In this question, you will learn how to denoise a signal using the Fourier series.
The signal you see below is a noisy signal. It is in the form of a function f(x). The variable
X contains the x-coordinates of the points and Y contains the height of the function.
You must find the original signal. The original signal (not noisy) is a function
g(x)=a0+a1sin(x)+a2sin(2x)+...+a5sin(5x)
from matplotlib import pyplot as plt
import numpy as np
import numpy.random as NPR
student_no = 2060277 # Change this number to your student number
npr.seed(student_no)
a, b = -np.pi, np.pi
X = np.linspace(a, b, 200)
Y = np.zeros_like(X) + npr.randint(-4,4)
for i in range(3):
Y = Y + npr.randint(1,5)np.sin(npr.randint(0,6)X)+ npr.normal(0, 0.5, X.shape[0])
plt.plot(X, Y)
plt.show()
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My code :
A = np.array(X)
B = np.array(Y)
integrale = 0
for i in range(199):
integrale = integrale + (A[i+1]-A[i])*B[i]*np.sin(i)
a0 = integrale/(2*np.pi)
an = integrale/np.pi
if 5 >= i > 0:
print("Coefficient a_n :", an)
elif i==0:
print("Coefficient a_n :", a0)
The values in the output are really too low, I'm supposed to obtain 5 natural numbers for a_n and 1 for a_0. The graph containing the noisy signal is here. It's determine by the function above My code.
