# Documentation

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# liftfilt

Apply elementary lifting steps on quadruplet of filters

## Syntax

```[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,ELS) liftfilt(LoD,HiD,LoR,HiR,ELS,TYPE,VALUE) ```

## Description

`[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,ELS)` returns the four filters `LoDN`, `HiDN`, `LoRN`, and `HiRN` obtained by an elementary lifting step (`ELS`) starting from the four filters `LoD`, `HiD`, `LoR`, and `HiR`. The four input filters verify the perfect reconstruction condition.

`ELS` is a structure such that

• `TYPE = ELS.type` contains the type of the elementary lifting step. The valid values for `TYPE` are `'p'` (primal) or `'d'` (dual).

• `VALUE = ELS.value` contains the Laurent polynomial `T` associated with the elementary lifting step (see `laurpoly`). If `VALUE` is a vector, the associated Laurent polynomial `T` is equal to `laurpoly(VALUE,0)`.

In addition, `ELS` may be a scaling step. In that case, `TYPE` is equal to `'s'` (scaling) and `VALUE` is a scalar different from zero.

`liftfilt(LoD,HiD,LoR,HiR,ELS,TYPE,VALUE)` gives the same outputs.

### Note

If `TYPE = 'p'` , `HiD` and `LoR` are unchanged.
If `TYPE = 'd'` , `LoD` and `HiR` are unchanged.
If `TYPE = 's' `, the four filters are changed.
If `ELS` is an array of elementary lifting steps, `liftfilt(...,ELS)` performs each step successively.

`liftfilt(...,FLAGPLOT)` plots the successive biorthogonal pairs—scaling function and wavelet.

## Examples

```% Get Haar filters. [LoD,HiD,LoR,HiR] = wfilters('haar'); % Lift the Haar filters. twoels(1) = struct('type','p','value',... laurpoly([0.125 -0.125],0)); twoels(2) = struct('type','p','value',... laurpoly([0.125 -0.125],1)); [LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,twoels); % The biorthogonal wavelet bior1.3 is obtained up to % an unsignificant sign. [LoDB,HiDB,LoRB,HiRB] = wfilters('bior1.3'); samewavelet = ... isequal([LoDB,HiDB,LoRB,HiRB],[LoDN,-HiDN,LoRN,HiRN]) samewavelet = 1 ```