sdynpy.signal_processing.sdynpy_srs.sum_decayed_sines

• Module: sdynpy.signal_processing.sdynpy_srs

• Source: GitHub

Signature¶

def sdynpy.signal_processing.sdynpy_srs.sum_decayed_sines(sample_rate, block_size, sine_frequencies=None, sine_tone_range=None, sine_tone_per_octave=None, sine_amplitudes=None, sine_decays=None, sine_delays=None, required_srs=None, srs_breakpoints=None, srs_damping=0.05, srs_type=9, compensation_frequency=None, compensation_decay=0.95, number_of_iterations=3, convergence=0.8, error_tolerance=0.05, tau=None, num_time_constants=None, decay_resolution=None, scale_factor=1.02, acceleration_factor=1.0, plot_results=False, srs_frequencies=None, ignore_compensation_pulse=False, verbose=False)

Generate a Sum of Decayed Sines signal given an SRS.

Note that there are many approaches to do this, with many optional arguments so please read the documentation carefully to understand which arguments must be passed to the function.

Parameters¶

• sample_rate : float The sample rate of the generated signal.

• block_size : int The number of samples in the generated signal.

• sine_frequencies : np.ndarray, optional The frequencies of the sine tones. If this argument is not specified, then the sine_tone_range argument must be specified.

• sine_tone_range : np.ndarray, optional A length-2 array containing the minimum and maximum sine tone to generate. If this is argument is not specified, then the sine_frequencies argument must be specified instead.

• sine_tone_per_octave : int, optional The number of sine tones per octave. If not specified along with sine_tone_range, then a default value of 4 will be used if the srs_damping is >= 0.05. Otherwise, the formula of sine_tone_per_octave = 9 - srs_damping*100 will be used.

• sine_amplitudes : np.ndarray, optional The initial amplitude of the sine tones used in the optimization. If not specified, they will be set to the value of the SRS at each frequency divided by the quality factor of the SRS.

• sine_decays : np.ndarray, optional An array of decay value time constants (often represented by variable tau). Tau is the time for the amplitude of motion to decay 63% defined by the equation 1/(2*np.pi*freq*zeta) where freq is the frequency of the sine tone and zeta is the fraction of critical damping. If not specified, then either the tau or num_time_constants arguments must be specified instead.

• sine_delays : np.ndarray, optional An array of delay values for the sine components. If not specified, all tones will have zero delay.

• required_srs : np.ndarray, optional The SRS to match defined at each of the sine_frequencies. If this argument is not passed, then the srs_breakpoints argument must be passed instead. The default is None.

• srs_breakpoints : np.ndarray, optional A numpy array with shape (n,2) where the first column is the frequencies at which each breakpoint occurs, and the second column is the value of the SRS at that breakpoint. SRS values at the sine_frequencies will be interpolated in a log-log sense from this breakpoint array. If this argument is not specified, then the required_srs must be passed instead.

• srs_damping : float, optional Fraction of critical damping to use in the SRS calculation (e.g. you should specify 0.03 to represent 3%, not 3). The default is 0.03.

• srs_type : int The type of spectrum desired: If srs_type > 0 (pos) then the SRS will be a base acceleration-absolute acceleration model If srs_type < 0 (neg) then the SRS will be a base acceleration-relative displacement model (expressed in equivalent static acceleration units). If abs(srs_type) is: 1--positive primary, 2--negative primary, 3--absolute maximum primary 4--positive residual, 5--negative residual, 6--absolute maximum residual 7--largest of 1&4, maximum positive, 8--largest of 2&5, maximum negative 9 -- maximax, the largest absolute value of 1-8 10 -- returns a matrix s(9,length(fn)) with all the types 1-9.

• compensation_frequency : float The frequency of the compensation pulse. If not specified, it will be set to 1/3 of the lowest sine tone

• compensation_decay : float The decay value for the compensation pulse. If not specified, it will be set to 0.95.

• number_of_iterations : int, optional The number of iterations to perform. At least two iterations should be performed. 3 iterations is preferred, and will be used if this argument is not specified.

• convergence : float, optional The fraction of the error corrected each iteration. The default is 0.8.

• error_tolerance : float, optional Allowable relative error in the SRS. The default is 0.05.

• tau : float, optional If a floating point number is passed, then this will be used for the sine_decay values. Alternatively, a dictionary can be passed with the keys containing a length-2 tuple specifying the minimum and maximum frequency range, and the value specifying the value of tau within that frequency range. If this latter approach is used, all sine_frequencies must be contained within a frequency range. If this argument is not specified, then either sine_decays or num_time_constants must be specified instead.

• num_time_constants : int, optional If an integer is passed, then this will be used to set the sine_decay values by ensuring the specified number of time constants occur in the block_size. Alternatively, a dictionary can be passed with the keys containing a length-2 tuple specifying the minimum and maximum frequency range, and the value specifying the value of num_time_constants over that frequency range. If this latter approach is used, all sine_frequencies must be contained within a frequency range. If this argument is not specified, then either sine_decays or tau must be specified instead.

• decay_resolution : float, optional A scalar identifying the resolution of the fractional decay rate (often known by the variable zeta). The decay parameters will be rounded to this value. The default is to not round.

• scale_factor : float, optional A scaling applied to the sine tone amplitudes so the achieved SRS better fits the specified SRS, rather than just touching it. The default is 1.02.

• acceleration_factor : float, optional Optional scale factor to convert acceleration into velocity and displacement. For example, if sine amplitudes are in G and displacement is desired in inches, the acceleration factor should be set to 386.089. If sine amplitudes are in G and displacement is desired in meters, the acceleration factor should be set to 9.80665. The default is 1, which assumes consistent units (e.g. acceleration in m/s^2, velocity in m/s, displacement in m).

• plot_results : bool, optional If True, a figure will be plotted showing the acceleration, velocity, and displacement signals, as well as the desired and achieved SRS.

• srs_frequencies : np.ndarray, optional If specified, these frequencies will be used to compute the SRS that will be plotted when the plot_results value is True.

• ignore_compensation_pulse : bool, optional If True, the compensation pulse will be ignored.

• verbose : True, optional If True, additional diagnostics will be printed to the console.

Returns¶

• acceleration_signal : ndarray The acceleration signal that satisfies the SRS.

• velocity_signal : ndarray The velocity of the acceleration signal.

• displacement_signal : ndarray The displacement of the acceleration signal.

• sine_frequencies : ndarray An array of frequencies for each sine tone, including the compensation pulse

• sine_amplitudes : ndarray An array of amplitudes for each sine tone, including the compensation pulse

• sine_decays : ndarray An array of decay values for each sine tone, including the compensation pulse

• sine_delays : ndarray An array of delay values for each sine tone, including the compensation pulse

• fig : matplotlib.Figure A reference to the plotted figure. Only returned if plot_results is True.

• ax : matplotlib.Axes A reference to the plotted axes. Only returned if plot_results is True.