2009/11/03 by Ayush Bhandari, Pina Marziliano · 1 citation
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods #Digital Filter Design and Implementation #Bandlimiting #Fractional Fourier transform #Fourier transform #Signal reconstruction #Sampling (signal processing) #Mathematics #Algorithm #Discrete-time signal #Multidimensional signal processing #Nonuniform sampling #Discrete Fourier transform (general) #Discrete-time Fourier transform #SIGNAL (programming language) #Frequency domain #Non-uniform discrete Fourier transform #Nyquist–Shannon sampling theorem #Spectral density estimation #Computer science #Fourier analysis #Signal processing #Mathematical analysis #Analog signal #Signal transfer function #Filter (signal processing) #Telecommunications #Computer vision #Transmission (telecommunications)
paper · doi:10.1109/lsp.2009.2035242
openalex publication_date 2009/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain-a transformation which generalizes the conventional Fourier transform-has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem for fractional bandlimited (or fractional Fourier bandlimited) signals are the same as for the Fourier domain case i.e. sampling (and reconstruction) in FrFT domain can be seen as an orthogonal projection of a signal onto a subspace of fractional bandlimited signals. As neat as this extension of Shannon's framework is, it inherits the same fundamental limitation that is prevalent in the Fourier regime-what happens if the signals have singularities in the time domain (or the signal has a nonbandlimited spectrum)? In this paper, we propose a uniform sampling and reconstruction scheme for a class of signals which are nonbandlimited in FrFT sense. Specifically, we assume that samples of a smoothed version of a periodic stream of Diracs (which is sparse in time-domain) are accessible. In its parametric form, this signal has a finite number of degrees of freedom per unit time. Based on the representation of this signal in FrFT domain, we derive conditions under which exact recovery of parameters of the signal is possible. Knowledge of these parameters leads to exact reconstruction of the original signal.