Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

Optimal Sampling and Interpolation

Effects of sampling on closed form bandlimited signal interval interpolation.

A bandlimited signal is to be recovered over a finite interval. There are two closed form sampling theoremtype algorithms that can perform this restoration. This paper explores the effects of sampling rate on the restoration uncertainty. Increasing the amount of data near the interpolation interval can either increase or decrease the restoration noise level. In the former case, there is an opti...

Discrete Sampling and Interpolation: Orthogonal Interpolation for Discrete Bandlimited Signals

We study the problem of finding unitary submatrices of the discrete Fourier transform matrix. This problem is related to a diverse set of questions on idempotents on ZN , tiling ZN , difference graphs and maximal cliques. Each of these is related to the problem of interpolating a discrete bandlimited signal using an orthogonal basis.

Sampling theorem for polynomial interpolation

The classic polynomial interpolation approach is used to derive a sampling theorem for the class of signals that are the response of systems described by differential equations with constant coefficients. In particular, the polynomial that interpolates the signal between the sampling points for increasing order will give increasing accuracy for stable one-sided sequences, if the sampling rate i...

Sampling and other Stuff

Lemma 1.2 Given y, z, x, w ∈ ZZp, such that x 6= w, and choosing a, b randomly and uniformly from ZZp, the probability that y ≡ ax+ b (mod p) and z = aw + b (mod p) is 1/p2. Proof: This equivalent to claiming that the system of equalities y ≡ ax+ b (mod p) and z = aw+ b have a unique solution in a and b. To see why this is true, subtract one equation from the other. We get y−z ≡ a(x−w) (mod p)....