The effect of noise on numerical integration

noiseless.png

noiseless.py

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt

# Testing data that can be replaced with file load-in
x=np.linspace(0,100,201)
accel=np.zeros_like(x)
accel[30:32]=1
accel[50:52]=-1

velocity=integrate.cumtrapz(accel,x,initial=0)

plt.plot(x,accel,label="Pulses")
plt.plot(x,velocity,label="Integrate")
plt.legend()
plt.show()

noisy.png

noisy.py

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt

# Testing data that can be replaced with file load-in
x=np.linspace(0,100,201)
accel=np.zeros_like(x)
accel[30:32]=1
accel[50:52]=-1
ran=np.random.rand(201)
ran-=0.5
ran*=0.04
accel+=ran

velocity=integrate.cumtrapz(accel,x,initial=0)

plt.plot(x,accel,label="Pulses")
plt.plot(x,velocity,label="Integrate")
plt.legend()
plt.show()