Overview of the DiscreteTransforms Package - Maple Help

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Overview of the DiscreteTransforms Package

Calling Sequence

DiscreteTransforms[command](arguments)

command(arguments)

Description

• 

The DiscreteTransforms package contains commands for computing transforms of discrete data.

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The commands of the package are (currently) limited to hardware precision, which means that the results are independent of Digits, and that all computations occur in double precision (approximately 15 decimal digits).

  

The Fourier commands in the package work with almost any compatible data type, but are most efficient when used with the natural data type that is used to compute the transform. The wavelet commands in the package work purely with real, float[8] data.

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Each command in the DiscreteTransforms package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

  

As the underlying implementation of the DiscreteTransforms package is a module, it is also possible to use the form DiscreteTransforms:-command to access a command from the package. For more information, see Module Members.

List of DiscreteTransforms Package Commands

  

The following is a list of available commands:

FourierTransform

computes a discrete Fourier transform of the complex input data.

InverseFourierTransform

computes a discrete inverse Fourier transform of the complex input data.

WaveletCoefficients

obtain orthogonal and biorthogonal wavelet masks.

DiscreteWaveletTransform

computes the discrete wavelet transform of real data.

InverseDiscreteWaveletTransform

computes the inverse discrete wavelet transform of real data.

WaveletPlot

plot the mother and father wavelets from the scaling and wavelet coefficients.

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For information about efficient use of the FourierTransform and InverseFourierTransform commands, see FourierTransform/efficiency.

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To display the help page for a particular DiscreteTransforms command, see Getting Help with a Command in a Package.

Examples

withDiscreteTransforms

DiscreteWaveletTransform,FourierTransform,InverseDiscreteWaveletTransform,InverseFourierTransform,WaveletCoefficients,WaveletPlot

(1)

Z:=Vector4,i→evalf151+cos2πi4+Isin2πi4,datatype=complex8

Z:=1.+1.I0.+0.I1.1.I2.+0.I

(2)

FourierTransformZ,inplace=true

2.+0.I0.+2.I0.+0.I0.+0.I

(3)

InverseFourierTransformZ,inplace=true

1.+1.I0.+0.I1.1.I2.+0.I

(4)

w1,w2:=WaveletCoefficientsDaubechies,4

w1,w2:=0.1294095225512600.2241438680420130.8365163037378080.482962913144534,0.4829629131445340.8365163037378080.2241438680420130.129409522551260

(5)

V:=Vectorrow10,i→i,datatype=float8

V:=1.2.3.4.5.6.7.8.9.10.

(6)

V1,V2:=DiscreteWaveletTransformV,w1,w2

V1,V2:=2.2204460492503110-164.4408920985006310-164.4408920985006310-160.3.53553390593274,2.310789034541155.139216159287347.9676432840335310.796070408779712.6771540786184

(7)

InverseDiscreteWaveletTransformV1,V2,w1,w2

1.2.000000000000003.000000000000004.000000000000005.000000000000006.000000000000007.000000000000008.9.10.0000000000000

(8)

See Also

DiscreteTransforms[DiscreteWaveletTransform], DiscreteTransforms[FourierTransform], DiscreteTransforms[InverseDiscreteWaveletTransform], DiscreteTransforms[InverseFourierTransform], DiscreteTransforms[WaveletCoefficients], DiscreteTransforms[WaveletPlot], DiscreteTransforms[Wavelets], module, with


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