How to generate exponential pulse time series data in python
Use of exponential pulse time series data
It is used when you want to easily generate a pulse with python when you want to generate a pseudo time series data and simulate it in order to detect the pulse of a photon detector.
If you can understand it by reading the code, please refer to google Colab page.
How to generate a pulse
Probably the simplest pulse waveform would use the difference in the exponential function. Let a be the pulse decay time constant, b be the pulse rise time constant, and A be the amplitude.
python
A \times ( e^{-t/a} - e^{-t/b} )
Call like.
How to generate one pulse
python
#Form a waveform by the difference between two exponential functions
def pulse(a = 1.0, t1 = 1e-3, t2 = 5e-3, dlen=1024, dt = 1e-4):
t = np.linspace(0, dt * (dlen-1), dlen)
y = a * (np.exp(-t/t2) - np.exp(-t/t1) )
return t, y
By default, dlen = 1024 is used to generate 1024 sample data, and the time interval dt = 1e-4 is assumed to be about 0.1 ms. Assuming a rise time of 1ms and a fall time of 5ms with t1 = 1e-3 and t2 = 5e-3.
If you generate a pulse with this,
It becomes like.
A little more elaborate generation method
Let's generate a slightly longer pulse.
#Example of adding zero data
t0, y0 = pulse(a = 0, dlen = 100)
t = np.hstack((t,t[-1]+t0))
y = np.hstack((y,y0))
#Amplitude 0.Add 5 pulses
t1, y1 = pulse(a = 0.5, dlen = 1024)
t = np.hstack((t,t[-1]+t1))
y = np.hstack((y,y1))
#Amplitude 0.Add 8 pulses
t1, y1 = pulse(a = 0.8, dlen = 1024)
t = np.hstack((t,t[-1]+t1))
y = np.hstack((y,y1))
#Amplitude 0.Add 3 pulses
t1, y1 = pulse(a = 0.3, dlen = 1024)
t = np.hstack((t,t[-1]+t1))
y = np.hstack((y,y1))
plt.plot(t,y,".")
When this is plotted, it looks like this.
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