension $F(x) / F(x^2 + 1 / x^2)$

- Taking stalk of a product of sheaves
- Result due to Cohn, unique division ring whose unit group is a given group?
- The expected payoff of a dice game
- My proof of “the set of diagonalizable matrices is Zariski-dense in $M_n(\mathbb F)$”.
- Equivalence of Definitions of Principal $G$-bundle
- Subgroups of finite index have finitely many conjugates
- Vertical bar sign in Discrete mathematics
- Help proving the primitive roots of unity are dense in the unit circle.
- Solve $x^4+3x^3+6x+4=0$… easier way?
- Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
- How to show that the triangle is equilateral triangle?
- $x^{y^z}$: is it $x^{(y^z)}$ or $(x^y)^z$?
- Deciding whether $2^{\sqrt2}$ is irrational/transcendental
- How to prove that compact subspaces of the Sorgenfrey line are countable?
- Divisibility of polynomial