idwtper (Wavelet Toolbox)

Single-level inverse discrete 1-D wavelet transform (periodized).

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

Description

idwtper is a one-dimensional wavelet analysis function.

X = idwtper(cA,cD,'wname') returns the single-level reconstructed approximation coefficients vector X based on approximation and detail vectors cA and cD at a given level, using the periodized inverse wavelet transform. 'wname' is a string containing the wavelet name (see wfilters).

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

For X = idwtper(cA,cD,Lo_R,Hi_R):

Lo_R is the reconstruction low-pass filter.

Hi_R is the reconstruction high-pass filter.

If la = length(cA) = length(cD) then length(X) = 2*la.

For X = idwtper(cA,cD,'wname',L) or X = idwtper(cA,cD,Lo_R,Hi_R,L), L is the length of the result.

idwtper is the inverse function of dwtper in the sense that the abstract statement idwtper(dwtper(X,'wname'),'wname') gets back to X.

Examples

% Set initial signal and get filters.
x = sin(0.3*[1:300]); lx = length(x)
lx =
    300

w = 'db9'; 
[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters(w);

% DWT with zero-padding signal extension.
[cazp,cdzp] = dwt(x,w);

% The transform uses some extra coefficients, 
% at most 2 if lx is odd. 
lxtzp = 2*length(cazp)
lxtzp =
    316

% Reconstruction. 
xzp = idwt(cazp,cdzp,w,lx); 

% Error with zero-padding. 
errzp = max(abs(x-xzp))
errzp =
    7.3231e-12

% Periodized DWT. 
[cap,cdp] = dwtper(x,w);

% The transform uses a minimum of extra coefficients. 
lxtp = 2*length(cap)
lxtp =
    300

% Reconstruction. 
xp = idwtper(cap,cdp,w,lx);

% Error with periodized DWT. 
errp = max(abs(x-xp))
errp =
    1.4588e-11

Note: In general, the following abstract statement is not true: idwtper(dwt(X,'wname'),'wname') = X .