waverec

Multilevel 1-D discrete wavelet transform reconstruction

Syntax

x = waverec(c,l,wname)

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

Description

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

Multilevel 1-D Wavelet Reconstruction

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

c — Wavelet decomposition

vector

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

l — Bookkeeping vector

vector

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

wname — Analyzing wavelet

character vector | string scalar

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.

LoR,HiR — Wavelet reconstruction filters

even-length real-valued vectors

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

x — Reconstructed signal

vector

Reconstructed signal, returned as a vector.

References

[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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The input wname must be constant.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The input wname must be constant.

• For optimized GPU code generation, specify the bookkeeping vector l as a compile-time constant.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• Only 'sym' and 'per' extension modes are supported. See dwtmode.

Version History

Introduced before R2006a