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Multiscale local 1-D polynomial transform

`[`

returns
the multiscale local polynomial 1-D transform (MLPT) of input signal `coefs`

,`T`

,`coefsPerLevel`

,`scalingMoments`

]
= mlpt(`x`

,`t`

)`x`

sampled
at the sampling instants, `t`

. If `x`

or `t`

contain `NaN`

s,
the union of the `NaN`

s in `x`

and `t`

is
removed before obtaining the `mlpt`

.

`[`

returns
the transform for `coefs`

,`T`

,`coefsPerLevel`

,`scalingMoments`

]
= mlpt(`x`

,`t`

,`numLevel`

)`numLevel`

resolution levels.

`[`

uses uniform sampling instants
for `coefs`

,`T`

,`coefsPerLevel`

,`scalingMoments`

]
= mlpt(`x`

)`x`

as the time instants if `x`

does
not contain `NaN`

s. If `x`

contains `NaN`

s,
the `NaN`

s are removed from `x`

and
the nonuniform sampling instants are obtained from the numeric elements
of `x`

.

`[`

specifies `coefs`

,`T`

,`coefsPerLevel`

,`scalingMoments`

]
= mlpt(___,`Name,Value`

)`mlpt`

properties
using one or more `Name,Value`

pair arguments and
any of the previous input arguments.

Maarten Jansen developed the theoretical foundation of the multiscale
local polynomial transform (MLPT) and algorithms for its efficient
computation [1][2][3]. The MLPT uses a lifting scheme, wherein a kernel
function smooths fine-scale coefficients with a given bandwidth to
obtain the coarser resolution coefficients. The `mlpt`

function uses only local polynomial
interpolation, but the technique developed by Jansen is more general
and admits many other kernel types with adjustable bandwidths [2].

[1] Jansen, Maarten. “Multiscale Local Polynomial Smoothing in a Lifted
Pyramid for Non-Equispaced Data.” *IEEE Transactions on Signal
Processing* 61, no. 3 (February 2013): 545–55.
https://doi.org/10.1109/TSP.2012.2225059.

[2] Jansen, Maarten, and Mohamed Amghar. “Multiscale Local Polynomial
Decompositions Using Bandwidths as Scales.” *Statistics and
Computing* 27, no. 5 (September 2017): 1383–99.
https://doi.org/10.1007/s11222-016-9692-8.

[3] Jansen, Maarten, and Patrick Oonincx. *Second Generation
Wavelets and Applications*. London ; New York: Springer,
2005.