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# appcoef

1-D approximation coefficients

## Syntax

A = appcoef(C,L,'wname',N)
A = appcoef(C,L,'wname')
A = appcoef(C,L,Lo_R,Hi_R)
A = appcoef(C,L,Lo_R,Hi_R,N)

## Description

appcoef is a one-dimensional wavelet analysis function.

appcoef computes the approximation coefficients of a one-dimensional signal.

A = appcoef(C,L,'wname',N) computes the approximation coefficients at level N using the wavelet decomposition structure [C,L] (see wavedec for more information).

'wname' is a string containing the wavelet name. Level N must be an integer such that 0 N length(L)-2.

A = appcoef(C,L,'wname') extracts the approximation coefficients at the last level: length(L)-2.

Instead of giving the wavelet name, you can give the filters.

For A = appcoef(C,L,Lo_R,Hi_R) or A = appcoef(C,L,Lo_R,Hi_R,N), Lo_R is the reconstruction low-pass filter and Hi_R is the reconstruction high-pass filter (see wfilters for more information).

## Level 3 Approximation Coefficients

This example shows how to extract the level 3 approximation coefficients.

Load the signal consisting of electricity usage data.

```load leleccum;
sig = leleccum(1:3920);
```

Obtain the DWT down to level 5 with the 'sym4' wavelet.

```[C,L] = wavedec(sig,5,'sym4');
```

Extract the level-3 approximation coefficients. Plot the original signal and the approximation coefficients.

```Lev = 3;
a3 = appcoef(C,L,'sym4',Lev);
subplot(2,1,1)
plot(sig); title('Original Signal');
subplot(2,1,2)
plot(a3); title('Level-3 Approximation Coefficients');
```

You can substitute any value from 1 to 5 for Lev to obtain the approximation coefficients for the corresponding level.

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### 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.