The filters tag has no wiki summary.

**-1**

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### What is the difference between disturbance and noise for dynamic systems? [on hold]

In most references from dynamic system theory, the following linear continuous dynamic system is considered.
$$\frac{\text{d}x(t)}{\text{d}t}=Ax(t)+Bu(t)+Dd_{1}(t)\quad (1)$$
$$y(t)=Cx(t)+Ed_{2}(t) ...

**4**

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**0**answers

157 views

### Intersections of open sets and $\alpha$-favorable spaces

I would like to ask about some classes of topological spaces whether they have been studied, what are they called (if they have a name) and whether they have some interesting properties. For the ...

**2**

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**0**answers

24 views

### Analogous filter to Kalman filter that maximized mode instead (as opposed to minimizing variance)

I may have a potential application where maximizing the mode (as opposed to typically minimizing the variance) would be useful for state estimates. The situation may arise from skewed distributions ...

**6**

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**1**answer

334 views

### A characterization of the poset of filters on a set

For the lattices of all subsets of a given set it is known an axiomatic characterization: A poset is isomorphic to a set of all subsets of some set iff it is a complete atomic boolean algebra.
The ...

**4**

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**1**answer

214 views

### Connection between subnet and superfilter

Let's define a net and subnet in this way:
A net is any function of the form $n:(P,\le)\to X$ where $(P,\le)$ is a (preordered) directed set.
A net $m:(P',\le)\to X$ is a subnet of the net ...

**2**

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**0**answers

266 views

### Research in Algebraic Geometry involving Filters.

In Gillman and Jerrison's book, "Rings of Continuous Functions", they show a nice relationship between the set of z-ideals in C(X) and the set of filters on X. One can go for with this relationship; ...

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124 views

### Theory of (definable) ideals on a multi-dimensional countable set

I'm wondering if there are any results about definable ideals/filters on $\omega\times\omega$, $\omega\times\omega\times\omega$, etc.
To give a sense of the kind of results I might be looking for: ...

**0**

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**2**answers

281 views

### Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function

Given a line function $y = ax + b$, it is easy to calculate the sum-of-squares distance between the line and a window of samples $(1, y_1), (2, y_2), ..., (n, y_n)$ (where $y_1$ is the oldest sample ...

**1**

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**1**answer

136 views

### Digital Filters [closed]

Can somebody help with the constructing filter by amplitude and phase spectrum? Is it possible?
I try to google it, but unsuccessufully.
I have some thoughts about solving it by system of linear ...

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votes

**1**answer

831 views

### Direct product of filters

Product $a\times b$ of filters $a$ and $b$ is defined as the filter (on the set of binary relations) defined by the base $\{ A\times B | A\in a,B\in b \}$.
I will denote the principal filter ...

**-8**

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**2**answers

1k views

### Filters and intersection of two binary relations

Let $\mathfrak{F}$ is the complete lattice of filters (including the improper filter) on some set, ordered
inverse to set-theoretic inclusion.
I will denote $\left\langle f \right\rangle \mathcal{X} ...

**0**

votes

**1**answer

292 views

### About ordering and equivalence of filters

Let $U$ is a set. I will speak about filters on this set.
If $f$ is a function and $a$ is a filter then I define $f \left[ a \right]$ as
the filter whose base is $\lbrace f[A] | A \in a \rbrace$.
I ...

**8**

votes

**5**answers

688 views

### Spaces of filters

This question arose more from curiosity than from an actual problem. There are situations when you embed some space $X$ in a set of filters on $X$, which inherits properties of $X$ or has even better ...

**0**

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**1**answer

336 views

### Do filters complementive to a given filter form a complete lattice?

Really I should first ask this question here on MathOverflow and only then post it as an open problem in Open Problem Garden and propose it as a polymath problem. Indeed I did the reverse and now hope ...