We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take $sim Nlog N$ time, where $N$ is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.
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机译:我们处理从原始函数的样本中高效,准确地对函数的线性典范变换(LCT)样本进行数字计算的问题。提出并比较了两种方法。第一种基于将LCT分解为线性调频乘法,傅立叶变换和缩放操作。第二种方法基于将LCT分解为分数阶Fourier变换,然后进行缩放和线性调频乘法。两种算法都花费$ sim Nlog N $时间,其中$ N $是信号的时间带宽积。准确性的唯一必要偏差是连续傅立叶变换与离散傅立叶变换之间的近似值。因此,就速度和准确性而言,这些算法在计算傅立叶变换时,以与快速傅立叶变换算法相似的性能来计算LCT。
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