I am manually compute the inverse FFT using the numpy FFT components by the below codes, to compare the rebuild signal with the original signal(sin function). As shown in the results, the error(original -rebuilt) is increasing along the x axis. Does anyone know the reasons and how to correct it. If I used the build-in function ifft to rebuild the signal,the error doesn't have this increase tread along x axis. import numpy as np from scipy import * from matplotlib import pyplot as plt tempdata = np.loadtxt("sinx_80.dat") x_positions = tempdata[:, 0] delta_x=x_positions[1] - x_positions[0] roughness_data = tempdata[:, 1] fft_1d = np.fft.fft(roughness_data) num_x = len(fft_1d) freq_x = np.fft.fftfreq(num_x, d=delta_x) reconstructed_surface=np.zeros(num_x) x_grid = (x_positions - x_positions[0]) for n in range(num_x): amplitude = np.abs(fft_1d[n]) / (num_x) phase = np.angle(fft_1d[n]) reconstructed_surface += amplitude * np.cos(2 * np.pi * (freq_x[n] * x_grid) + phase) difference = roughness_data - reconstructed_surface max_error = np.max(np.abs(difference)) rms_error = np.sqrt(np.mean(difference**2)) print(f"Max Error: {max_error}") print(f"RMS Error: {rms_error}") plt.figure(figsize=(12, 8)) plt.subplot(3, 1, 1) plt.plot(x_positions, roughness_data, label="Original Data", color="blue") plt.title("Original Data") plt.legend() plt.grid() plt.subplot(3, 1, 2) plt.plot(x_positions, reconstructed_surface, label="Reconstructed Data", color="orange") plt.title("Reconstructed Data") plt.legend() plt.grid() plt.subplot(3, 1, 3) plt.plot(x_positions, difference, label="Difference (Original - Reconstructed)", color="red") plt.title("Difference") plt.legend() plt.grid() plt.show() Continue reading...
