falseywinchnet / pyitd

Intrinsic Time-Scale Decomposition

PyITD Intrinsic Time-Scale Decomposition

Introduction

This is a Python implementation of Intrinsic Time-Scale Decomposition (ITD). ITD is a patented decomposition method developed under grant. NIH/NINDS grants nos. 1R01NS046602-01 and 1R43NS39240-01. This algorithm is patented US7966156B1 by Frei And Osorio, 2024-10-06 Adjusted expiration

"We introduce a new algorithm, the intrinsic time-scale decomposition (ITD), for efficient and precise time–frequency–energy (TFE) analysis of signals. The ITD method overcomes many of the limitations of both classical (e.g. Fourier transform or wavelet transform based) and more recent (empirical mode decomposition based) approaches to TFE analysis of signals that are nonlinear and/or non-stationary in nature. The ITD method decomposes a signal into (i) a sum of proper rotation components, for which instantaneous frequency and amplitude are well defined, and (ii) a monotonic trend. The decomposition preserves precise temporal information regarding signal critical points and riding waves, with a temporal resolution equal to the time-scale of extrema occurrence in the input signal. We also demonstrate how the ITD enables application of single-wave analysis and how this, in turn, leads to a powerful new class of real-time signal filters, which extract and utilize the inherent instantaneous amplitude and frequency/phase information in combination with other relevant morphological features." Authors: Mark Frei, Ivan Osorio (2007).

The Intrinsic Time-Scale Decomposition (ITD) is a purely algorithmic, non-lossy iterative decomposition of a time series {Y (i)}N i=1. At the first stage, the signal is decomposed into a proper rotation R1(i), an oscillating mode in which maxima and minima are positive and negative, respectively, and a residual B1(i) called baseline . The baseline B1 is now decomposed in the same fashion, producing a proper rotation R2 and a baseline B2 , and so on. The process stops when the resulting baseline has only two extrema, or is a constant.

B2 = B1 - R1, and so on. The decomposition mode is fully reversable with typically perfect reconstitution. The final output for the decomposition is a monotonic upward trend.

ITD avoids a priori assumptions about the content/morphology of the signal being analysed (e.g. make the decomposition ‘basis free’) ITD also performs the analysis in an efficient and rapid manner with O(n) computations

ITD provides: efficient signal decomposition into ‘proper rotation’ components, for which instantaneous frequency and amplitude are well defined, along with the underlying monotonic signal trend, without the need for laborious and ineffective sifting or splines, precise temporal information regarding instantaneous frequency and amplitude of component signals with a temporal resolution equal to the time-scale of occurrence of extrema in the input signal, a new class of real-time signal filters that utilize the newly available instantaneous amplitude and frequency/phase information together with additional features and morphology information obtained via single-wave analysis. Moreover, the resulting feature extraction and feature-based filtering can be performed in real-time and is easily adapted to extract feature signals of interest at the time-scales on which they naturally occur, while preserving their morphology and relative phases.

ITD overcomes certain limitations of Empirical Mode Decomposition(EMD) including: overshooting and and undershooting of the interpolating cubic splines generating spurious extrema distortion and relocation of existing extrema smearing of time-frequency-energy information inability or extreme difficulty in producing a correct rotation

https://arxiv.org/pdf/1404.3827v1.pdf good summary of the approach https://sci-hub.hkvisa.net/10.1098/rspa.2006.1761 original publication See these articles for more information.

Available splines

• knot estimation

Available stopping criteria

• knot count
• Fixed number of iterations

Extrema detection

• matplotlib findpeaks

Installation

No package available yet. Work in progress.

Notes

The repo contains a working ITD implementation in a ipython notebook, and an in progress numba optimized version

pyitd's Issues

itd function returns "out of time" error

I am using the following piece of code to try itd method but end up with 'out of time' error. The data looks ok with some trends. Appreciate if you could advise a solution. Thanks!
`
inputData2 = [170.825,171.293,168.477,168.117,170.145,170.675,170.765,175.049,176.100,179.441,178.031,179.526,179.962,180.870,184.388,184.747,182.109,181.969,181.240,180.045,179.321,183.274,184.428,183.728,184.778,185.228,186.217,186.986,189.306,186.577,188.546,188.596,188.616,188.831,190.214,188.191,186.442,189.046,189.086,190.282,188.346,188.686,184.638,182.000,181.879,182.429,182.469,184.488,183.249,184.313,186.986,187.886,186.716,187.706,187.396,187.626,180.950,179.161,179.261,179.351,178.724,178.406,178.391,174.133,171.755,172.928,172.186,170.965,170.755,170.245,172.635,171.825,172.185,172.635,172.140,172.315,171.715,170.065,171.425,173.396,172.495,171.775,171.905,172.125,171.985,176.513,176.542,177.152,177.612,177.209,179.032,176.897,170.535,168.079,166.620,165.139,164.600,162.510,161.181,158.462,158.342,158.802,159.891,158.942,157.923,156.993,154.454,154.439,153.215,152.896,153.305,154.634,152.986,150.187,151.536,150.357,150.239,150.232,150.856,139.045,135.070,133.711,133.766,134.277,137.779,139.293,137.462,139.891,139.872,137.924,136.461,136.774,136.394,135.675,136.449,137.254,135.948,134.826,135.075,134.576,134.426,134.336,135.895,135.335,136.055,137.585,137.105,136.989,138.655,138.755,137.705,138.225,138.245,139.864,143.223,143.443,144.023,144.133,144.093,143.483,143.833,144.533,143.353,142.409,143.320,144.083,143.663,145.013,137.075,134.796,134.396,134.091,134.196,133.133,131.276,130.767,131.196,130.996,131.706,130.620,130.048,131.246,131.761,128.097,129.537,130.367,130.597,129.617,129.257,127.307,128.946,129.457,129.817,129.327,130.875,131.956,132.781,133.996,131.766,132.876,132.621,132.846,133.786,132.476,134.056,134.641,133.089,130.687,131.827,131.726,133.321,133.877,135.025,135.275,136.651,139.139,132.576,127.597,125.748,125.948,126.269,125.958,125.198,125.578,123.346,124.458,123.988,123.878,123.538,122.799,125.128,125.738,124.349,124.131,123.338,122.474,123.918,122.249,125.968,126.758,124.718,123.528,123.268,124.158,124.098,125.848,126.318,127.277,125.508,125.818,126.638,127.327,122.394,121.630,122.229,121.152,120.009,120.138,122.169,123.533,125.747,124.798,124.088,122.819,122.329,121.359,122.519,124.598,124.317,124.448,125.388,126.253,125.088,129.337,132.086,132.036,130.322,130.567,131.516,131.636,127.988,126.668,128.793,130.142,130.507,131.966,132.056,134.826,134.426,132.506,132.756,133.191,131.628,131.266,124.808,124.209,122.949,122.534,121.898,121.239,120.729,116.430,114.646,116.563,115.151,117.470,116.890,116.670,113.701,113.441,116.820,117.580,117.390,114.981,115.830,115.510,113.621,115.870,115.569,115.091,115.278,114.971,110.927,113.561,118.840,118.120,119.429,119.777,119.569,115.750,114.311,113.321,113.081,113.874,113.980,112.241,117.410,116.130,118.659,118.510,118.950,118.900,118.850,120.879,118.750,117.990,118.540,120.119,118.810,119.639,118.828,121.019,121.619,120.059,119.919,119.909,120.479,125.585,127.388,126.080,123.818,122.574,121.967,121.909,122.199,120.789,122.673,122.789,124.445,124.059,124.628,122.619,123.308,125.053,125.008,125.238,126.068,125.958,130.576,130.637,131.856,132.026,131.506,132.286,132.576,130.657,131.866,132.946,130.897,130.077,129.987,128.927,131.896,134.196,132.246,132.486,132.811,132.270,131.726,134.301,134.446,136.105,137.315,136.885,137.125,138.305,135.120,133.636,135.085,134.811,135.795,135.515,134.935,137.635,136.065,137.595,136.845,136.338,136.850,135.395,140.031,139.504,138.440,137.785,138.225,136.795,132.156,130.187,136.725,134.975,135.725,134.211,135.195,134.176,139.617,140.874,138.075,138.305,137.275,140.109,141.524,140.564,141.444,140.721,141.192,141.144,142.639,142.973,146.393,146.223,147.492,147.332,144.476,144.473,145.983,140.374,139.194,139.424,139.659,138.125,137.995,137.725,149.732,150.162,152.892,152.391,154.809,155.220,157.460,158.529,160.349,160.149,160.659,161.919,163.538,163.228,160.754,162.998,163.733,163.598,164.548,164.908,162.908,168.907,166.427,167.867,168.827,165.538,166.887,166.617,161.269,159.219,161.269,161.745,160.899,160.889,159.059,159.109,159.679,159.329,159.329,157.710,156.730,156.730,156.290,153.331,153.601,151.541,152.191,152.931,154.051,153.051,153.071,153.432,152.051,153.161,153.051,153.131,153.777,157.852,158.489,157.575,158.769,158.879,160.339,163.358,164.258,162.628,161.529,162.893,164.448,165.148,164.091,163.518,163.658,162.798,162.658,163.003,160.408,161.015,160.157,159.579,158.999,158.230,157.615,157.728,156.970,156.870,156.700,156.591,156.350,156.870,157.540,158.738,157.580,161.720,164.560,169.230,171.624,170.720,170.570,171.092,171.980,172.170,171.350,165.450,165.855,166.790,166.050,166.820,168.160,168.760,168.140,168.638,167.880,166.830,166.185,165.760,166.100,161.990,160.220,160.550,160.620,160.840,159.090,159.870,158.700,160.420,159.650,159.965,160.360,160.723,161.200,163.000,167.490,167.882,168.350,169.069,170.240,171.690,172.000,174.940,175.060,173.942,173.040,173.339,170.010,171.030,170.870,171.644,171.570,172.005,173.370,175.350,186.170,182.410,180.644,178.470,179.520,179.696,180.720,180.980,180.519,180.310,179.008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inputArray = np.asarray(inputData2)

itd=ITD()

rotations = itd.itd(inputArray)
`