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FFTSmooth v2¶

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Summary ¶

Performs smoothing of a spectrum using various filters.

Properties ¶

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:

Zeroing ¶

Filter: “Zeroing”
Params: “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.

Butterworth ¶

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.

Usage ¶

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
0.20  0.30
0.20  0.30
0.37  0.47
10.20  10.30
0.37  0.47
0.20  0.30
8.20  8.30
0.20  0.30
0.20  0.30
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
0.20  0.29  0.30  -0.05
0.20  0.29  0.30  0.44
0.37  0.46  0.43  2.49
10.20  10.26  9.59  4.58
0.37  0.46  0.43  2.63
0.20  0.29  0.16  1.77
8.20  8.20  7.05  2.74
0.20  0.29  0.16  1.48
0.20  0.29  0.30  0.39
0.20  0.29  0.30  0.20

Usage ¶

# Create a workspace
ws = CreateSampleWorkspace()

# Apply the Butterworth filter to all spectra
smooth = FFTSmooth( ws, Filter='Butterworth', Params='5,2', AllSpectra=True )