pulse_transitions

This library implements a python version of the Pulse and Transition Metrics function category in Matlab.

Example Use Case

For the full example see examples/second_order_system.py.

import numpy as np
from scipy.signal import lsim
from scipy.signal import lti

from pulse_transitions import detect_edges
from pulse_transitions import detect_signal_levels
from pulse_transitions import get_edge_metrics


# Example: synthetic underdamped step response
def generate_step_response(t, damping=0.2, freq=10):
    # Second-order system parameters
    wn = freq          # Natural frequency (rad/s)
    zeta = damping        # Damping ratio

    # Transfer function: H(s) = wn^2 / (s^2 + 2*zeta*wn*s + wn^2)
    num = [wn**2]
    den = [1, 2*zeta*wn, wn**2]

    # Create the system
    system = lti(num, den)

    u = [0]*len(t[t<0]) + [1]*len(t[t>=0])
    t_shift = t-min(t)
    t_out, y_out, _ = lsim(system, U=u, T=t_shift)

    return t, y_out

# Generate data
t = np.linspace(-0.25, 1, 1000)
t_out, y = generate_step_response(t, freq=25/(max(t)))

threshold_fractions=(0.1, 0.9)

# Estimate levels (e.g. using histogram or endpoints)
levels = detect_signal_levels(x=t, y=y, method="histogram")
low, high = levels

# Detect edges
edge = detect_edges(t, y, levels=levels, fractional_thresholds=threshold_fractions)[0]

# Compute overshoot / undershoot
metrics = get_edge_metrics(x=t, y=y, fractional_thresholds=threshold_fractions, levels=levels)

Measuring one edge of a signal that has several

A trace that steps through several levels (a TDR trace has a new level after every discontinuity) has no single pair of levels. measure_edge takes the edge nearest a place you give, rising or falling, and measures it between the flat parts either side of it (or levels you pass):

from pulse_transitions import EdgeNotFound, measure_edge

try:
    measured = measure_edge(t, y, around=2.5, max_distance=0.2, fractional_thresholds=(0.2, 0.8))
except EdgeNotFound as error:  # also an IndexError and a ValueError
    print(error)
else:
    bottom, top = measured.levels
    print(measured.edge.start, measured.edge.end, measured.duration)

Edge.start and Edge.end are the first and the last threshold crossing in time order, so a falling edge crosses its high threshold at start.

Errors

Unknown keyword arguments raise TypeError rather than being ignored (thresholds= is fractional_thresholds=). Functions that look for an edge return [] or None when there is none; measure_edge raises EdgeNotFound.

Installation

pypi

pip install pulse_transitions

GitHub Release

pip install https://github.com/snhobbs/pulse_transitions/archive/refs/tags/<TAGNAME>.zip

From Source

git clone https://github.com/snhobbs/pulse_transitions/
pip install .

Matpulse Functions

Background & Resources

HP Journal

There's an excellent description of the algorithms used by HP here.

Control Library

• GitHub
• Docs