\(\renewcommand\AA{\unicode{x212B}}\)
FFTSmooth dialog.
Table of Contents
| Name | Direction | Type | Default | Description |
|---|---|---|---|---|
| InputWorkspace | Input | MatrixWorkspace | Mandatory | The name of the input workspace. |
| OutputWorkspace | Output | MatrixWorkspace | Mandatory | The name of the output workspace. |
| WorkspaceIndex | Input | number | 0 | Workspace index for smoothing |
| Filter | Input | string | Zeroing | The type of the applied filter. Allowed values: [‘Zeroing’, ‘Butterworth’] |
| Params | Input | string | The filter parameters: For Zeroing, 1 parameter: ‘n’ - an integer greater than 1 meaning that the Fourier coefficients with frequencies outside the 1/n of the original range will be set to zero. For Butterworth, 2 parameters: ‘n’ and ‘order’, giving the 1/n truncation and the smoothing order. | |
| IgnoreXBins | Input | boolean | False | Ignores the requirement that X bins be linear and of the same size. Set this to true if you are using log binning. The output X axis will be the same as the input either way. |
| AllSpectra | Input | boolean | False | Smooth all spectra |
FFTSmooth uses the FFT algorithm to create a Fourier transform of a spectrum, applies a filter to it and transforms it back. The filters remove higher frequencies from the spectrum which reduces the noise.
The second version of the FFTSmooth algorithm has two filters:
Filter: “Butterworth”
Params: A string containing two positive integer parameters separated by a comma, such as 20,2.
“n”- the first integer, specifies the cutoff frequency for the filter, in the same way as for the “Zeroing” filter. That is, the cutoff is at m/n where m is the original range. “n” is required to be strictly more than 1.
“order”- the second integer, specifies the order of the filter. For low order values, such as 1 or 2, the Butterworth filter will smooth the data without the strong “ringing” artifacts produced by the abrupt cutoff of the “Zeroing” filter. As the order parameter is increased, the action of the “Butterworth” filter will approach the action of the “Zeroing” filter.
For both filter types, the resulting spectrum has the same size as the original one.
Example: Zeroing with Params=2
ws = CreateSampleWorkspace(function="Multiple Peaks",XMax=20,BinWidth=0.2,BankPixelWidth=1,NumBanks=1)
#add a bit of predictable noise
noiseAmp=0.1
noiseArray= []
for i in range(ws.blocksize()):
noiseAmp = -noiseAmp
noiseArray.append(noiseAmp)
for j in range(ws.getNumberHistograms()):
ws.setY(j,ws.readY(j)+noiseArray)
wsSmooth = FFTSmooth(ws, Params='2')
print("bin Orig Smoothed")
for i in range (0,100,10):
print("{} {:.2f} {:.2f}".format(i, ws.readY(0)[i], wsSmooth.readY(0)[i]))
Output:
bin Orig Smoothed
0 0.20 0.30
10 0.20 0.30
20 0.37 0.47
30 10.20 10.30
40 0.37 0.47
50 0.20 0.30
60 8.20 8.30
70 0.20 0.30
80 0.20 0.30
90 0.20 0.30
Example: Using the Butterworth filter
ws = CreateSampleWorkspace(function="Multiple Peaks",XMax=20,BinWidth=0.2,BankPixelWidth=1,NumBanks=3)
#add a bit of predictable noise
noiseAmp=0.1
noiseArray= []
for i in range(ws.blocksize()):
noiseAmp = -noiseAmp
noiseArray.append(noiseAmp)
for j in range(ws.getNumberHistograms()):
ws.setY(j,ws.readY(j)+noiseArray)
wsButter2_2 = FFTSmooth(ws, Filter="Butterworth", Params='2,2', AllSpectra=True)
wsButter5_2 = FFTSmooth(ws, Filter="Butterworth", Params='5,2', AllSpectra=True)
wsButter20_2 = FFTSmooth(ws, Filter="Butterworth", Params='20,2', AllSpectra=True)
print("bin Orig 2_2 5_2 20_2")
for i in range (0,100,10):
print("{} {:.2f} {:.2f} {:.2f} {:.2f}".format(i, ws.readY(0)[i], wsButter2_2.readY(0)[i], wsButter5_2.readY(0)[i], wsButter20_2.readY(0)[i]))
Output:
bin Orig 2_2 5_2 20_2
0 0.20 0.29 0.30 -0.05
10 0.20 0.29 0.30 0.44
20 0.37 0.46 0.43 2.49
30 10.20 10.26 9.59 4.58
40 0.37 0.46 0.43 2.63
50 0.20 0.29 0.16 1.77
60 8.20 8.20 7.05 2.74
70 0.20 0.29 0.16 1.48
80 0.20 0.29 0.30 0.39
90 0.20 0.29 0.30 0.20
# Create a workspace
ws = CreateSampleWorkspace()
# Apply the Butterworth filter to all spectra
smooth = FFTSmooth( ws, Filter='Butterworth', Params='5,2', AllSpectra=True )
Categories: AlgorithmIndex | Arithmetic\FFT | Transforms\Smoothing
C++ header: FFTSmooth2.h (last modified: 2021-03-31)
C++ source: FFTSmooth2.cpp (last modified: 2021-05-24)