Sliding Discrete Linear Canonical Transform

The linear canonical transform (LCT) has been shown to be one of the most powerful tools in signal processing, and in this paper, we propose an adaptive approach for the computation of the discrete LCT (DLCT), termed the sliding discrete linear canonical transform (SDLCT). First, we introduce a scheme for the single-point DLCT, which can effectively calculate a single or a few linear canonical spectra. Second, the SDLCT is proposed based on an iterative algorithm to meet the requirements of online spectral analysis when only a subset of <inline-formula> <tex-math notation="LaTeX">$N$</tex-math></inline-formula> frequencies are required from an <inline-formula> <tex-math notation="LaTeX">$\tilde{N}\hbox{--}$</tex-math></inline-formula>point discrete LCT (<inline-formula> <tex-math notation="LaTeX">$N\leq \tilde{N}$</tex-math></inline-formula>). The additivity and reversibility properties of the proposed algorithms are also discussed in detail. Third, the DLCT convolution operation is obtained to reduce the spectral leakage of the proposed algorithm, and time-domain windowing is implemented via frequency-domain convolution. Finally, we present two methods to assess performance with regard to computational complexity and precision and to show the correctness of the derived results.