wfilters

Wavelet filters

Syntax

[LoD,HiD,LoR,HiR] = wfilters(wname)

[F1,F2] = wfilters(wname,type)

Description

[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

Compute Four Filters

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

wname — Name of orthogonal or biorthogonal wavelet

"haar" | "db1" | "db2" | "coif1" | "coif2" | ...

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

Wavelet Family	Type	Wavelets
Daubechies	Orthogonal	"db1" or "haar", "db2", ..., "db10", ..., "db45"
Coiflets	Orthogonal	"coif1", ..., "coif5"
Symlets	Orthogonal	"sym2", ..., "sym8", ...,"sym45"
Fejér-Korovkin filters	Orthogonal	"fk4", "fk6", "fk8", "fk14", "fk22"
Best-localized Daubechies	Orthogonal	"bl7", "bl9", "bl10"
Morris minimum-bandwidth	Orthogonal	"mb4.2", "mb8.2", "mb8.3", "mb8.4" "mb10.3", "mb12.3", "mb14.3", "mb16.3" "mb18.3", "mb24.3", "mb32.3"
Beylkin	Orthogonal	"beyl"
Vaidyanathan	Orthogonal	"vaid"
Han linear-phase moments	Orthogonal	"han2.3", "han3.3", "han4.5", "han5.5"
Discrete Meyer	Orthogonal	"dmey"
BiorSplines	Biorthogonal	"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"
ReverseBior	Biorthogonal	"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"

Note

For N equal to 1, 2, and 3, the dbN and symN wavelets are identical.

type — Type of filter pair

"d" | "r" | "l" | "h"

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

LoD — Decomposition lowpass filter

real-valued vector

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

HiD — Decomposition highpass filter

real-valued vector

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

LoR — Reconstruction lowpass filter

real-valued vector

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

HiR — Reconstruction highpass filter

real-valued vector

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

F1, F2 — Filter pair

real-valued vectors

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

type	Description	Filter 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