I am new to signal processing. And I am puzzled when studying FFT. I create time series plus a random noise in Python:
import numpy as np
x = np.linspace(-50,50,N)
noise = np.random.random(N)*0.1
y = np.sin(2*np.pi*x/10) + noise
Then perform FFT to the time series and get power spectrum. But I find the spectrum is totally different when I execute my script each time. I know it must be the random noise's effect, which are different in different execution. However, as you can see, the sine function is periodic, so we should see clearly a signal in the power spectrum. The puzzle is, the very strong periodic "signal" is submerged in the noise in frequency domain FOR SOMETIME.
I want to know how the noise in time domain affect the noise&signal in frequency domain.