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FDWT


math gts
Since v1.0.0
Available on all platforms
See also

The FDWT function performs a Forward Discrete Wavelet Transform on a Geo Time Series™.

A number of different Wavelets are available, the list is inspired by that available on the Wavelet Browser.

The list of Wavelets which can be used is the following:

NameWavelet
haarHaar
db1Daubechies 1
db2Daubechies 2
db3Daubechies 3
db4Daubechies 4
db5Daubechies 5
db6Daubechies 6
db7Daubechies 7
db8Daubechies 8
db9Daubechies 9
db10Daubechies 10
db11Daubechies 11
db12Daubechies 12
db13Daubechies 13
db14Daubechies 14
db15Daubechies 15
db16Daubechies 16
db17Daubechies 17
db18Daubechies 18
db19Daubechies 19
db20Daubechies 20
sym2Symlets 2
sym3Symlets 3
sym4Symlets 4
sym5Symlets 5
sym6Symlets 6
sym7Symlets 7
sym8Symlets 8
sym9Symlets 9
sym10Symlets 10
sym11Symlets 11
sym12Symlets 12
sym13Symlets 13
sym14Symlets 14
sym15Symlets 15
sym16Symlets 16
sym17Symlets 17
sym18Symlets 18
sym19Symlets 19
sym20Symlets 20
coif1Coiflets 1
coif2Coiflets 2
coif3Coiflets 3
coif4Coiflets 4
coif5Coiflets 5
bior1.1Biorthogonal 1.1
bior1.3Biorthogonal 1.3
bior1.5Biorthogonal 1.5
bior2.2Biorthogonal 2.2
bior2.4Biorthogonal 2.4
bior2.6Biorthogonal 2.6
bior2.8Biorthogonal 2.8
bior3.1Biorthogonal 3.1
bior3.3Biorthogonal 3.3
bior3.5Biorthogonal 3.5
bior3.7Biorthogonal 3.7
bior3.9Biorthogonal 3.9
bior4.4Biorthogonal 4.4
bior5.5Biorthogonal 5.5
bior6.8Biorthogonal 6.8
rbio1.1Reverse biorthogonal 1.1
rbio1.3Reverse biorthogonal 1.3
rbio1.5Reverse biorthogonal 1.5
rbio2.2Reverse biorthogonal 2.2
rbio2.4Reverse biorthogonal 2.4
rbio2.6Reverse biorthogonal 2.6
rbio2.8Reverse biorthogonal 2.8
rbio3.1Reverse biorthogonal 3.1
rbio3.3Reverse biorthogonal 3.3
rbio3.5Reverse biorthogonal 3.5
rbio3.7Reverse biorthogonal 3.7
rbio3.9Reverse biorthogonal 3.9
rbio4.4Reverse biorthogonal 4.4
rbio5.5Reverse biorthogonal 5.5
rbio6.8Reverse biorthogonal 6.8
dmeyDiscrete Meyer, FIR approximation

The FDWT can only be applied to Geo Time Series™ with a number of values which is a power of 2.

Assuming the input GTS has 2n values, the result of the FDWT transformation is a GTS with 2n values (the wavelet coefficients) with timestamps from 0 to 2n-1.

The ticks of the n levels are contiguous, with the first tick being for level n, the next 2 for level n-1, the next 4 for level n-2, up to the last 2n-1 for level 1.

Level 1 has the finest time resolution but the coarsest frequency resolution. Each level has half (coarser) the time resolution and double (finer) the frequency resolution as the previous level.

Signature

Examples

NEWGTS 1 512 <% 'i' STORE $i NaN NaN NaN $i 360.0 / 2 PI * * SIN $i 512.0 / 2 PI * * COS + ADDVALUE %> FOR 'db9' FDWT