np.fft.fft not producing expected results for large datasets in NumPy 1.24.3
I'm using NumPy version 1.24.3 to perform a Fast Fourier Transform on a large dataset, but I keep getting unexpected results. Specifically, when I apply `np.fft.fft` on an array with 10 million elements, the output seems to be cut off and doesn't match the expected frequency components. For testing, I'm using a simple sine wave signal: ```python import numpy as np import matplotlib.pyplot as plt t = np.linspace(0, 1, 10000) # Time vector signal = np.sin(2 * np.pi * 50 * t) + 0.5 * np.sin(2 * np.pi * 120 * t) # Signal with 50Hz and 120Hz # Upsampling the signal signal_large = np.repeat(signal, 1000) # Upsampling to 10 million samples # Performing FFT fft_result = np.fft.fft(signal_large) # Plotting the magnitudes plt.plot(np.abs(fft_result)) plt.title('FFT Magnitudes') plt.xlabel('Frequency Bin') plt.ylabel('Magnitude') plt.show() ``` When I run this code, the resulting plot shows a significant drop in magnitude at higher frequencies, which I wasn't expecting. I've checked the Nyquist criterion and ensured I'm sampling at a sufficient rate, but it still seems like some of the higher frequency components are missing. I also tried using `np.fft.fftfreq` to understand the frequency bins better, but the output doesn't align with the expected results: ```python freq_bins = np.fft.fftfreq(len(signal_large), d=1/10000) print(freq_bins) ``` I suspect it might have something to do with the large size of the dataset or the way I am upsampling the original signal. Has anyone else faced similar issues with `np.fft.fft` on large datasets, or can you suggest any best practices for ensuring accurate FFT results in such cases? The project is a REST API built with Python.