# icwt

Inverse continuous 1-D wavelet transform

## Syntax

## Description

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

= icwt(`cfs`

)`cfs`

using Morlet's single integral formula.
`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.

inverts the CWT over the frequency range specified in
`xrec`

= icwt(___,`f`

,`freqrange`

)`freqrange`

. `f`

is the scale-to-frequency
conversion obtained from `cwt`

.

*In R2022a: If you invert the CWT over a specified frequency range, you
must precede those inputs either by a wavelet name or an empty input for the default
Morse wavelet. For more information, see icwt behavior change.*

inverts the CWT over the range of periods specified in
`xrec`

= icwt(___,`period`

,`periodrange`

)`periodrange`

. `p`

is an array of
durations obtained from `cwt`

with a duration input. The
`period`

is the `cwt`

output obtained using a
`duration`

input. The period range
must be increasing and contained in `period`

.

*In R2022a: If you invert the CWT over a specified range of periods, you
must precede those inputs either by a wavelet name or an empty input for the default
Morse wavelet. For more information, see icwt behavior change.*

specifies one or more additional name-value arguments. For example, `xrec`

= icwt(___,`Name=Value`

)```
xrec =
icwt(cfs,TimeBandwidth=40,VoicesPerOctave=20)
```

specifies a
time-bandwidth product of 40 and 20 voices per octave.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[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.

## Extended Capabilities

## Version History

**Introduced in R2016b**