powerbw

DWT filter bank power bandwidth

Syntax

bwtable = powerbw(fb)

Description

bwtable = powerbw(fb) returns a MATLAB^® table bwtable containing the theoretical and measured bandwidths of the discrete wavelet transform (DWT) filter bank fb. The table contains the following variables by level:

• DWT frequency bands

• Measured wavelet and scaling filter 3 dB bandwidths

• Proportions of the total energy in the reported bands

Examples

DWT Filter Bank Power Bandwidth

Obtain the 3 dB bandwidths of a level-4 discrete wavelet transform with the Fejér-Korovkin fk18 wavelet. Obtain the frequency responses of the wavelets. Plot the one-sided frequency responses for the wavelet filters.

fb = dwtfilterbank('Wavelet','fk18','Level',4);
bw = powerbw(fb);
[psidft,f] = freqz(fb);
freqz(fb)

Choose the wavelet bandpass filter whose peak magnitude is equal to 2. Obtain the lower and upper bounds of the 3 dB bandwidth of the filter.

wv = 2;
wvBw = bw.Wavelet3dBBandwidth(wv,:);

Plot the magnitude frequency response of the filter and the 3 dB limits. Since the frequency response has a maximum value equal to 2, confirm the lower and upper frequency bounds intersect the frequency response at $$\sqrt{2}$$.

filLength = size(psidft,2);
plot(f(filLength/2+1:end),abs(psidft(wv,filLength/2+1:end)))
hold on
plot([wvBw(1) wvBw(1)],[0 2],'r')
plot([wvBw(2) wvBw(2)],[0 2],'r')
grid on
title(['Proportion of Wavelet Power in 3 dB Band: ',num2str(bw.WaveletPowerIn3dBBand(wv))])
xlabel('Normalized Frequency (cycles/sample)')
ylabel('Magnitude')

Input Arguments

fb — Discrete wavelet transform filter bank

dwtfilterbank object

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

Output Arguments

bwtable — Theoretical and measured bandwidths

table

Theoretical and measured bandwidths of the DWT filter bank fb, returned as a MATLAB table. bwtable is L-by-8, where L is the wavelet transform level of the filter bank. Levels are ordered by decreasing resolution. bwtable has the following eight variables:

Level — Level of DWT decomposition

positive integer

Level of DWT decomposition, returned as a positive integer.

DWTBand — Theoretical DWT frequency bands

two-element real-valued vector

Theoretical DWT frequency bands by level, returned as a two-element real-valued vector.

Wavelet3dBBandwidth — Measured wavelet 3 dB bandwidths

two-element real-valued vector

Measured wavelet 3 dB bandwidths by level, returned as a two-element real-valued vector.

Scaling3dBBandwidth — Measured scaling filter 3 dB bandwidths

two-element real-valued vector

Measured scaling filter 3 dB bandwidths by level, returned as a two-element real-valued vector.

WaveletPowerIn3dBBand — Proportion of total wavelet power

positive scalar

Proportion of total wavelet power in the measured 3 dB band by level, returned as a positive scalar.

ScalingPowerIn3dBBand — Proportion of total scaling filter power

positive scalar

Proportion of total scaling filter power in the measured 3 dB band by level, returned as a positive scalar.

WaveletPowerInDWTBand — Proportion of total wavelet power

positive scalar

Proportion of total wavelet power in the theoretical DWT band by level, returned as a positive scalar.

ScalingPowerInDWTBand — Proportion of total scaling filter power

positive scalar

Proportion of total scaling filter power in the theoretical DWT band by level, returned as a positive scalar.