All Questions
Tagged with fourier-transform algorithms
8 questions
2
votes
0
answers
204
views
Finding specific coefficients of product of high-dimensional Fourier series faster than FFT
I need a fast algorithm to perform a specific Fourier-type computation in my physics research. Suppose I have the following two Fourier series in three dimensions
$$
a(t_1,t_2,t_3)=\sum_{j=-n}^{n}\...
- 620
3
votes
0
answers
93
views
Efficient multiplication of Cayley-Dickson numbers
The question was already asked here, but doesn't have any meaningful answer, hence I'd like to re-post it.
Assuming that we have an algebra with conjugation, we can use Cayley-Dickson construction to ...
- 1,171
3
votes
0
answers
347
views
Is this FFT algorithm known?
Recently I've been thinking about alternatives to the usual Cooley-Tukey FFT for multiplying polynomials. I think I've come up with a pretty nifty algorithm for multiplying polynomials. So my question ...
- 31
0
votes
0
answers
140
views
Binary polynomial evaluation
Let $p$ be a prime number and let $P(x) = a_0 + a_1x + a_2x^2 + \dots + a_{n-1}x^{n-1}$ be a polynomial in $\mathbb{Z}_p[x]$ with binary coefficients, i.e., such that $a_i \in \{0,1\}$ for all $i = 0,...
- 61
1
vote
0
answers
143
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Polynomial interpolation of binary vectors
Let $\mathbb{F}$ be a finite field and let $\boldsymbol{x} = (x_1, x_2, \dots, x_n)$ be $n$
pairwise distinct points in $\mathbb{F}$.
Given the vector $\boldsymbol{y} = (y_1, y_2, \dots, y_n)$, with $...
- 61
2
votes
1
answer
315
views
Find a collection of values of polynomial
Given a polynomial $f(x)\in \mathbb C[x]$ where $\deg f(x)=n-1.$ Assume that we need to find a collection of values of this polynomial corresponding to the following set of $x$-values: $\{ e^{ik} \}$ ...
- 21
12
votes
1
answer
562
views
Fast convolution of sparse functions
Let $F:\mathbb{R}\to \mathbb{Z}$ be a step function with at most $k$ discontinuities, at given rationals $a_1<a_2<\dotsc<a_k$. Let $g:\mathbb{R}\to \mathbb{Z}$ be given as a linear ...
- 20.2k
6
votes
1
answer
307
views
G-Correlation of Vectors
Let $\vec{a},\vec{b} \in \mathbb{R}^{n}$. Consider the function $f: S_n \to \mathbb{R}$ given by $f(\sigma):= \sum_{i=1}^{n} a_i b_{\sigma(i)}$. Let $G$ be a subgroup of $S_n$, given by $O(\log n)$ ...
- 14.6k