# qfactor

DWT filter bank quality factor

## Syntax

``qf = qfactor(fb)``

## Description

example

````qf = qfactor(fb)` returns the quality factor for the discrete wavelet transform (DWT) filter bank `fb`.The quality factor `qf` is defined to be the geometric mean frequency of the lower and upper 3 dB bandwidth frequencies divided by the 3 dB bandwidth. For orthogonal wavelets, the measured quality factor approximates the theoretical value of √2.```

## Examples

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Obtain the quality factor for the Coiflet `coif4`. Since the wavelet is orthogonal, confirm the quality factor approximates the theoretical value of $\sqrt{2}$.

```wvOrth = 'coif4'; fb = dwtfilterbank('Wavelet',wvOrth); orthogAnalysis = qfactor(fb); abs(orthogAnalysis-sqrt(2))```
```ans = 5.7311e-11 ```

Compare with the quality factor for the biorthogonal wavelet `bior6.8`. Since the wavelet is biorthogonal, confirm the quality factor does not approximate $\sqrt{2}$.

```wvBior = 'bior6.8'; fb2 = dwtfilterbank('Wavelet',wvBior); biorthogAnalysis = qfactor(fb2); abs(biorthogAnalysis-sqrt(2))```
```ans = 0.1339 ```

By default, `fb` and `fb2` filter banks have the default filter type `Analysis`. Create two new filter banks of filter type `Synthesis` for the same wavelets. Compare the quality factors with the filter type `Analysis` filter banks. Confirm the quality factors using the orthogonal wavelet are equal.

```fb3 = dwtfilterbank('Wavelet',wvOrth,'FilterType','Synthesis'); fb4 = dwtfilterbank('Wavelet',wvBior,'FilterType','Synthesis'); orthogSynthesis = qfactor(fb3); abs(orthogSynthesis-sqrt(2))```
```ans = 5.7311e-11 ```
```biorthogSynthesis = qfactor(fb4); abs(biorthogSynthesis-sqrt(2))```
```ans = 0.1141 ```

## Input Arguments

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