wfilters

Wavelet filters

Syntax

``[LoD,HiD,LoR,HiR] = wfilters(wname)``
``[F1,F2] = wfilters(wname,type)``

Description

example

````[LoD,HiD,LoR,HiR] = wfilters(wname)` returns the four lowpass and highpass, decomposition and reconstruction filters associated with the orthogonal or biorthogonal wavelet `wname`.```
````[F1,F2] = wfilters(wname,type)` returns the pair of `type` filters associated with the orthogonal or biorthogonal wavelet `wname`. For example, `wfilters("db6","h")` returns the pair of highpass filters `HiD` and `HiR` associated with the `db6` wavelet.```

Examples

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Set the wavelet name.

`wname = "db5";`

Compute the four filters associated with wavelet name specified by `wname` and plot the results.

```[LoD,HiD,LoR,HiR] = wfilters(wname); subplot(2,2,1) stem(LoD) title("Decomposition Lowpass Filter") subplot(2,2,2) stem(HiD) title("Decomposition Highpass Filter") subplot(2,2,3) stem(LoR) title("Reconstruction Lowpass Filter") subplot(2,2,4) stem(HiR) title("Reconstruction Highpass Filter") xlabel("The four filters for "+wname)```

Input Arguments

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Name of orthogonal or biorthogonal wavelet, specified as one of the values listed here.

Wavelet Family

Type

Wavelets

DaubechiesOrthogonal`"db1"` or `"haar"`, `"db2"`, `...`, `"db10"`, `...`, `"db45"`
CoifletsOrthogonal`"coif1"`, `...`, `"coif5"`
SymletsOrthogonal`"sym2"`, `...`, `"sym8"`, `...`,`"sym45"`
Fejér-Korovkin filtersOrthogonal`"fk4"`, `"fk6"`, `"fk8"`, `"fk14"`, `"fk22"`
Best-localized DaubechiesOrthogonal`"bl7"`, `"bl9"`, `"bl10"`
Morris minimum-bandwidthOrthogonal`"mb4.2"`, `"mb8.2"`, `"mb8.3"`, `"mb8.4"`
`"mb10.3"`, `"mb12.3"`, `"mb14.3"`, `"mb16.3"`
`"mb18.3"`, `"mb24.3"`, `"mb32.3"`
BeylkinOrthogonal`"beyl"`
VaidyanathanOrthogonal`"vaid"`
Han linear-phase momentsOrthogonal`"han2.3"`, `"han3.3"`, `"han4.5"`, `"han5.5"`
Discrete MeyerOrthogonal`"dmey"`
BiorSplinesBiorthogonal`"bior1.1"`, `"bior1.3"`, `"bior1.5"`
`"bior2.2"`, `"bior2.4"`, `"bior2.6"`, `"bior2.8"`
`"bior3.1"`, `"bior3.3"`, `"bior3.5"`, `"bior3.7"`
`"bior3.9"`, `"bior4.4"`, `"bior5.5"`, `"bior6.8"`
ReverseBiorBiorthogonal`"rbio1.1"`, `"rbio1.3"`, `"rbio1.5"`
`"rbio2.2"`, `"rbio2.4"`, `"rbio2.6"`, `"rbio2.8"`
`"rbio3.1"`, `"rbio3.3"`, `"rbio3.5"`, `"rbio3.7"`
`"rbio3.9"`, `"rbio4.4"`, `"rbio5.5"`, `"rbio6.8"`

Type of filter pair to return, specified as one of the values listed here.

`type`Description
`"d"`

Decomposition filters (`LoD` and `HiD`)

`"r"`

Reconstruction filters (`LoR` and `HiR`)

`"l"`

Lowpass filters (`LoD` and `LoR`)

`"h"`

Highpass filters (`HiD` and `HiR`)

Output Arguments

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Decomposition lowpass filter, returned as a real-valued vector, associated with the wavelet `wname`.

Decomposition highpass filter, returned as a real-valued vector, associated with the wavelet `wname`.

Reconstruction lowpass filter, returned as a real-valued vector, associated with the wavelet `wname`.

Reconstruction highpass filter, returned as a real-valued vector, associated with the wavelet `wname`.

Filter pair of requested `type`, returned, specified as one of the pairs of filters listed here.

`type`DescriptionFilter Pair
`"d"`

Decomposition filters

`LoD` and `HiD`

`"r"`

Reconstruction filters

`LoR` and `HiR`

`"l"`

Lowpass filters

`LoD` and `LoR`

`"h"`

Highpass filters

`HiD` and `HiR`

References

[1] Daubechies, Ingrid. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics 61. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

[2] Mallat, S.G. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 11, no. 7 (July 1989): 674–93. https://doi.org/10.1109/34.192463.

Version History

Introduced before R2006a