# waverec

1-D wavelet reconstruction

## Syntax

``x = waverec(c,l,wname)``
``x = waverec(c,l,LoR,HiR)``

## Description

example

````x = waverec(c,l,wname)` reconstructs the 1-D signal `x` based on the multilevel wavelet decomposition structure [`c`,`l`] and the wavelet specified by `wname`. See `wavedec`.Note `x = waverec(c,l,wname)` is equivalent to ```x = appcoef(c,l,wname,0)```.```
````x = waverec(c,l,LoR,HiR)` reconstructs the signal using the specified lowpass and highpass wavelet reconstruction filters `LoR` and `HiR`, respectively.```

## Examples

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Load a signal. Perform a level 3 wavelet decomposition of the signal using the `db6` wavelet.

```load leleccum wv = 'db6'; [c,l] = wavedec(leleccum,3,wv);```

Reconstruct the signal using the wavelet decomposition structure.

`x = waverec(c,l,wv);`

Check for perfect reconstruction.

`err = norm(leleccum-x)`
```err = 1.1137e-09 ```

## Input Arguments

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Wavelet decomposition, specified as a real-valued vector. The vector contains the wavelet coefficients. The bookkeeping vector `l` contains the number of coefficients by level. See `wavedec`.

Bookkeeping vector, specified as a vector of positive integers. The bookkeeping vector is used to parse the coefficients in the wavelet decomposition `c` by level. See `wavedec`.

Analyzing wavelet, specified as a character vector or string scalar.

### Note

`waverec` supports only Type 1 (orthogonal) or Type 2 (biorthogonal) wavelets. See `wfilters` for a list of orthogonal and biorthogonal wavelets.

Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. `LoR` is the lowpass reconstruction filter, and `HiR` is the highpass reconstruction filter. The lengths of `LoR` and `HiR` must be equal. See `wfilters` for additional information.

## Output Arguments

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Reconstructed signal, returned as a real-valued vector.

 Daubechies, I. Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: SIAM Ed, 1992.

 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.

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

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