# idwt

Single-level 1-D inverse discrete wavelet transform

## Syntax

## Description

returns the single-level one-dimensional wavelet reconstruction
`x`

= idwt(`cA`

,`cD`

,`wname`

)`x`

based on the approximation and detail coefficients
`cA`

and `cD`

, respectively, using the
wavelet specified by `wname`

. For more information, see
`dwt`

.

Let `la`

be the length of `cA`

(which also
equals the length of `cD`

), and `lf`

the
length of the reconstruction filters associated with `wname`

(see `wfilters`

). If the DWT
extension mode is set to periodization, then the length of
`x`

is equal to 2`la`

. Otherwise, the length of `x`

is equal to 2`la`

- 2`lf`

+2. For more information, see `dwtmode`

.

returns the length-`x`

= idwt(___,`l`

)`l`

central portion of the reconstruction.
This argument can be added to any of the previous input syntaxes

## Examples

## Input Arguments

## Algorithms

Starting from the approximation and detail coefficients at level *j*,
*cA**j* and
*cD _{j}*, the inverse discrete wavelet
transform reconstructs

*cA*, inverting the decomposition step by inserting zeros and convolving the results with the reconstruction filters.

_{j−1}where

— Insert zeros at even-indexed elements

— Convolve with filter

*X*— Take the central part of

*U*with the convenient length

## References

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

[2] Mallat, S. G. “A Theory
for Multiresolution Signal Decomposition: The Wavelet Representation.”
*IEEE Transactions on Pattern Analysis and Machine Intelligence*.
Vol. 11, Issue 7, July 1989, pp. 674–693.

[3] Meyer, Y. *Wavelets
and Operators*. Translated by D. H. Salinger. Cambridge, UK: Cambridge
University Press, 1995.

## Extended Capabilities

## Version History

**Introduced before R2006a**