# orthfilt

Orthogonal wavelet filters

## Description

## Examples

## Input Arguments

## Output Arguments

## Algorithms

For an orthogonal wavelet in the multiresolution framework, start with the scaling function ϕ and the wavelet function ψ. One of the fundamental relations is the twin-scale relation:

$$\frac{1}{2}\varphi \left(\frac{x}{2}\right)={\displaystyle \sum _{n\in Z}{w}_{n}}\varphi (x-n)$$

All the filters used in the `dwt`

and `idwt`

functions are intimately related to the sequence $${({w}_{n})}_{n\in Z}$$. If ϕ is compactly supported, the sequence
(*w _{n}*) is finite and can be viewed as an
FIR filter. The scaling filter

`W`

is a lowpass FIR filter of length
2N, with the sum 1, and with the norm of 1/√2.For example, for a `db3`

scaling filter,

w = dbwavf("db3") w = 0.2352 0.5706 0.3252 -0.0955 -0.0604 0.0249 sum(w) = 1.000 norm(w) = 0.7071

Define four FIR filters from filter `W`

of length 2N and norm
1.

The function computes the four filters using the following scheme.

`HiR`

and `LoR`

are quadrature mirror filters:
`HiR(k) = (-1)`

^{k}```
LoR(2N + 1 -
k)
```

, for `k = 1, 2, … , 2N`

. Because `wrev`

reverses vectors, `HiD`

and
`LoD`

are also quadrature mirror filters.

## References

[1] Daubechies, Ingrid.
*Ten Lectures on Wavelets*. CBMS-NSF Regional Conference Series
in Applied Mathematics 61. Philadelphia, Pa: Society for Industrial and Applied
Mathematics, 1992.

## Extended Capabilities

## Version History

**Introduced before R2006a**