Inverse continuous wavelet transform (CWT) for linearly spaced scales
xrec = icwtlin(cwtstruct)
xrec = icwtlin(wav,meanSIG,cfs,scales,dt)
xrec = icwtin(...,'plot'
)
xrec = icwtlin (...,'signal'
,SIG,'plot'
)
xrec = icwtlin(...,Name,Value)
returns
the inverse continuous wavelet transform (CWT) of the CWT coefficients obtained at linearlyspaced scales.xrec
= icwtlin(cwtstruct
)
Note:
To use

returns
the inverse CWT of the coefficients in xrec
= icwtlin(wav
,meanSIG
,cfs
,scales
,dt
)cfs
. The inverse CWT is obtained using the wavelet wav
,
the linearly spaced scales scales
,
the sampling period dt
, and the mean signal value meanSig
.
plots
the reconstructed signal xrec
= icwtin(...,'plot'
)xrec
along with the
CWT coefficients and CWT moduli. If the analyzing wavelet is complexvalued,
the plot includes the real and imaginary parts of the CWT coefficients.
places
a radio button in the bottomleft corner of the
plot. Enabling the radio button superimposes the plot of the input
signal xrec
= icwtlin (...,'signal'
,SIG
,'plot'
)SIG
on the plot of the reconstructed signal. SIG
can
be a structure array, a cell array, or a vector. If SIG
is
a structure array, there must be two fields: val
and period
.
The val
field contains the signal and the period
field
contains the sampling period. If SIG
is
a cell array, SIG{1}
contains the signal and SIG{2}
is
the sampling period.
returns
the inverse CWT transform with additional options specified by one
or more xrec
= icwtlin(...,Name,Value
)Name,Value
pair arguments.

A structure array that is the output of
If you create Using


Vector of scales to use in the signal reconstruction. Specifying a subset of scales results in a scalelocalized approximation of the analyzed signal. 

Reconstructed signal. Signal approximation based on the input CWT coefficient matrix, analyzing wavelet, selected scales, and sampling period. The purpose of the CWT inversion algorithm is not to produce a perfect reconstruction of the input signal. The inversion preserves time and scalelocalized features in the reconstructed signal. The amplitude scaling in the reconstructed signal, however, can be significantly different. This difference in scaling can occur whether or not you use all the CWT coefficients in the inversion. 
Compute the inverse CWT of a sum of sine waves with disjoint support.
% Define the signal N = 100; t = linspace(0,1,N); Y = sin(8*pi*t).*(t<=0.5) + sin(16*pi*t).*(t>0.5) ; % Define parameters before analysis dt = 0.001; maxsca = 1; s0 = 2*dt; ds = 2*dt; scales = s0:ds:maxsca; wname = 'morl'; SIG = {Y,dt}; WAV = {wname,[]}; % Compute the CWT using cwtft with linear scales cwtS = cwtft(SIG,'scales',scales,'wavelet',WAV); % Compute inverse CWT using linear scales Yrec = icwtlin(cwtS,'Signal',Y,'plot');
Reconstruct an approximation to a noisy Doppler signal based on thresholded coefficients. Use the universal threshold. Assume the sampling period is 0.05 seconds.
load noisdopp; Y = noisdopp; N = length(Y); % Define parameters before analysis % Assume sampling period is 0.05 dt = 0.05; maxsca = 100; s0 = 2*dt; ds = 4*dt; scales = s0:ds:maxsca; wname = 'morl'; SIG = {Y,dt}; WAV = {wname,[]}; % Compute CWT cwtS = cwtft(SIG,'scales',scales,'wavelet',WAV,'plot'); % Select subset of coefficients cwtS1 = cwtS; Hfreq = cwtS.cfs(1:10,:); % Set threshold thr = sqrt(2*log(N))*median(abs(Hfreq(:)))/0.6745; newCFS = cwtS.cfs; % Set coefficients smaller than threshold in absolute value to 0 newCFS(abs(newCFS)<thr) = 0; cwtS1.cfs = newCFS; % Reconstruction from the modified structure YRDen = icwtlin(cwtS1,'signal',Y,'plot');
Enable the Reconstructed Signal On/Off radio button in the bottomleft corner.
[1] Daubechies, I. Ten Lectures on Wavelets, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 1992.
[2] Farge, M. "Wavelet Transforms and Their Application to Turbulence", Ann. Rev. Fluid. Mech., 1992, 24, 395–457.
[3] Mallat, S. A Wavelet Tour of Signal Processing, San Diego, CA: Academic Press, 1998.
[4] Sun,W. "Convergence of Morlet's Reconstruction Formula", preprint, 2010.
[5] Torrence, C. and G.P. Compo. "A Practical Guide to Wavelet Analysis", Bull. Am. Meteorol. Soc., 79, 61–78, 1998.