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Multilevel 1-D discrete wavelet transform reconstruction



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.


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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 = 1.0089e-09

Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

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.

Data Types: single | double

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


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.

Data Types: single | double

Output Arguments

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Reconstructed signal, returned as a vector.


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

See Also

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