Direct FFT oversampling without zero-padding

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Abstract
The Fast Fourier Transform (FFT) is the most powerful and widely used method for transforming signals from the time domain to the frequency domain, being employed in cutting-edge research fields. Achieving high-accuracy FFT involves increasing the number of frequency points through frequency oversampling, typically by extending the time-domain signal with zeros (zero-padding) and applying the FFT to the extended signal. While increasing the number of zeros enhances the precision of the results, it also substantially raises the computational load. To address the high computational demands associated with traditional frequency oversampling, this paper proposes a direct oversampling method. By employing a non-integer number of cycles within the FFT kernel, the method achieves spectral analysis results identical to those obtained with zero-padded oversampling but with a significantly lower computational cost. Specifically, it reduces the complexity from O(Mlog2M) to O(Mlog2N), where N is the original signal length and M is the oversampled frequency resolution. This approach eliminates zero-padding altogether, providing a mathematically equivalent and more efficient alternative for applications requiring high spectral resolution.

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