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Multiscale local 1-D polynomial transform

```
[coefs,T,coefsPerLevel,scalingMoments]
= mlpt(x,t)
```

```
[coefs,T,coefsPerLevel,scalingMoments]
= mlpt(x,t,numLevel)
```

```
[coefs,T,coefsPerLevel,scalingMoments]
= mlpt(x)
```

```
[coefs,T,coefsPerLevel,scalingMoments]
= mlpt(___,Name,Value)
```

`[`

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, M. "Multiscale Local Polynomial
Smoothing in a Lifted Pyramid for Non-Equispaced Data". *IEEE
Transactions on Signal Processing*. Vol. 61, Number 3,
2013, pp. 545–555.

[2] Jansen, M., and M. Amghar. "Multiscale
local polynomial decompositions using bandwidths as scales". *Statistics
and Computing* (forthcoming). 2016.

[3] Jansen, M., and Patrick Oonincx. *Second
Generation Wavelets and Applications*. London: Springer,
2005.

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