saftig.filtering.polylms

experiment in building a polynomial lms filter

Classes

PolynomialLMSFilter

Experimental non-linear LMS-like filter implementation

Functions

_lms_loop(witness, target, n_filter, idx_target, ...)

Run an LMS filter over intput sequences.

Module Contents

saftig.filtering.polylms._lms_loop(witness, target, n_filter, idx_target, filter_state, normalized, step_scale, coefficient_clipping, order)

Run an LMS filter over intput sequences.

Parameters:

  • witness (numpy.typing.NDArray) – Witness sensor data

  • target (numpy.typing.NDArray) – Target sensor data (is ignored)

  • n_filter (int) – Length of the FIR filter (how many samples are in the input window per output sample)

  • idx_target (int) – Position of the prediction

  • filter_state (numpy.typing.NDArray) – The initial FIR filter state

  • normalized (bool) – if True: NLMS, else LMS

  • step_scale (float) – the learning rate of the LMS filter

  • n_channel – Number of witness sensor channels

  • order (int) – polynomial order of the filter

  • pad – if True, apply padding zeros so that the length matches the target signal

  • update_state – if True, the filter state will be changed. If false, the filter state will remain

  • coefficient_clipping (float) –

Returns:

Prediction, Filter state, Target offset, Prediction length

Return type:

tuple[numpy.typing.NDArray, numpy.typing.NDArray, int, int]

class saftig.filtering.polylms.PolynomialLMSFilter(n_filter, idx_target, n_channel=1, normalized=True, step_scale=0.5, coefficient_clipping=np.nan, order=1)

Bases: saftig.filtering.common.FilterBase

Experimental non-linear LMS-like filter implementation Implements: \(x[n] = \sum_p\sum_i\sum_t {w_i[n-t]}^pH_{it}\) where p is the polynomial order, i the channel and t the index within the filter

Parameters:

  • n_filter (int) – Length of the FIR filter (how many samples are in the input window per output sample)

  • idx_target (int) – Position of the prediction

  • n_channel (int) – Number of witness sensor channels

  • normalized (bool) – If True: NLMS, else LMS

  • step_scale (float) – The learning rate of the LMS filter

  • coefficient_clipping (float) – If set to a positive float, FIR filter coefficients will be limited to this value. This can increase filter stability.

  • order (int) – Polynomial order of the filter

>>> import saftig as sg
>>> n_filter = 128
>>> witness, target = sg.evaluation.TestDataGenerator(0.1).generate(int(1e5))
>>> filt = sg.filtering.PolynomialLMSFilter(n_filter, 0, 1, step_scale=0.1, order=2, coefficient_clipping=4)
>>> filt.condition(witness, target)
>>> prediction = filt.apply(witness, target) # check on the data used for conditioning
>>> residual_rms = sg.evaluation.rms((target-prediction)[1000:])
>>> residual_rms > 0.05 and residual_rms < 0.15 # the expected RMS in this test scenario is 0.1
True
filter_state: numpy.typing.NDArray
normalized: bool
step_scale: float
coefficient_clipping: float
order: int
filter_name: str = 'PolyLMS'
reset()

reset the filter coefficients to zero

condition(witness, target)

Use an input dataset to condition the filter

Parameters:

  • witness (collections.abc.Sequence | numpy.typing.NDArray) – Witness sensor data

  • target (collections.abc.Sequence | numpy.typing.NDArray) – Target sensor data

apply(witness, target, pad=True, update_state=False)

Apply the filter to input data

Parameters:

  • witness (collections.abc.Sequence | numpy.typing.NDArray) – Witness sensor data

  • target (collections.abc.Sequence | numpy.typing.NDArray) – Target sensor data (is ignored)

  • pad (bool) – if True, apply padding zeros so that the length matches the target signal

  • update_state (bool) – if True, the filter state will be changed. If false, the filter state will remain

Returns:

prediction

Return type:

numpy.typing.NDArray