kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
77 wiersze
3.6 KiB
Markdown
77 wiersze
3.6 KiB
Markdown
# Signal Filtering and Generation of Synthetic Time-Series
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## Reference
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- John F. Ehlers, "[Cycle Analytics for Traders: Advanced Technical Trading Concepts](http://www.mesasoftware.com/ehlers_books.htm)".
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- D. Prichard and J. Theiler, "[Generating surrogate data for time series with several simultaneously measured variables](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: the meboot R package](https://www.jstatsoft.org/article/view/v029i05)".
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## Characteristics
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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 generation of synthetic (surrogate) time-series.
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- Filters (*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 (*synthetic.py*):
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- **synthetic_wave** Generates multi-sine wave given periods, amplitudes, and phases.
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- **synthetic_sampling** Generates surrogates using randomized-sampling (bootstrap) with or without replacement.
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- **synthetic_FFT** Generates surrogates using the phase-randomized Fourier-transform algorithm.
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- **synthetic_MEboot** Generates surrogates using the maximum entropy bootstrap algorithm.
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- File *filters.py* includes also functions to plot the filter signal, frequency response, and group delay.
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- File *synthetic.py* includes also functions to differentiate, integrate, normalize, and scale the discrete time-series.
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- Usage: *python test.py example*.
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## Main Parameters
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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 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 `(:, )`, `(:, 1)`, or `(1, :)`.
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`b` Transfer response coefficients (numerator).
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`a` Transfer response coefficients (denominator).
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`Y` Filtered dataset (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 (all of them use the dataset in *spx.csv*). The results are shown [here](Result_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 discrete differences.
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- **ME_boot** Example showing the generation of surrogates time-series using the maximum entropy bootstrap algorithm and 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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