# powerbw

CWT filter bank 3 dB bandwidths

## Description

example

bw = powerbw(fb) returns 3 dB (half-power) bandwidths for the wavelet filters in the filter bank fb. bw is a Ns-by-4 MATLAB® table, where Ns is the number of wavelet bandpass frequencies (equal to the number of scales). For every filter in fb, the table contains the corresponding bandpass frequency, the 3 dB bandwidth, and the lower frequency and upper frequency limits of the 3 dB bandwidth.

The 3 dB bandwidth limits mark where the filter power is half its peak value. The magnitude frequency response at the limits is equal to 1/√2 times the peak magnitude. Since the passbands in fb are normalized with peak magnitudes approximately equal to 2, the magnitude frequency response at each limit is approximately equal to 2/√2. The 3 dB bandwidth is also known as the half-power bandwidth because $20{\mathrm{log}}_{10}\frac{1}{\sqrt{2}}\approx -3.$

## Examples

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Create a CWT filter bank.

fb = cwtfilterbank;

Obtain the 3 dB (half-power) bandwidths of the filter bank. Obtain the frequency responses of the wavelets.

bw = powerbw(fb);
[psidft,f] = freqz(fb);

Choose a wavelet bandpass filter from the filter bank. Extract from the table bw the 3 dB limits of the bandpass filter.

wv = 5;
frq = bw.Frequencies(wv);
lfb = bw.LowFrequencyBorder(wv);
hfb = bw.HighFrequencyBorder(wv);

Plot the frequency response and 3 dB limits. Since the frequency response is scaled to have a maximum value equal to 2, inspect the plot to confirm the lower and upper frequency borders intersect the frequency response at $\sqrt{2}$.

plot(f,psidft(wv,:))
grid on
hold on
plot([lfb lfb],[0 2],'r')
plot([hfb hfb],[0 2],'r')
xlabel('Normalized Frequency (cycles/sample)')
ylabel('Magnitude')
title(['Bandpass Frequency: ' num2str(frq) ' cycles/sample'])

## Input Arguments

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Continuous wavelet transform (CWT) filter bank, specified as a cwtfilterbank object.

## Output Arguments

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3 dB (half-power) bandwidths, returned as an Ns-by-4 table, where Ns is the number of wavelet bandpass frequencies (equal to the number of scales). The table has four variables:

Bandpass frequency, returned as a positive scalar (see centerFrequencies).

Data Types: double

Half-power bandwidth, returned as a positive scalar.

Data Types: double

Lower frequency edge of the 3 dB bandwidth, returned as a positive scalar.

Data Types: double

High frequency edge of the 3 dB bandwidth, returned as a positive scalar.

Data Types: double

Data Types: table

## Version History

Introduced in R2018a