import numpy as np
import matplotlib.pyplot as plt

"""generate signal"""
oversampling_factor = 5.0  # when initial Fs = 1600 - interpolate with (1600 * oversampling_factor)
Fs = 1000.0  # sampling frequency
n = 500.0
x = np.arange(n)
y_time = [np.random.randn() for item in range(0, int(n))]  # create white noise

"""interpolate"""
x_interpolated = np.arange(0.5, n, 1.0)  # only shifted
y_interpolated1 = np.interp(x_interpolated, x, y_time)
x_interpolated2 = np.arange(0.0, n, 1.0/oversampling_factor)  # oversampled
y_interpolated2 = np.interp(x_interpolated2, x, y_time)

"FFT"
y_freq = np.abs(np.fft.rfft(y_time)) / len(y_time)  # original signal
y_freq_shifted = np.abs(np.fft.rfft(y_interpolated1)) / len(y_interpolated1)  # shifted signal
y_freq_oversampled = np.abs(np.fft.rfft(y_interpolated2)) / len(y_interpolated2)  # oversampled signal

x_freq = np.fft.rfftfreq(len(y_time), d=(1.0 / Fs))
x_freq_shifted = np.fft.rfftfreq(len(y_interpolated1), d=(1.0 / Fs))
x_freq_oversampled = np.fft.rfftfreq(len(y_interpolated2), d=(1.0 / (Fs * oversampling_factor)))  # original signal

"""plot the results"""
plt.subplot(211)
plt.plot(x, y_time)
plt.xlim([0, n])
plt.xlabel('sample')
plt.subplot(212)
plt.plot(x_freq, y_freq, label='original')
plt.plot(x_freq_shifted, y_freq_shifted, label='shifted')
plt.plot(x_freq_oversampled, y_freq_oversampled, label='oversampled')
plt.legend()
plt.xlim([0, Fs/2])
plt.xlabel('frequency [Hz]')
plt.show()