Single-level discrete 1-D wavelet transform

`[cA,cD] = dwt(X,`

* 'wname'*)

[cA,cD] = dwt(X,Lo_D,Hi_D)

[cA,cD] = dwt(...,'mode',MODE)

The `dwt`

command performs
a single-level one-dimensional wavelet decomposition with respect
to either a particular wavelet (* 'wname'*,
see

`wfilters`

for more information)
or particular wavelet decomposition filters (`Lo_D`

and `Hi_D`

)
that you specify.`[cA,cD] = dwt(X,`

computes
the approximation coefficients vector * 'wname'*)

`cA`

and detail
coefficients vector `cD`

, obtained by a wavelet decomposition
of the vector `X`

. The string `'wname'`

`[cA,cD] = dwt(X,Lo_D,Hi_D)`

computes the
wavelet decomposition as above, given these filters as input:

`Lo_D`

is the decomposition low-pass filter.`Hi_D`

is the decomposition high-pass filter.

`Lo_D`

and `Hi_D`

must be
the same length.

Let `lx`

= the length of `X`

and `lf`

=
the length of the filters `Lo_D`

and `Hi_D`

;
then ```
length(cA) = length(cD)
= la
```

where `la = ceil(lx/2)`

, if the DWT
extension mode is set to periodization. For the other extension modes, ```
la
= floor(lx+lf-1)/2
```

.

For more information about the different Discrete Wavelet Transform
extension modes, see `dwtmode`

.

`[cA,cD] = dwt(...,'mode',MODE)`

computes
the wavelet decomposition with the extension mode `MODE`

that
you specify. `MODE`

is a string containing the desired
extension mode.

Example:

[cA,cD] = dwt(x,'db1','mode','sym');

Daubechies, I. (1992), *Ten lectures on wavelets*,
CBMS-NSF conference series in applied mathematics. SIAM Ed.

Mallat, S. (1989), "A theory for multiresolution signal
decomposition: the wavelet representation," *IEEE
Pattern Anal. and Machine Intell.*, vol. 11, no. 7, pp.
674–693.

Meyer, Y. (1990), *Ondelettes et opérateurs*,
Tome 1, Hermann Ed. (English translation: *Wavelets and operators*,
Cambridge Univ. Press. 1993.)

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