Object Reference : Object View and Procedure Reference : Series
Compute the wavelet transform of the series.
Series View: series_name.wavelet(options)
transform=arg (default=“dwt”)
Wavelet transform type: “dwt” (discrete wavelet transform – DWT), “modwt” (maximum overlap DWT – MODWT), “mra” (DWT multiresolution analysis – DWT MRA), or “momra” (MODWT MRA).
Note that when performing DWT or MRA, if the series length is not dyadic, a dyadic fix may be set with the “fixlen=” option
fixlen=arg (default=“mean”)
Fix dyadic lengths in DWT and MRA transforms: “zeros” (pad remainder with zeros), “mean” (pad remainder with mean of series), “median” (pad remainder with median of series), “shorten” (cut series length to dyadic length preceding series length).
maxscale=integer (default = max possible)
Maximum scale for wavelet transform.
The max possible is obtained as follows. Let denote the series length and decompose into its dyadic component and a remainder: , . The default maxscale is then set with the following rules:
DWT: (1) if then , otherwise (2) if expanding the series, and (3) if contracting the series .
filter=arg (default=“h”)
Wavelet filter class: “h” (Haar), “d” (Daubechies), “la” (least asymmetric).
If “filter=h” or “filter=la”, the filter length may be specified using “flen=”.
Wavelet filter boundary conditions are specified using the “bound=” option
Wavelet filter excess length as an even number between 2 and 20.
For use when “filter=d” (default= 4) or “filter=la” (default=8).
bound=arg (default = “p”)
Filter boundary handling: “p” (periodic), “r” (reflective).
Wavelet filter coefficients affected by the boundary will not be highlighted in the output graphs.
Force the dialog to appear from within a program.
Print results.
The line above will perform the discrete wavelet transform of the series DGP using a Haar wavelet filter and up to the seventh wavelet scale.
dgp.wavelet(transform=modwt, maxscale=3, lter=D)
The line above will perform the maximum overlap discrete wavelet transform using a Daubechies wavelet filter of length 4 and up to the third wavelet scale.
dgp.wavelet(transform=mra, maxscale=4, lter=la, en=10, xlen=zeros)
The line above will perform a DWT multi-resolution analysis of the series DGP using a least asymmetric wavelet filter of length 10 and up to the fourth wavelet scale. It will also fix the non-dyadic length of the series by padding with zeros.
dgp.wavelet(transform=momra, maxscale=4, filter=d, flen=12, hidebound)
The line above will perform a MODWT multi-resolution analysis using a Daubechies wavelet filter of length 12 and up to the fourth wavelet scale. It will also turn off highlighting of wavelet coefficients on the boundary.
See “Wavelet Analysis” and “Wavelet Transforms” for discussion. See also “Wavelet Objects”.
See also Series::waveanova, Series::waveoutlier, Series::wavethresh, and Series::makewavelets.