IPQMFDESIGN Function (PV-WAVE Extreme Advantage)

Image Processing Toolkit User Guide > Reference A–I > IPQMFDESIGN Function (PV-WAVE Extreme Advantage)

Generates one of several quadrature mirror filters for use with the IPWAVELET function. A four-coefficient Daubechies wavelet filter is returned by default.

Usage

result = IPQMFDESIGN( )

Input Parameters

None.

Returned Value

result—A filter object containing a 1D QMF filter as the kernel for use with the IPWAVELET function. (See IPREAD_FILTER Function (PV-WAVE Extreme Advantage) for more information on the filter object format.)

Keywords

Only one of the following keywords may be set at a time:

Biorthogonal—A one or two-digit number: the first number specifies the number of vanishing moments in the reconstruction scaling function, and the second number (if present) specifies the number of vanishing moments in the decomposition scaling function for a one moment symmetric/antisymmetric, two moment symmetric/symmetric or three moment symmetric/antisymmetric biorthongal wavelet filter. Valid values are:

Symmetric/Antisymmetric, one moment: 1, 13, 15

Symmetric/Symmetric, two moments: 2, 22, 24, 26, 28

Symmetric/Antisymmetric, three moments: 3, 31, 33, 35, 37, 39

Coifman—Specifies the number of coefficients in the Coifman wavelet filter. Valid numbers are 6, 12, 18, 24, 30.

Daubechies—Specifies the number of coefficients in the Daubechies wavelet filter. Valid numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20. (Default: 4)

Discussion

A quadrature mirror filter H(z) is defined by the following equation:

|H(z)|2 + |H(–z)|2 = 1

IPQMFDESIGN generates three different types of wavelet filters as specified by using one of the following keywords: Daubechies, Coifman, and Biorthogonal. If none of these keywords are specified, the default is Daubechies = 4.

note	The Daubechies, Coifman, and Biorthogonal keywords can’t be used together in the same calling sequence.

Example

; Generate a 6-coefficient Daubechies wavelet filter.

image = DIST(256)

daub6 = IPQMFDESIGN(Daubechies = 6)

; Generate a 12-coefficient Coifman wavelet filter.

coif12 = IPQMFDESIGN(Coifman = 12)

; Generate a 1, 3 Biorthogonal wavelet filter.

bior13 = IPQMFDESIGN(Biorthogonal = 13)

; Apply the wavelet transform to an image using each of

; the different filters, separately.

wvlt_daub6 = IPWAVELET(image, daub6, -1)

wvlt_coif12 = IPWAVELET(image, coif12, -1)

wvlt_bior13 = IPWAVELET(image, bior13, -1)

; Display the results.

Window, 0

TVSCL, wvlt_daub6

Window, 1

TVSCL, wvlt_coif12

Window, 2

TVSCL, wvlt_boir13