Frequency resolution improvement by sub-bins and an inverse matrix in discrete Fourier transform

We proposed a method to use sub-bins (SBs) and the inverse matrix to reduce the spectral leakage in discrete Fourier transform (DFT) over the conventional spectral resolution. SBs were assigned between two conventional bins. Utilizing the real signal, the process reproducing complex amplitudes at each SB was described and confirmed through simulations with the pseudo-inverse matrix. In experiments, with the 256 number of data, the frequency interval of k=107 and 108 was 4 divided by SBs. The single-peak spectrum at each SB frequency was measured clearly. Using the two signals with frequencies corresponding to two SBs within the conventional bin interval, the spectrum with two peaks was also measured. The linearity was confirmed for the input range from 0.1-5 V. The feasibility of this method to improve the frequency resolution has been shown for various optical applications.