waverec

Multilevel 1-D discrete wavelet transform reconstruction

Syntax

x = waverec(c,l,wname)

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

x = waverec(___,Mode=extmode)

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. For more information, 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.

x = waverec(___,Mode=extmode) uses the specified discrete wavelet transform (DWT) extension mode extmode. This syntax can be used with either of the previous syntaxes.

Examples

Multilevel 1-D Wavelet Reconstruction

Load an ECG signal.

load wecg

Perform a level 3 wavelet decomposition of the signal using the db6 wavelet. Specify the asym extension mode.

[c,l] = wavedec(wecg,3,"db6",Mode="asym");

Reconstruct the signal using the wavelet decomposition structure. To ensure perfect reconstruction, specify the same extension mode used to obtain the decomposition.

x = waverec(c,l,"db6",Mode="asym");

Verify perfect reconstruction.

err = norm(wecg-x)

err = 
2.5198e-11

Input Arguments

c — Wavelet decomposition

vector

Wavelet decomposition, specified as a vector. The vector contains the wavelet coefficients. For more information, 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 — Wavelet

character vector | string scalar

Wavelet, specified as a character vector or string scalar. wname must specify the same wavelet used with wavedec to obtain the decomposition [c,l].

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. For perfect reconstruction, LoR and HiR must be the reconstruction filters associated with the same wavelet used to obtain the wavelet decomposition c and l. For more information, see wfilters.

Data Types: single | double

extmode — Extension mode

"zpd" | "sp0" | "spd" | ...

Since R2023b

Extension mode to use for the inverse DWT, specified as:

mode	DWT Extension Mode
"zpd"	Zero extension
"sp0"	Smooth extension of order 0
"spd" (or "sp1")	Smooth extension of order 1
"sym" or "symh"	Symmetric extension (half point): boundary value symmetric replication
"symw"	Symmetric extension (whole point): boundary value symmetric replication
"asym" or "asymh"	Antisymmetric extension (half point): boundary value antisymmetric replication
"asymw"	Antisymmetric extension (whole point): boundary value antisymmetric replication
"ppd", "per"	Periodized extension If the signal length is odd and mode is "per", an extra sample equal to the last value is added to the right and the extension is performed in "ppd" mode. If the signal length is even, "per" is equivalent to "ppd".

The global variable managed by dwtmode specifies the default extension mode. For perfect reconstruction, use the same extension mode that was used to obtain c and l from wavedec.

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 11, no. 7 (July 1989): 674–93. https://doi.org/10.1109/34.192463.

[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:

• waverec supports only the "sym" and "per" extension modes.

• By default, waverec uses the "sym" extension mode unless the extension mode is "per". For more information, see wavedec.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023b: Specify DWT Extension Mode

The waverec function can use a DWT extension mode you specify which is different from the default global extension mode.