# cwt

Continuous 1-D wavelet transform

## Syntax

## Description

returns the continuous wavelet transform (CWT) of `wt`

= cwt(`x`

)`x`

.
The
CWT is obtained using the analytic Morse wavelet with the symmetry parameter,
gamma ($$\gamma $$), equal to 3 and the time-bandwidth product equal to 60.
`cwt`

uses 10 voices per octave. The minimum and maximum
scales are determined automatically based on the energy spread of the wavelet in
frequency and time.

The `cwt`

function uses L1 normalization. With L1
normalization, if you have equal amplitude oscillatory components in your data
at different scales, they will have equal magnitude in the CWT. Using L1
normalization shows a more accurate representation of the signal. See L1 Norm for CWT and Continuous Wavelet Transform of Two Complex Exponentials.

`[___,`

returns the filter bank used in the CWT. See `coi`

,`fb`

] = cwt(___)`cwtfilterbank`

.

`[___,`

returns the scaling coefficients for the wavelet transform.`fb`

,`scalingcfs`

] = cwt(___)

`[___] = cwt(___,`

specifies one or more additional name-value arguments. For example, `Name=Value`

)```
wt
= cwt(x,TimeBandwidth=40,VoicesPerOctave=20)
```

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

`cwt(___)`

with no output arguments plots the
CWT scalogram. The scalogram is the absolute value of the CWT plotted as a
function of time and frequency. Frequency is plotted on a logarithmic scale. The
cone of influence showing where edge effects become significant is also plotted.
Gray regions outside the dashed white line delineate regions where edge effects
are significant. If the input signal is complex-valued, the positive
(counterclockwise) and negative (clockwise) components are plotted in separate
scalograms.

If you do not specify a sampling frequency or sampling period, the frequencies are plotted in cycles per sample. If you specify a sampling frequency, the frequencies are in hertz. If you specify a sampling period, the scalogram is plotted as a function of time and periods. If the input signal is a timetable, the scalogram is plotted as a function of time and frequency in hertz and uses the RowTimes as the basis for the time axis.

To see the time, frequency, and magnitude of a scalogram point, enable data tips in the figure axes toolbar and click the desired point in the scalogram.

**Note**

Before plotting, `cwt`

clears (`clf`

) the current
figure. To plot the scalogram in a subplot, use a plotting function. See
Plot CWT Scalogram in Subplot.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

The syntax for the old

`cwt`

function continues to work but is no longer recommended. Use the current version of`cwt`

. Both the old and current versions use the same function name. The inputs to the function determine automatically which version is used. See cwt function syntax has changed.When performing multiple CWTs, for example inside a for-loop, the recommended workflow is to first create a

`cwtfilterbank`

object and then use the`wt`

object function. This workflow minimizes overhead and maximizes performance. See Using CWT Filter Bank on Multiple Time Series.

## Algorithms

## 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): 6036–6041. 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): 146–160. 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, Jonathan M. “Element
Analysis: A Wavelet-Based Method for Analysing Time-Localized Events in Noisy Time
Series.” *Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences* 473, no. 2200 (April 30, 2017): 20160776.
https://doi.org/10.1098/rspa.2016.0776.

## Extended Capabilities

## Version History

**Introduced in R2016b**