Main Content

Inverse continuous 1-D wavelet transform

inverts the
continuous wavelet transform (CWT) coefficient matrix `xrec`

= icwt(`wt`

)`wt`

using
default values. `icwt`

assumes that you obtained the CWT using
`cwt`

with the default analytic Morse
(3,60) wavelet. This wavelet has a symmetry of 3 and a time bandwidth of 60.
`icwt`

also assumes that the CWT uses default scales. If
`wt`

is a 2-D matrix, `icwt`

assumes that
the CWT was obtained from a real-valued signal. If `wt`

is a 3-D
matrix, `icwt`

assumes that the CWT was obtained from a
complex-valued signal. For a 3-D matrix, the first page of the
`wt`

is the CWT of the positive (counterclockwise) component
and the second page of `wt`

is the negative (clockwise)
component. The pages represent the analytic and anti-analytic parts of the CWT,
respectively.

returns
the inverse CWT with additional options specified by one or more `xrec`

= icwt(___,`Name,Value`

)`Name,Value`

pair
arguments.

[1] Lilly, J. M., and S. C. Olhede.
"Generalized Morse Wavelets as a Superfamily of Analytic Wavelets." *IEEE
Transactions on Signal Processing* 60, no. 11 (November 2012): 6036–41.
https://doi.org/10.1109/TSP.2012.2210890.

[2] Lilly, J.M., and S.C. Olhede.
"Higher-Order Properties of Analytic Wavelets." *IEEE Transactions on Signal
Processing* 57, no. 1 (January 2009): 146–60.
https://doi.org/10.1109/TSP.2008.2007607.

[3] Lilly, J. M. *jLab: A data
analysis package for Matlab*, version 1.6.2. 2016.
http://www.jmlilly.net/jmlsoft.html.

[4] Lilly, J. M., and J.-C.
Gascard. "Wavelet Ridge Diagnosis of Time-Varying Elliptical Signals with Application to
an Oceanic Eddy." *Nonlinear Processes in Geophysics* 13, no. 5
(September 14, 2006): 467–83. https://doi.org/10.5194/npg-13-467-2006.

[5] Duval-Destin, M., M. A.
Muschietti, and B. Torresani. “Continuous Wavelet Decompositions, Multiresolution, and
Contrast Analysis.” *SIAM Journal on Mathematical Analysis* 24, no.
3 (May 1993): 739–55. https://doi.org/10.1137/0524045.

[6] Daubechies, Ingrid.
*Ten Lectures on Wavelets*. CBMS-NSF Regional Conference Series
in Applied Mathematics 61. Philadelphia, Pa: Society for Industrial and Applied
Mathematics, 1992.

[7] Torrence, Christopher, and
Gilbert P. Compo. “A Practical Guide to Wavelet Analysis.” *Bulletin of the
American Meteorological Society* 79, no. 1 (January 1, 1998): 61–78.
https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.

[8] Holschneider, M., and Ph.
Tchamitchian. “Pointwise Analysis of Riemann’s 'Nondifferentiable' Function.”
*Inventiones Mathematicae* 105, no. 1 (December 1991): 157–75.
https://doi.org/10.1007/BF01232261.

`cwt`

| `cwtfilterbank`

| `cwtfreqbounds`

| `duration`

| `dwt`

| `wavedec`

| `wavefun`

| `waveinfo`

| `wcodemat`

| `wcoherence`

| `wsst`