upcoef

Direct reconstruction from 1-D wavelet coefficients

Syntax

y = upcoef(o,x,wname)

y = upcoef(o,x,LoR,HiR)

y = upcoef(o,x,wname,n)

y = upcoef(o,x,LoR,HiR,n)

y = upcoef(o,x,wname,n,l)

y = upcoef(o,x,LoR,HiR,n,l)

Description

upcoef is a one-dimensional wavelet analysis function.

y = upcoef(o,x,wname) returns the 1-step reconstructed coefficients of type o of the vector x using the wavelet specified by wname.

y = upcoef(o,x,LoR,HiR) uses the specified lowpass and highpass reconstruction filters LoR and HiR, respectively.

y = upcoef(o,x,wname,n) returns the n-step reconstructed coefficients.

y = upcoef(o,x,LoR,HiR,n) uses the specified lowpass and highpass reconstruction filters LoR and HiR, respectively.

y = upcoef(o,x,wname,n,l) returns the length-l central portion of the n-step reconstruction.

y = upcoef(o,x,LoR,HiR,n,l) uses the specified lowpass and highpass reconstruction filters LoR and HiR, respectively.

Examples

Reconstruct Wavelet Coefficients

Save the current extension mode, then set the extension mode to zero-padding.

origMode = dwtmode('status','nodisp');
dwtmode('zpd','nodisp')

Reconstruct approximation signals, obtained from a single coefficient at levels 1 to 6. Use the db6 wavelet.

cfs = 1;
essup = 10; % Essential support of the scaling filter db6. 

for i=1:6 
    % Reconstruct at the top level an approximation 
    % which is equal to zero except at level i where only 
    % one coefficient is equal to 1. 
    rec = upcoef("a",cfs,"db6",i);

    % essup is the essential support of the 
    % reconstructed signal.
    % rec(j) is very small when j is ≥ essup. 
    subplot(6,1,i)
    plot(rec(1:essup))
    xlim([1 325])
    if i<3
        ylim([-1 1])
    elseif i<5
        ylim([-0.5 0.5])
    else
        ylim([-0.2 0.2])
    end
    essup = essup*2; 
end 
subplot(6,1,1) 
title(["Approximation Signals Obtained From a Single " ...
    "Coefficient at Levels 1 to 6"])

The same can be done for details. Reconstruct details signals, obtained from a single coefficient at levels 1 to 6. Use the db6 wavelet.

cfs = [1]; 
mi = 12; ma = 30;   % Essential support of 
                    % the wavelet filter db6. 
                    
rec = upcoef("d",cfs,"db6",1); 
figure
subplot(6,1,1)
plot(rec(3:12))
axis tight
ylim([-1 1])
for i=2:6 
    % Reconstruct at top level a single detail 
    % coefficient at level i. 
    rec = upcoef("d",cfs,"db6",i);
    subplot(6,1,i)
    plot(rec(mi*2^(i-2):ma*2^(i-2)))
    axis tight
    if i<3
        ylim([-1 1])
    elseif i<5
        ylim([-0.5 0.5])
    else
        ylim([-0.2 0.2])
    end
end 
subplot(6,1,1) 
title(["Detail Signals Obtained From a Single " ... 
    "Coefficient at Levels 1 to 6"])

Restore the extension mode to the original setting.

dwtmode(origMode,'nodisp')

Input Arguments

o — Type of reconstructed coefficients

"a" | "d"

Type of reconstructed coefficients, specified as "a" or "d", for approximation or details coefficients, respectively.

Data Types: string

x — Signal

vector

Signal, specified as a vector.

Data Types: double

wname — Wavelet

character vector | string scalar

Wavelet, specified as a character vector or string scalar. The wavelet must be recognized by wavemngr. See wfilters for the wavelets available in each family.

Data Types: char | string

n — Number of reconstruction steps

1 (default) | positive integer

Number of reconstruction steps, specified as a positive integer.

Data Types: double

l — Length of central portion

0 (default) | nonnegative integer

Length of central portion of reconstruction to return, specified as a nonnegative integer. If l = 0, upcoef returns the entire reconstruction.

Data Types: double

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: double

Output Arguments

y — Reconstructed coefficients

vector

Reconstruction coefficients of x, returned as a vector.

Data Types: double

Algorithms

upcoef is equivalent to an n-time repeated use of the inverse wavelet transform.

Version History

Introduced before R2006a