# We fix the parameter of the Cauchy model amplitude = [5] scale = [3] model = ot.CauchyModel(scale, amplitude) gp = ot.SpectralGaussianProcess(model, myTimeGrid) # Get a time series or a sample of time series # myTimeSeries = gp.getRealization() mySample = gp.getSample(1000) mySegmentNumber = 10 myOverlapSize = 0.3 # Build a spectral model factory myFactory = ot.WelchFactory(ot.Hanning(), mySegmentNumber, myOverlapSize) # Estimation on a TimeSeries or on a ProcessSample # myEstimatedModel_TS = myFactory.build(myTimeSeries) myEstimatedModel_PS = myFactory.buildAsUserDefinedSpectralModel(mySample) # Change the filtering window myFactory.setFilteringWindows(ot.Hamming()) # Get the FFT algorithm myFFT = myFactory.getFFTAlgorithm() # Get the frequencyGrid frequencyGrid = myEstimatedModel_PS.getFrequencyGrid() # With the model, we want to compare values
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
filteringWindow = ot.Hanning()
numPoints = 512
data = ot.Sample(numPoints, 2)
for i in range(numPoints):
x = -0.1 + (1.2 * i) / (numPoints - 1.0)
data[i, 0] = x
data[i, 1] = filteringWindow(x)
graph = ot.Graph()
graph.setXTitle('$tau$')
graph.setYTitle('W')
graph.add(ot.Curve(data))
graph.setColors(['red'])
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(filteringWindow))
filtering_axis = fig.add_subplot(111)
View(graph, figure=fig, axes=[filtering_axis], add_legend=False)
covmodel = ot.ExponentialModel(scale, amplitude) # Create a stationary Normal process with that covariance model process = ot.GaussianProcess(covmodel, tgrid) # Create a time series and a sample of time series tseries = process.getRealization() sample = process.getSample(1000) # %% # Build a factory of stationary covariance function covarianceFactory = ot.StationaryCovarianceModelFactory() # Set the spectral factory algorithm segmentNumber = 5 spectralFactory = ot.WelchFactory(ot.Hanning(), segmentNumber) covarianceFactory.setSpectralModelFactory(spectralFactory) # Check the current spectral factory print(covarianceFactory.getSpectralModelFactory()) # %% # Case 1 : Estimation on a ProcessSample # The spectral model factory computes the spectral density function # without using the block and overlap arguments of the Welch factories estimatedModel_PS = covarianceFactory.build(sample) # Case 2 : Estimation on a TimeSeries # The spectral model factory compute the spectral density function using
# We fix the parameter of the Cauchy model
amplitude = [5.0]
scale = [3.0]
model = ot.CauchyModel(amplitude, scale)
process = ot.SpectralGaussianProcess(model, tgrid)
# Get a time series or a sample of time series
tseries = process.getRealization()
sample = process.getSample(1000)
# %%
# Build a spectral model factory
segmentNumber = 10
overlapSize = 0.3
factory = ot.WelchFactory(ot.Hanning(), segmentNumber, overlapSize)
# %%
# Estimation on a TimeSeries or on a ProcessSample
estimatedModel_TS = factory.build(tseries)
estimatedModel_PS = factory.build(sample)
# %%
# Change the filtering window
factory.setFilteringWindows(ot.Hamming())
# %%
# Get the frequencyGrid
frequencyGrid = ot.SpectralGaussianProcess(estimatedModel_PS,
tgrid).getFrequencyGrid()