idwt (Wavelet Toolbox)

idwt	Examples See Also

Single-level inverse discrete 1-D wavelet transform.

Syntax

X = idwt(cA,cD,'wname')
X = idwt(cA,cD,Lo_R,Hi_R)
X = idwt(cA,cD,'wname',L)
X = idwt(cA,cD,Lo_R,Hi_R,L)

Description

The idwt command performs a single-level one-dimensional wavelet reconstruction with respect to either a particular wavelet ('wname', see wfilters) or particular wavelet reconstruction filters (Lo_R and Hi_R) you specify.

X = idwt(cA,cD,'wname') returns the single-level reconstructed approximation coefficients vector X based on approximation and detail coefficients vectors cA and cD, and using the wavelet 'wname'.

X = idwt(cA,cD,Lo_R,Hi_R)reconstructs as above using filters you specify:

Lo_R is the reconstruction low-pass filter
Hi_R is the reconstruction high-pass filter

Lo_R and Hi_R must be the same length. If la is the length of cA (which also equals the length of cD) and lf is the length of the filters Lo_R and Hi_R, then length(X) = 2*la-lf+2.

X = idwt(cA,cD,'wname',L) or X = idwt(cA,cD,Lo_R,Hi_R,L), returns the length-L central portion of the result obtained using idwt(cA,cD,'wname'). L must be less than 2*la-lf+2.

Examples

idwt is the inverse function of dwt in the sense that the abstract statement
idwt(dwt(X,'wname'),'wname') gives back X. Consider this example.

% Construct elementary one-dimensional signal s. 
    randn('seed',531316785) 
    s = 2 + kron(ones(1,8),[1 -1]) + ... 
        ((1:16).^2)/32 + 0.2*randn(1,16);

% Perform single-level dwt of s using db2.
    [ca1,cd1] = dwt(s,'db2'); 
    subplot(221); plot(ca1); 
    title('Approx. coef. for db2'); 
    subplot(222); plot(cd1); 
    title('Detail coef. for db2');

% Perform single-level inverse discrete wavelet transform, 
% illustrating that idwt is the inverse function of dwt. 
    ss = idwt(ca1,cd1,'db2'); 
    err = norm(s-ss);     % Check reconstruction. 
    subplot(212); plot([s;ss]'); 
    title('Original and reconstructed signals'); 
    xlabel(['Error norm = ',num2str(err)])

% For a given wavelet, compute the two associated
% reconstruction filters and inverse transform using 
% the filters directly.
    [Lo_R,Hi_R] = wfilters('db2','r'); 
    ss = idwt(ca1,cd1,Lo_R,Hi_R);

Algorithm

Starting from the approximation and detail coefficients at level j, cA_j and cD_j, the inverse discrete wavelet transform reconstructs cA_j-1, inverting the decomposition step by inserting zeros and convolving the results with the reconstruction filters.