$$\renewcommand\AA{\unicode{x212B}}$$

# FFTDerivative v1¶

## Summary¶

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

## 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):


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