# modwt: (Inverse) Maximal Overlap Discrete Wavelet Transform In waveslim: Basic wavelet routines for one-, two- and three-dimensional signal processing

## Description

This function performs a level J decomposition of the input vector using the non-decimated discrete wavelet transform. The inverse transform performs the reconstruction of a vector or time series from its maximal overlap discrete wavelet transform.

## Usage

 ```1 2``` ```modwt(x, wf = "la8", n.levels = 4, boundary = "periodic") imodwt(y) ```

## Arguments

 `x` a vector or time series containing the data be to decomposed. There is no restriction on its length. `y` Object of class `"modwt"`. `wf` Name of the wavelet filter to use in the decomposition. By default this is set to `"la8"`, the Daubechies orthonormal compactly supported wavelet of length L=8 (Daubechies, 1992), least asymmetric family. `n.levels` Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2). `boundary` Character string specifying the boundary condition. If `boundary=="periodic"` the defaulTRUE, then the vector you decompose is assumed to be periodic on its defined interval, if `boundary=="reflection"`, the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

## Details

The code implements the one-dimensional non-decimated DWT using the pyramid algorithm. The actual transform is performed in C using pseudocode from Percival and Walden (2001). That means convolutions, not inner products, are used to apply the wavelet filters.

The MODWT goes by several names in the statistical and engineering literature, such as, the “stationary DWT”, “translation-invariant DWT”, and “time-invariant DWT”.

The inverse MODWT implements the one-dimensional inverse transform using the pyramid algorithm (Mallat, 1989).

## Value

Object of class `"modwt"`, basically, a list with the following components

 `d?` Wavelet coefficient vectors. `s?` Scaling coefficient vector. `wavelet` Name of the wavelet filter used. `boundary` How the boundaries were handled.

B. Whitcher

## References

Gencay, R., F. Selcuk and B. Whitcher (2001) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press.

Percival, D. B. and P. Guttorp (1994) Long-memory processes, the Allan variance and wavelets, In Wavelets and Geophysics, pages 325-344, Academic Press.

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

`dwt`, `idwt`, `mra`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```## Figure 4.23 in Gencay, Selcuk and Whitcher (2001) data(ibm) ibm.returns <- diff(log(ibm)) # Haar ibmr.haar <- modwt(ibm.returns, "haar") names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4") # LA(8) ibmr.la8 <- modwt(ibm.returns, "la8") names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4") # shift the MODWT vectors ibmr.la8 <- phase.shift(ibmr.la8, "la8") ## plot partial MODWT for IBM data par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)") for(i in 1:5) plot.ts(ibmr.haar[[i]], axes=FALSE, ylab=names(ibmr.haar)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)") for(i in 1:5) plot.ts(ibmr.la8[[i]], axes=FALSE, ylab=names(ibmr.la8)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) ```

### Example output

```waveslim: Wavelet Method for 1/2/3D Signals (version = 1.7.5)
```

waveslim documentation built on May 29, 2017, 3:23 p.m.