As generalization of the fractional Fourier transform （FRFT）, the linear canonical transform （LCT） has been used in several areas, including optics and signal processing. Many properties for this transform are alr...As generalization of the fractional Fourier transform （FRFT）, the linear canonical transform （LCT） has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform （FFT）, which has much lower computational load than the construction method in the linear canonical domain.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.60232010 and 60572094)the Ministerial Foundation of China(Grant No.6140445).
文摘As generalization of the fractional Fourier transform （FRFT）, the linear canonical transform （LCT） has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform （FFT）, which has much lower computational load than the construction method in the linear canonical domain.
