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项目作者： woolgathering

项目描述 ：
Python package implementing Sethares and Staley's Periodicity Transforms
高级语言： Python
项目地址: git://github.com/woolgathering/pyPeriod.git
创建时间： 2020-09-13T19:41:35Z
项目社区：https://github.com/woolgathering/pyPeriod
开源协议：MIT License
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pyPeriod

This package now includes a few different periodicity transforms and will likley be further updated in the future.

Periods

Sethares and Staley’s Periodicity Transforms in Python. See the paper here.

Efficiency was improved by modifying the projection algorithm so that we take advantage of the very fast matrix operations in Numpy. The result is identical. There are two flags in the project method: trunc_to_integer_multiple and orthogonalize.

  • trunc_to_integer_multiple allows for the input to be truncated to an integer multiple of the period one is testing for. Say p = 3 and N = len(x), we allow the algorithm to truncate x so that 3|N. Assuming a period is constant in the analysis window (with regard to values), setting this as True tends to produce a better result and minimizes the residual more than otherwise.
  • orthogonalize removes prime factors of p from the projection. That is, for some period p and its projection y, we project y onto the prime factors of p to get y_hat. Then we do y - y_hat and return the result. This idea was taken from “Orthogonal, exactly periodic subspace decomposition” (D.D. Muresan, T.W. Parks), 2003, and the process simplified. Setting both trunc_to_integer_multiple and orthogonalize to True results in a projection that is identical to that acquired using the process described in Muresan and Parks. Note that orthogonalize has no effect in the M-best family as it makes no sense.

RamanujanPeriods

Periodic decomposition using Ramanujan summation, taken from the work of P. P. Vaidyanathan and Srikanth V. Tenneti. This class is nowhere near completion (I have parts of the entire thing laying around my machine…) but this does a basic decomposition using the basis vectors derived from the Ramanujan sum.

A method is included in this class (find_periods_with_weights) which will return the periods found by the Ramanujan transform above some threshold (thresh). Using this with get_periods() essentially combines the the Ramanujan transform with the quadratic program of QOPeriods and allows for good (albeit slow) results without fidding with parameters as is often the case in QOPeriods.

QOPeriods

This is an adaptation of the Sethares and Staley transform where the residual is computed by framing the problem as a quadratic program and each projection is orthogonalized. This produces a better result (up to a point) and is the basis for my forthcoming PhD dissertation on audio applications of these transforms. Note that because this particular ‘’residualization’’ employs a quadratic program, the results of all previously found periods can and often will change. The criteria of when to stop pursuing further periods in the face of residual noise is an ongoing problem and likley unique to each situation. To this end, find_periods() can be passed an argument called test_function which in turn is passed the residual and expects a boolean return on whether or not to process again.

A method is also included in this class called get_periods() that allows one to retrieve the original periods for further analysis.

EXPECT BREAKING CHANGES IN THE FUTURE AS THESE ARE UPDATED AND CHANGED.

Installation

Easiest:

  1. pip install pyPeriod

Development

From Github:

  1. pip install git+https://github.com/woolgathering/pyPeriod

Via cloning:

  1. git clone https://github.com/woolgathering/pyPeriod.git
  2. pip install -r pyPeriod/requirements.txt
  3. pip install ./pyPeriod

Usage

  1. import numpy as np
  2. from pyPeriod import Periods
  3. from random import uniform
  5. # define a signal
  6. sr = 1000 # samplerate
  7. f1 = 10 # frequency
  8. f2 = 17
  9. noise = 0.2 # percent noise
  11. # Make some signals with some noise. The second signal has a slightly offset phase.
  12. a = [np.sin((x*np.pi*2*f1)/sr)+(uniform(-1*noise, noise)) for x in range(2000)]
  13. b = [np.sin(((x*np.pi*2*f2)/sr) + (np.pi*1.1))+(uniform(-1*noise, noise)) for x in range(2000)]
  14. c = np.array(a)+np.array(b) # combine the signals
  16. # normalize, though the algorithms can handle any range of signals (best if DC is removed)
  17. c /= np.max(np.abs(c),axis=0)
  20. ##################################
  21. ## Periods (Sethares and Staley, Muresan and Parks if orthogonalize and trunc_to_integer_multiple are True)
  22. ##################################
  23. p = Periods(c) # make an instance of Period (Sethares and Staley)
  24. # p = Periods(c, trunc_to_integer_multiple=True, orthogonalize=True) # make an instance of Period (Muresan and Parks)
  26. """
  27. The output of each algorithm are three arrays consisting of:
  28.   periods: the integer values of the periods found
  29.   powers: the floating point values of the amount of "energy" removed by each period found
  30.   bases: the arrays, equal in length to the input signal length, that contain the periodicities found
  31. """
  33. # find periodicities using the small-to-large algorithm
  34. periods, powers, bases = p.small_to_large(thresh=0.1)
  36. # find periodicities using the M-best algorithm
  37. periods, powers, bases = p.m_best(n_periods=10)
  39. # find periodicities using the M-best gamma algorithm
  40. periods, powers, bases = p.m_best_gamma(n_periods=10)
  42. # find periodicities using the best correlation algorithm
  43. periods, powers, bases = p.best_correlation(n_periods=10)
  45. # find periodicities using the best frequency algorithm
  46. periods, powers, bases = p.best_frequency(win_size=None, n_periods=10)
  47. ## The window size, if not provided, is the same length as the input signal. A
  48. ## larger window is zero-padded, a smaller window is truncated (not good).
  51. ##################################
  52. ## QOPeriods
  53. ##################################
  55. # biggest different between this and Periods is that there is no need to pass
  56. # the data at construction
  57. p = QOPeriod() # make an instance
  59. # output is a tuple of a dictionary that contains all the information needed
  60. # to reconstruct the input signal
  61. output, residual = p.find_periods(c, n_periods=2, thresh=0.05)
  63. # get the original periods back as a tuple
  64. isolated_periods = period.get_periods(output['weights'], output['basis_dictionary'])
  66. ##################################
  67. ## RamanujanPeriods
  68. ##################################
  70. # biggest different between this and Periods is that there is no need to pass
  71. # the data at construction
  72. p = RamanujanPeriods() # make an instance
  74. # output is a tuple of a dictionary that contains all the information needed
  75. # to reconstruct the input signal
  76. output, residual = p.find_periods(c, thresh=0.2) # threshold is a fraction of the max energy in the periodogram
  78. # get the original periods back as a tuple
  79. isolated_periods = period.get_periods(output['weights'], output['basis_dictionary'])

Algorithms

Only for Periods (i.e. Setheres and Staley (* indicates Muresan and Parks orthogonalization is possible))

  • Small-to-large*
  • M-best
  • M-best gamma
  • Best correlation*
  • Best frequency*

Documentation

Forthcoming. Between the source and the paper, it should be pretty easy to understand in the meantime.

Requirements

  • numpy>=1.19.2
  • scipy>=1.7.1

Update Log

0.2.0

  1. - Added two classes (`QOPeriods` and `RamanujanPeriods`).
  2. - Removed samplerate requirement for `Periods.best_frequency()`.

Contributors

  • Jacob Sundstrom: University of California, San Diego