framebounds

DWT filter bank frame bounds

Syntax

[a,b] = framebounds(fb)

Description

[a,b] = framebounds(fb) returns the frame bounds for the discrete wavelet transform (DWT) filter bank fb. For an orthogonal wavelet filter bank, the theoretical frame bounds a and b are equal to 1.

Examples

DWT Filter Bank Frame Bounds

Obtain the frame bounds for the orthogonal Daubechies db6 wavelet.

wv = 'db6';
fb = dwtfilterbank('Wavelet',wv)

fb = 
  dwtfilterbank with properties:

                Wavelet: 'db6'
           SignalLength: 1024
                  Level: 6
      SamplingFrequency: 1
             FilterType: 'Analysis'
    CustomWaveletFilter: []
    CustomScalingFilter: []

[a,b] = framebounds(fb)

a = 
1.0000

b = 
1.0000

The filter bank has the default filter type Analysis. Create a second filter bank using the same orthogonal wavelet but with the filter type Synthesis. Obtain the frame bounds of this filter bank, which are equal to the previous frame bounds.

fbSynthesis = dwtfilterbank('Wavelet',wv,'FilterType','Synthesis');
[a2,b2] = framebounds(fbSynthesis)

a2 = 
1.0000

b2 = 
1.0000

Create a filter bank for the biorthogonal bior3.9 wavelet. Obtain the frame bounds. The frame bounds are not equal to 1.

wv = 'bior3.9';
fbA = dwtfilterbank('Wavelet',wv);
[c,d] = framebounds(fbA)

c = 
0.6250

d = 
3.2982

Create a second filter bank using the same biorthogonal wavelet but with the filter type Synthesis. Obtain the frame bounds of this filter bank. Since the wavelet is biorthogonal, the frame bounds change.

fbASynthesis = dwtfilterbank('Wavelet',wv,'FilterType','Synthesis');
[c2,d2] = framebounds(fbASynthesis)

c2 = 
0.5502

d2 = 
2.0015

Input Arguments

fb — Discrete wavelet transform filter bank

dwtfilterbank object

Discrete wavelet transform (DWT) filter bank, specified as a dwtfilterbank object.

Output Arguments

a — Lower frame bound

positive real number

Lower frame bound of the DWT filter bank fb, returned as a positive real number.

b — Upper frame bound

positive real number

Upper frame bound of the DWT filter bank fb, returned as a positive real number.

Version History

Introduced in R2018a