Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

Area of Science:

• Signal Processing
• Metrology
• Optics

Background:

• Conventional discrete Fourier transform (DFT) has limitations in frequency resolution.
• Improving frequency resolution is crucial for precise measurements in various scientific fields.

Purpose of the Study:

• To propose and validate a method for improving frequency resolution in DFT using sub-bins.
• To demonstrate the effectiveness of sub-bins for precise measurement of Doppler signals.

Main Methods:

• Developing sub-bin assignments within conventional DFT bin intervals by reducing sampled data.
• Conducting simulations and experiments using signal oscillators, digital oscilloscopes, and PCs.
• Measuring sub-bin spectra, linearity, and Doppler signals from a He-Ne laser optical interferometer.

Main Results:

• Successfully measured sub-bin spectra between conventional DFT bins, aligning with simulations.
• Demonstrated linearity of sub-bin spectrum intensity across a range of input signal amplitudes.
• Achieved a one-order improvement in displacement precision (32 nm) for an optical interferometer using sub-bins.

Conclusions:

• Sub-bins offer a viable method to enhance frequency resolution in DFT.
• The proposed sub-bin technique significantly improves precision in optical metrology applications.
• Sub-bins are a versatile tool applicable across diverse scientific and engineering domains.