Signals In Fractional Fourier Transform Domain Research Articles

Theoretical and experimental study of hybrid optical computing engine for arbitrary-order FRFT.

Fractional Fourier transform (FRFT) is the generalization of Fourier transform. It provides many significant advantages, such as fractional order as the new degree of freedom and high efficiency and great performance for non-stationary signal analysis/processing, that other operations including Fourier transform cannot. Here, we report a hybrid optical system for computation of arbitrary-order FRFT of temporal signals. In experiment, the fractional-domain information of input temporal signals could be directly acquired by detector. In addition, the optical computing results are in good agreement with numerical results. Then we apply the optical computing engine to demodulation of chirp spread spectrum signals. Using sub-Nyquist sampling, the proposed technology could greatly save the number of measurements in demodulation. The compression ratio could be as low as 0.4%, because of the high compression performance of chirp signals in FRFT domain. As a result, the proposed technology has unique advantages in analysis and information extraction for non-stationary signals, especially for chirp-like signals, and may become a powerful optical time-frequency analysis tool for temporal signals.

Study of VLF Communication Technique Based on FRFT

The atmospheric noise generated by lightning phenomena is the main source of interference in VLF communications, it is rather difficult to detect the communication signal that not only merged in strong channel noise, but probably interfered by high-tension impulse caused by thunder. This paper, Alpha stable distribution noise model is proposed to simulate atmospheric noise firstly, then, we study a new technique of Chirp Spread Spectrum (CSS) communication based on Fractional Fourier Transform (FRFT), This paper studies a new VLF communication technique of the Chirp Spread Spectrum (CSS) communication based on Fractional Fourier Transform (FRFT), and it demodulates message utilizing energy gathering property of chirp signal in FRFT domain.

Simulation of VLF CSS System in Atmospheric Noise

Very Low Frequency (VLF) communication is designed to operate in the frequency between 3 kHz and 30 kHz. The atmospheric noise generated by lightning phenomena is the main source of interference in VLF communications, it is rather difficult to detect the communication signal that not only merged in strong channel noise, but probably interfered by high-tension impulse caused by thunder. This paper, Alpha stable distribution noise model is proposed to simulate atmospheric noise firstly, then, we study a new technique of Chirp Spread Spectrum (CSS) communication based on Fractional Fourier Transform (FRFT), This paper studies a new VLF communication technique of the Chirp Spread Spectrum (CSS) communication based on Fractional Fourier Transform (FRFT), and it demodulates message utilizing energy gathering property of chirp signal in FRFT domain.

Sampling and Reconstruction of Sparse Signals in Fractional Fourier Domain

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.