IIRrational: Rational Function fitting for System ID

Release v2.5.1. (Installation)

IIRrational is an function-fitting library for signal processing and system identification. Fitting both poles and zeros for a rational function is a nonlinear optimization problem and typical formulations require an initial guess for convergence.

This library uses a two stage approach, where the second stage is a typical gradient descent optimization, but the first is a linear technique with fast and reliable convergence, but requires gratuitous over-fitting.

Features and Conveniences

  • No initial guess required (most of the time)

  • Automatic order reduction (using heuristics)

  • guaranteed stable poles or zeros upon request.

  • uses SNR weight vector

  • generates fisher matrix / covariance matrix of parameterizations

  • propagates errorbars to the fit

  • S-domain for implementable filters

  • matlab support through the msurrogate package

see What to Expect and quickstart

import IIRrational.v2
from IIRrational.testing import IIRrational_data

dataset = IIRrational_data('simple2')
results = IIRrational.v2.data2filter(
    data = dataset.data,
    F_Hz = dataset.F_Hz,
    SNR  = dataset.SNR,
    F_nyquist_Hz = 16384,
axB = results.investigate_fit_plot()
axB = results.investigate_order_plot()
fit output

and to choose the order which should be used, the order plot will show the residuals

fit order

Example Output

Running the example above from the command line

IIRrationalV2fit :simple2: simple2_fit.mat --plot_fit simple2_fit_example.png --plot_order simple2_fit_example_order.png --choose baseline

This uses a special file :testdata: to get its data. It can import data from matlab data files, hdf5, yaml, json and CSV using the command line interface. Learn more through help:

IIRrationalV2fit -h

Which outputs on the commandline the logging and foton filter:

  F_Hz: [(1000,) float64 array]
  F_nyquist_Hz: None
  SNR: 10
  data: [(1000,) complex128 array]
  emphasis: None
  mode: full
  xfer: [(1000,) complex128 array]
------------:rational fitting:
4P   0.01    chebychev rational fit
3P   1.13    Initial Order: (Z=20, P=20, Z-P=0)
3P   1.72    Fastdrop Order: (Z=12, P=12, Z-P=0)
4P   2.32  mag fitting and phase patching
------------:sample variance (from magnitude):
3A   3.78    Weight Scaling determined:  0.9740626973315305
3A   3.78    Weight Scaling Used  0.9869461471283681
------------:Q-ranked order reduction:
4P   5.84    order reduced annealing
------------:selective order reduction:
5P  14.96    order reduced to 11, residuals=1.82e+01
5P  20.46    order reduced to 9, residuals=1.83e+01
5P  28.16    order reduced to 8, residuals=9.71e+00
5P  40.08    order reduced to 7, residuals=2.17e+00
5P  42.43    order reduced to 7, residuals=9.66e-01
5P  43.46    order reduced to 6, residuals=9.64e-01
2A  44.41  Baseline fit residuals: 9.64e-01, at order 6
------------:successive order reduction:
5P  45.45    order reduced to 4, residuals=4.05e+00
5P  46.23    order reduced to 4, residuals=1.02e+01
5P  46.81    order reduced to 3, residuals=6.40e+00
5P  47.02    order reduced to 3, residuals=3.16e+01
5P  47.15    order reduced to 2, residuals=4.22e+01
2I  47.16    max(z, p)       ChiSq.
                  order    avg. res.    med. res.    max. res.
            -----------  -----------  -----------  -----------
                      2    42.1719       39.7239      704.977
                      3     6.40444       2.9071      745.896
                      4     4.05173       1.85803     693.821
                      6     0.963768      1.28386      13.4802
plotting for -R, --plot_order=simple2_fit_example_order.png
-L, --LIGO_foton=Sf output:
  -0.104504805261 + 1.09613226443*i; -0.104504805261 - 1.09613226443*i;
  -0.98417325191 + 0.169021580444*i; -0.98417325191 - 0.169021580444*i;
  -0.00956418703895 + 0.998886697835*i; -0.00956418703895 - 0.998886697835*i;
  -0.0981823932483 + 2.99528020808*i; -0.0981823932483 - 2.99528020808*i;
  -0.114527880324; -0.0817740982447;
], 39.3478656882, "f")
plotting for -r, --plot_fit=simple2_fit_example.png

You may notice that the initial residuals from the automated fit are poor. Try calling it with the addiational argument –relative-degree -2 and the intial guess will have converged better.


when the library is installed, the command line tool may also be called via::

python -m IIRrational.v2 [args…]