# Daubechies wavelet and scaling filters

### Description

Ingrid Daubechies, a noted pioneer in wavelet theory, has
established a number of wavelet filter types, each with different
mathematical properties. This function calculates the wavelet
and scaling coefficients for a given filter type.
The wavelet coefficients,
*h(k)* for
*k=0,...,L-1* where
*L* is the filter length, are
related to the scaling coefficients through the quadrature mirror
filter (QMF) relation

*h(k)=(-1)^(k-L) g(L-1-k)*

### Usage

1 | ```
wavDaubechies(wavelet="s8", normalized=TRUE)
``` |

### Arguments

`normalized` |
a logical value. If |

`wavelet` |
a character string denoting the filter type. Supported types include: - EXTREMAL PHASE (daublet):
"haar", "d2", "d4", "d6", "d8", "d10", "d12", "d14", "d16", "d18", "d20" - LEAST ASYMMETRIC (symmlet):
"s2","s4", "s6", "s8", "s10", "s12", "s14", "s16", "s18", "s20" - BEST LOCALIZED:
"l2","l4", "l6", "l14", "l18", "l20" - COIFLET:
"c6", "c12", "c18", "c24", "c30"
Default: |

### Details

Only relevant for Daubechies filter types. Inconsistent ordering of the coefficients in Daubechies' book was recognized and corrected by Percival (see references). The "correct" order is given here.

### Value

an object of class `wavDaubechies`

.

### S3 METHODS

- plot
plot Daubechies filters.

Usage: plot(x, type="time")

- x
A

`wavDaubechies`

object.- type
A character string denoting the type of plot to produce. Choices are

`"time"`

,`"gain"`

, and`"phase"`

for an impulse response, squared gain, and phase plot, respectively. Default:`"time"`

.

print Daubechies filters.

Usage: print(x, verbose=TRUE)

- x
A

`wavDaubechies`

object.- verbose
A logical value. If

`TRUE`

, the filter coefficients are also printed. Default:`TRUE`

.

### References

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

I. Daubechies,
*Orthonormal Bases of Compactly Supported Wavelets*,
Communications on Pure and, Applied Mathematics, 41, 909–96.

### See Also

`wavGain`

, `wavDWT`

, `wavMODWT`

, `wavMODWPT`

.

### Examples

1 2 3 4 5 6 7 8 9 |