Direct FFT oversampling without zero-padding.

Area of Science:

• Signal Processing
• Computational Mathematics

Background:

• The Fast Fourier Transform (FFT) is crucial for time-to-frequency domain signal transformation.
• High-accuracy FFT often requires frequency oversampling via zero-padding, increasing computational load.
• Existing methods face computational challenges with increased precision requirements.

Purpose of the Study:

• To propose a direct oversampling method for FFT.
• To achieve high spectral resolution with reduced computational complexity.
• To offer a computationally efficient alternative to zero-padding.

Main Methods:

• Developed a direct oversampling technique for FFT.
• Implemented a non-integer number of cycles within the FFT kernel.
• Avoided zero-padding by directly calculating oversampled spectral points.

Main Results:

• The direct oversampling method yields results mathematically equivalent to zero-padded FFT.
• Achieved a significant reduction in computational complexity from O(Mlog2M) to O(Mlog2N).
• Demonstrated a more efficient approach for high spectral resolution analysis.

Conclusions:

• The proposed direct oversampling method offers a computationally efficient alternative to traditional FFT oversampling.
• This technique provides identical spectral analysis accuracy without the high computational cost of zero-padding.
• Enables advanced signal processing applications requiring high spectral resolution with lower resource demands.