kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
Add comment and update README.md
Gabriele Gilardi
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@ -150,4 +150,6 @@ Code_MatLab/
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# Docs directory
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Docs/
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# Data directory
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data/
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@ -649,7 +649,7 @@ class Filter:
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plt.ylabel('$h$ [db]')
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legend = ['Filter', '-3dB']
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plt.legend(legend)
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plt.title('Frequency Response', fontweight="bold")
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plt.title('Frequency Response')
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# Plot and format lag/group delay
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plt.subplot(1, 2, 2)
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@ -658,7 +658,8 @@ class Filter:
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plt.xlim(np.amin(wf), np.amax(wf))
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plt.xlabel(r'$\omega$ [rad/sample]')
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plt.ylabel('$gd$ [samples]')
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plt.title('Lag / Group Delay', fontweight="bold")
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plt.title('Lag / Group Delay')
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# Show plots
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plt.suptitle('Example "Response"')
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plt.show()
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@ -3,19 +3,112 @@ Signal Filtering and Generation of Synthetic Time-Series.
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Copyright (c) 2020 Gabriele Gilardi
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References
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----------
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- John F. Ehlers, "Cycle Analytics for Traders: Advanced Technical Trading
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Concepts", @ http://www.mesasoftware.com/ehlers_books.htm.
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- D. Prichard and J. Theiler, "Generating surrogate data for time series with
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several simultaneously measured variables",
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@ https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.73.951.
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- H. Vinod and J. Lopez-de-Lacalle, "Maximum entropy bootstrap for time series:
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the meboot R package, @ https://www.jstatsoft.org/article/view/v029i05.
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Characteristics
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---------------
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- The code has been written and tested in Python 3.7.7.
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- Implementation of several digital signal filters and functions for the
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generation of synthetic (surrogate) time-series.
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- Filter list (file <filters.py>):
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Generic Generic filter
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SMA Simple moving average
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EMA Exponential moving average
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WMA Weighted moving average
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MSMA Modified simple moving average
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MLSQ Modified least-squares quadratic
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ButterOrig Butterworth original filter
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ButterMod Butterworth modified filter
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SuperSmooth Supersmoother filter
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GaussLow Gauss low pass filter
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GaussHigh Gauss high pass filter
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BandPass Band-pass filter
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BandStop Band-stop filter
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ZEMA1 Zero-lag EMA (type 1)
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ZEMA2 Zero-lag EMA (type 2)
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InstTrend Instantaneous trendline
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SincFilter Sinc function filter
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Decycler De-cycler filter
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DecyclerOsc De-cycle oscillator
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ABG Alpha-beta-gamma filter
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Kalman One-dimensional steady-state Kalman filter
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- Synthetic time-series (file <synthetic.py>):
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synthetic_wave Generates multi-sine wave given periods,
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amplitudes, and phases.
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synthetic_sampling Generates surrogates using randomized-sampling
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(bootstrap) with or without replacement.
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synthetic_FFT Generates surrogates using the phase-randomized
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Fourier transform algorithm.
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synthetic_MEboot Generates surrogates using the maximum entropy
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bootstrap algorithm.
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- File <filters.py> includes also functions to plot the filter signal,
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frequency response, and group delay.
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- File <synthetic.py> includes also functions to differentiate, integrate,
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normalize, and scale the discrete time-series.
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- Usage: python test.py <example>.
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Parameters
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----------
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example
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Name of the example to run (Filters, Kalman, FFT_boot, ME_boot, Response).
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data_file
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File with the dataset (csv format). The extension is added automatically.
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X
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Dataset to filter/time-series (input). It must be a 1D array, i.e. of shape
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(:, ) or (:, 1) or (1, :).
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b
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Transfer response coefficients (numerator).
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a
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Transfer response coefficients (denominator).
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Y
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Filtered dataset (output).
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X_synt
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Surrogate/synthetic generated time-series (output)
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n_reps
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Number of surrogates/synthetic time-series to generate.
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Examples
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--------
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There are five examples (all of them use the dataset in *spx.csv*). The
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results are shown in file <Results_Examples.pdf>.
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- Filter: example showing filtering using an EMA, a Butterworth modified
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filter, and a type 2 Zero-lag EMA.
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- Kalman: example showing filtering using the three types of Kalman filter,
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alpha, alpha-beta, and alpha-beta-gamma.
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- FFT_boot: example showing the generation of surrogates time-series using
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the Fourier-transform algorithm and the discrete differences.
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- ME_boot: example showing the generation of surrogates time-series using the
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using maximum entropy bootstrap algorithm and the discrete differences.
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- Response: example showing the frequency response and lag/group delay for a
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band-pass filter.
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"""
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import sys
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import warnings
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import numpy as np
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import matplotlib.pyplot as plt
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import filters as flt
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import synthetic as syn
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# Added to avoid message warning "The group delay is singular at frequencies
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# [....], setting to 0" when plotting the lag for SMA filters.
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# np.seterr(all='ignore')
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# [....], setting to 0" when plotting the lag for SMA filters.
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warnings.filterwarnings('ignore')
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np.random.seed(1294404794)
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@ -29,7 +122,7 @@ example = sys.argv[1]
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data_file = 'spx'
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data = np.loadtxt(data_file + '.csv', delimiter=',')
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# Example with a few filters
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# Example with an EMA, a Butterworth modified filter, and a type 2 Zero-lag EMA
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if (example == 'Filters'):
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spx = flt.Filter(data)
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ema = spx.EMA(N=10)
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@ -49,38 +142,53 @@ elif (example == 'Kalman'):
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names = ['SPX', 'a-type', 'ab-type', 'abg-type']
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flt.plot_signals(signals, names=names, start=0, end=200)
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# Example of filter frequency and lag
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# Example of surrogates time-series using the Fourier-transform algorithm
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elif (example == 'FFT_boot'):
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n_reps = 4
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n_samples = len(data)
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# Generated the surrogates using the 1st discrete differences (in percent)
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dX = syn.value2diff(data, percent=True)
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dX_synt = syn.synthetic_FFT(dX, n_reps=n_reps) # (n_reps, n_samples)
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# Rebuild the actual surrogate time-series
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signals = [data]
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names = ['SPX']
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for i in range(n_reps):
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X_synt = syn.diff2value(dX_synt[i, :], data[0], percent=True)
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signals.append(X_synt)
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names.append('Synth. #' + str(i+1))
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# Plot all
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flt.plot_signals(signals, names=names, start=0, end=200)
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# Example of surrogates time-series using the maximum entropy bootstrap algorithm
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elif (example == 'ME_boot'):
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n_reps = 4
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n_samples = len(data)
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# Generated the surrogates using the 1st discrete differences (in value)
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dX = syn.value2diff(data, percent=False)
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dX_synt = syn.synthetic_MEboot(dX, n_reps=n_reps, alpha=0.1, bounds=False,
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scale=False) # (n_reps, n_samples)
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# Rebuild the actual surrogate time-series
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signals = [data]
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names = ['SPX']
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for i in range(n_reps):
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X_synt = syn.diff2value(dX_synt[i, :], data[0], percent=False)
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signals.append(X_synt)
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names.append('Synth. #' + str(i+1))
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# Plot all
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flt.plot_signals(signals, names=names, start=0, end=499)
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# Example of frequency response and lag/group delay for a band-pass filter
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elif (example == 'Response'):
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spx = flt.Filter(data)
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band = spx.BandPass(P=10, delta=0.3)
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spx.plot_response()
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# Example of surrogates time-series using the Fourier-transform algorithm
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elif (example == 'FFT_boot'):
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pass
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# Example of surrogates time-series using maximum entropy bootstrap algorithm
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elif (example == 'ME_boot'):
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pass
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else:
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print("Example not found")
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sys.exit(1)
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# dX = syn.value2diff(data, percent=True)
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# # X = syn.diff2value(dX, data[0], percent=True)
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# signals = [data, X]
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# flt.plot_signals(signals, start=0, end=200)
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# dX = syn.value2diff(data, percent=False)
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# dX_synt = syn.synthetic_sampling(dX, n_reps=1, replace=True)
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# dX_synt = syn.synthetic_FFT(dX, n_reps=2)
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# dX_synt = syn.synthetic_MEboot(dX, n_reps=4, alpha=0.1, bounds=False, scale=False)
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# for i in range(dX_synt.shape[0]):
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# # aa = dX_synt[:, i]
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# aa = syn.diff2value(dX_synt[i, :], data[0], percent=False)
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# plt.plot(aa)
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# plt.xlim(0, 200)
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# plt.plot(data)
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# plt.show()
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18
README.md
18
README.md
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@ -45,9 +45,9 @@
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## Main Parameters
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`example` Name of the example to run.
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`example` Name of the example to run (Filters, Kalman, FFT_boot, ME_boot, Response).
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`data_file` File name with the dataset (csv format). The extension is added automatically.
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`data_file` File with the dataset (csv format). The extension is added automatically.
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`X` Dataset to filter/time-series (input). It must be a 1D array, i.e. of shape `(:, )` or `(:, 1)` or `(1, :)`.
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@ -57,10 +57,20 @@
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`Y` Filtered dataset (output).
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`X_synt` Synthetic time-series (output)
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`X_synt` Surrogate/synthetic generated time-series (output)
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`n_reps` Number of surrogates/synthetic time-series to generate.
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## Examples
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There are five examples: **Filters**, **Kalman**, **Response**, **FFT_boot**, **ME_boot**. For all, the dataset in *spx.csv* is used.
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There are five examples (all of them use the dataset in *spx.csv*). The results are shown [here](Results_Examples.pdf).
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- **Filter** Example showing filtering using an EMA, a Butterworth modified filter, and a type 2 Zero-lag EMA.
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- **Kalman** Example showing filtering using the three types of Kalman filter, alpha, alpha-beta, and alpha-beta-gamma.
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- **FFT_boot** Example showing the generation of surrogates time-series using the Fourier-transform algorithm and the discrete differences.
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- **ME_boot** Example showing the generation of surrogates time-series using the using maximum entropy bootstrap algorithm and the discrete differences.
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- **Response** Example showing the frequency response and lag/group delay for a band-pass filter.
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