sdynpy.signal_processing.sdynpy_harmonic.vold_kalman_filter

vold_kalman_filter(sample_rate, signal, arguments, filter_order=None, bandwidth=None, method=None, return_amp_phs=False, return_envelope=False, return_r=False)[source]

Extract sinusoidal components from a signal using the second generation Vold-Kalman filter.

Parameters

  • sample_rate (float) – The sample rate of the signal in Hz.

  • signal (ndarray) – A 1D signal containing sinusoidal components that need to be extracted

  • arguments (ndarray) – A 2D array consisting of the arguments to the sinusoidal components of the form exp(1j*argument). This is the integral over time of the angular frequency, which can be approximated as 2*np.pi*scipy.integrate.cumulative_trapezoid(frequencies,timesteps,initial=0) if frequencies is the frequency at each time step in Hz timesteps is the vector of time steps in seconds. This is a 2D array where the number of rows is the number of different sinusoidal components that are desired to be extracted, and the number of columns are the number of time steps in the signal argument.

  • filter_order (int, optional) – The order of the VK filter, which should be 1, 2, or 3. The default is 2. The low-pass filter roll-off is approximately -40 dB per times the filter order.

  • bandwidth (ndarray, optional) – The prescribed bandwidth of the filter. This is related to the filter selectivity parameter r in the literature. This will be broadcast to the same shape as the arguments argument. The default is the sample rate divided by 1000.

  • method (str, optional) – Can be set to either ‘single’ or ‘multi’. In a ‘single’ solution, each sinusoidal component will be solved independently without any coupling. This can be more efficient, but will result in errors if the frequencies of the sine waves cross. The ‘multi’ solution will solve for all sinusoidal components simultaneously, resulting in a better estimate of crossing frequencies. The default is ‘multi’.

  • return_amp_phs (bool) – Returns the amplitude and phase of the reconstructed signals at each time step. Default is False

  • return_envelope (bool) – Returns the complex envelope and phasors at each time step. Default is False

  • return_r (bool) – Returns the computed selectivity parameters for the filter. Default is False

Raises

ValueError – If arguments are not the correct size or values.

Returns

  • reconstructed_signals (ndarray) – Returns a time history the same size as signal for each of the sinusoidal components solved for.

  • reconstructed_amplitudes (ndarray) – Returns the amplitude over time for each of the sinusoidal components solved for. Only returned if return_amp_phs is True.

  • reconstructed_phases (ndarray) – Returns the phase over time for each of the sinusoidal components solved for. Only returned if return_amp_phs is True.

  • reconstructed_envelope (ndarray) – Returns the complex envelope x over time for each of the sinusoidal components solved for. Only returned if return_envelope is True.

  • reconstructed_phasor (ndarray) – Returns the phasor c over time for each of the sinusoidal components solved for. Only returned if return_envelope is True.

  • r (ndarray) – Returns the selectivity r over time for each of the sinusoidal components solved for. Only returned if return_r is True.