appcoef

1-D approximation coefficients

Syntax

A = appcoef(c,l,wname)

A = appcoef(c,l,LoR,HiR)

A = appcoef(___,N)

A = appcoef(___,Mode=extmode)

Description

A = appcoef(c,l,wname) returns the approximation coefficients at the coarsest scale using the wavelet decomposition structure [c,l] of a 1-D signal and the wavelet specified by wname. For more information, see wavedec.

A = appcoef(c,l,LoR,HiR) uses the lowpass reconstruction filter LoR and highpass reconstruction filter HiR.

A = appcoef(___,N) returns the approximation coefficients at level N. If [c,l] is the M-level wavelet decomposition structure of a 1-D signal, then 0 ≤ N ≤ M = length(l)-2.

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

Examples

Extract Approximation Coefficients

Load the signal consisting of electricity usage data.

load leleccum

Obtain the DWT down to level 5 using the sym4 wavelet.

[c,l] = wavedec(leleccum,5,"sym4");

Extract the approximation coefficients at the coarsest scale. Plot the original signal and the approximation coefficients.

lev = 5;
a3 = appcoef(c,l,"sym4",lev);
tiledlayout(2,1)
nexttile
plot(leleccum)
axis tight
title("Original Signal")
nexttile
plot(a3)
axis tight
title("Level "+num2str(lev)+" Approximation Coefficients")

Input Arguments

c — Wavelet decomposition vector

vector

Wavelet decomposition vector of a 1-D signal, specified as a vector. For more information, see wavedec.

Example: [c,l] = wavedec(randn(1,256),4,"coif1") returns the wavelet decomposition of a vector down to level 4.

Data Types: single | double
Complex Number Support: Yes

l — Bookkeeping vector

vector of positive integers

Bookkeeping vector of the wavelet decomposition of a 1-D signal, specified as a vector of positive integers. The bookkeeping vector is used to parse the coefficients in the wavelet decomposition vector c by level. For more information, see wavedec.

Data Types: single | double

wname — Wavelet

character vector | string scalar

Wavelet used to generate the wavelet decomposition [c,l], specified as a character vector or string scalar. The wavelet is from one of the following wavelet families: Best-localized Daubechies, Beylkin, Coiflets, Daubechies, Fejér-Korovkin, Haar, Han linear-phase moments, Morris minimum-bandwidth, Symlets, Vaidyanathan, Discrete Meyer, Biorthogonal, and Reverse Biorthogonal. See wavemngr for the wavelets available in each family.

Example: "db4"

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

N — Approximation coefficients level

positive integer

Approximation coefficients level, specified as a positive integer. If [c,l] is the M-level wavelet decomposition structure of a 1-D signal, then 0 ≤ N ≤ M.

extmode — Extension mode

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

Since R2023b

Extension mode to use for the inverse discrete wavelet transform, specified as:

extmode	DWT Extension Mode
"zpd"	Zero padding
"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" reduces to "ppd". This rule also applies to images.

The global variable managed by dwtmode specifies the default extension mode.

Output Arguments

A — Approximation coefficients

vector

Approximation coefficients at level N, returned as a vector.

Algorithms

The input vectors c and l contain all the information about the signal decomposition.

Let NMAX = length(l)-2; then c = [A(NMAX) D(NMAX) ... D(1)] where A and the D are vectors. If N = NMAX, then a simple extraction is done; otherwise, appcoef computes iteratively the approximation coefficients using the inverse wavelet transform.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• Variable-size data support must be enabled.

• The input wname must be constant.

GPU Arrays

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

The appcoef function supports GPU array input with these usage notes and limitations:

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

• By default, appcoef uses the "sym" extension mode unless the extension mode is "per".

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

Version History

Introduced before R2006a

R2023b: Specify DWT Extension Mode

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