A fuzzy discrete Fourier transform for reduction of spectral leakage

The discrete Fourier transform (DFT) is a standard technique used in signal processing for examining the frequency spectrum of a sampled signal. While the DFT is a powerful tool, it is susceptible to spectral leakage. For example, leakage occurs when the frequency of an input signal does not exactly match one of the DFT output frequencies. In such cases, much of the energy of the input signal is spread across the entire spectrum of the DFT output, reducing the signal-to-noise ratio (SNR) of the signal. In this paper, a fuzzy DFT scheme is presented which gives up some precision in positioning the frequency of fluctuating or non-matched signals in favour of reducing or in some cases eliminating entirely spectral leakage