Sliding discrete fractional transforms

Fractional transforms are useful tools for processing of non-stationary signals. The methods of implementing sliding discrete fractional Fourier transform (SDFRFT), sliding discrete fractional cosine transform (SDFRCT) and sliding discrete fractional sine transform (SDFRST) for real time processing of signals are presented. The performances of these sliding transforms, with regard to computational complexity, variance of quantization error and signal-to-noise ratio (SNR), are presented and compared. The three sliding discrete fractional transforms are compared with sliding discrete Fourier transform (SDFT) in terms of SNR. Computational complexity in the case of sliding discrete fractional transform is less than that in the case of discrete fractional transform when a particular time–frequency bin is to be observed. In comparison with SDFT, the sliding discrete fractional transforms require less number of bits for representing coefficients. The SDFRST performs better in comparison with SDFRFT and SDFRCT.