Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction

@article{Sandryhaila2011AlgebraicSP,
  title={Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction},
  author={Aliaksei Sandryhaila and Jelena Kovacevic and Markus P{\"u}schel},
  journal={SIAM J. Matrix Analysis Applications},
  year={2011},
  volume={32},
  pages={364-384}
}
A polynomial transform is the multiplication of an input vector x ∈ C by a matrix Pb,α ∈ C , whose (k, l)-th element is defined as pl(αk) for polynomials pl(x) ∈ C[x] from a list b = {p0(x), . . . , pn−1(x)} and sample points αk ∈ C from a list α = {α0, . . . , αn−1}. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique… CONTINUE READING

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