\(\renewcommand\AA{\unicode{x212B}}\)

FFTDerivative v1

Enable screenshots using DOCS_SCREENSHOTS in CMake

Summary

Calculated derivatives of a spectra in the MatrixWorkspace using Fast Fourier Transform (FFT).

See Also

ExtractFFTSpectrum, FFT, MaxEnt, RealFFT, SassenaFFT, FFTSmooth

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	Input workspace for differentiation
OutputWorkspace	Output	MatrixWorkspace	Mandatory	Workspace with result derivatives
Order	Input	number	1	The order of the derivative

Description

Calcuates the derivative of the specta in a workspace using FFT v1.

Usage

Example: Different Orders of Derivative

wsOriginal = CreateSampleWorkspace(XMax=20,BinWidth=0.2,BankPixelWidth=1,NumBanks=1)
wsOrder1 = FFTDerivative(wsOriginal,Order=1)
wsOrder2 = FFTDerivative(wsOriginal,Order=2)
wsOrder3 = FFTDerivative(wsOriginal,Order=3)

print("bin Orig  1st    2nd   3rd")
for i in range (41,67,5):
    print("{}  {:.2f}  {:.2f}  {:.2f}  {:.2f}".format(i, wsOriginal.readY(0)[i], wsOrder1.readY(0)[i], wsOrder2.readY(0)[i], wsOrder3.readY(0)[i]))

Output:

bin Orig  1st    2nd   3rd
41  0.67  1.35  4.20  9.93
46  5.50  8.50  3.25  -29.37
51  9.90  -3.92  -17.99  23.34
56  2.60  -5.63  9.10  0.70
61  0.37  -0.32  1.30  -4.51
66  0.30  -0.00  0.01  -0.07

Example: Different Orders of Derivative

wsOriginal = CreateSampleWorkspace(XMax=20,BinWidth=0.2,BankPixelWidth=1,NumBanks=1)
wsOrder1 = FFTDerivative(wsOriginal,Order=1)
wsOrder2 = FFTDerivative(wsOriginal,Order=2)

wsOrder2Test = FFTDerivative(wsOrder1,Order=1)

print("The direct 2nd order derivative and the derivative of a derivative should match")
print(CompareWorkspaces(wsOrder2,wsOrder2Test,CheckAllData=True,Tolerance=1e10)[0])

Output:

The direct 2nd order derivative and the derivative of a derivative should match
True

Categories: AlgorithmIndex | Arithmetic\FFT

Source

C++ header: FFTDerivative.h

C++ source: FFTDerivative.cpp