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pythonmatheventssignal-processingnumerical-integration

Determining the event location on an oscillatory signal

I am doing an event-driven integration and one of the events should detect when a signal has the amplitude lower than some value/limit.

In example, a decaying sine signal:

signal = sin(t)*exp(-t/50)
limit = 0.05

Decaying sine signal

From the figure, it can be seen that the condtition should be met at t =~ 90. Although I can see it, I would like to get the location numerically during integration. How can I do this? How can I define the condition?

Note: If I just take the first crossing of the limit = 0.05 it occurs at t =~ 0.05, which is obviously not what I want.

Solution

  • You can compute the envelope using either scipy.signal.hilbert:

    import numpy as np
from scipy import signal

# Add some padding to limit the periodic extension effect
padlen = int(np.floor(0.1*len(x)))
y = np.pad(x, (0,padlen), mode='edge');
# Compute the envelope
envelope = np.abs(signal.hilbert(y));
# Truncate to the original signal length
envelope = envelope[:-padlen]

    Or using a simple diode detector implementation:

    def diode_detector(x,alpha):
    xmax = abs(x[0])
    y = np.array(x)
    for i in np.arange(len(x)):
        if (xmax < abs(x[i])):
            xmax = abs(x[i])
        else:
            xmax = alpha*xmax
        y[i] = xmax
    return y

# you may need to tweak the alpha parameter depending on your signal bandwidth
envelope = diode_detector(x,0.9997)

    Then it simply a question of computing the trigger location:

    T = t[1]-t[0]
print T*np.min(np.where(envelope < limit))