# wavZeroPhase: Zero phase shift factors for Daubechies symmlet and coiflet... In wmtsa: Wavelet Methods for Time Series Analysis

## Description

Daubechies coiflet and symmlet filters are approximate linear phase filters. Consequently, the wavelet and scaling coefficients of the DWT and MODWT can be circularly shifted for approximate zero phase alignment with the original time series. This function calculates the circular shift factors needed to bring the wavelet and scaling coefficients to approximate zero phase.

## Usage

 `1` ```wavZeroPhase(wavelet="s8", levels=1:3) ```

## Arguments

 `levels` an integer vector containing the decomposition levels. Default: `1:3`. `wavelet` a character string denoting the filter type. See `wavDaubechies` for details. Default: `"s8"`.

## Details

Only relevant for DWT or MODWT definitions as given in the above reference and is valid only for Daubechies symmlet and coiflet filters.

## Value

a list containing the shifts for each crystal of a DWTor MODWT for the specified decomposition `levels`. A negative shift factor implies an advance (circular shift to the left) of the wavelet transform crystals.

## References

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.

`wavDaubechies`, `wavDWT`, `wavMODWT`, `wavShift`.

## Examples

 ```1 2 3 4``` ```## calculate the zero phase shift factors for ## Daubechies coiflet 12-tap filters for levels ## 2 and 4. wavZeroPhase(wavelet="c12", levels=c(2,4)) ```

### Example output

```\$dwt
d2 d4 s2 s4
-4 -5 -5 -6

\$modwt
d2   d4   s2   s4
-17  -83  -23 -107

\$dwpt
w2.0  w2.1  w2.2  w2.3  w4.0  w4.1  w4.2  w4.3  w4.4  w4.5  w4.6  w4.7  w4.8
-5    -4    -3    -5    -6    -5    -4    -5    -5    -4    -4    -6    -6
w4.9 w4.10 w4.11 w4.12 w4.13 w4.14 w4.15
-4    -3    -5    -5    -4    -5    -6

\$modwpt
w2.0  w2.1  w2.2  w2.3  w4.0  w4.1  w4.2  w4.3  w4.4  w4.5  w4.6  w4.7  w4.8
-23   -17   -14   -20  -107   -83   -71   -95   -89   -65   -77  -101   -98
w4.9 w4.10 w4.11 w4.12 w4.13 w4.14 w4.15
-74   -62   -86   -92   -68   -80  -104
```

wmtsa documentation built on Dec. 6, 2017, 5:05 p.m.