Fast DFT computation for signals with spectral support

Charantej Reddy Pochimireddy, V. S. S. P. Tej, Aditya Siripuram
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Abstract

We consider the problem of computing the Discrete Fourier transform (DFT) of an N- length signal which has only k non-zero DFT coefficients at known locations. We say that a set of indices is spectral if there exists a DFT submatrix (square) with those columns that is unitary up to scaling. When the DFT support set is spectral and N is a prime power, we prove that this can be done in O(klogk) operations using k samples provided the DFT support. This is a generalization of a similar recent result for the case when N is a power of 2.
具有谱支持的信号的快速DFT计算
我们考虑一个N长度信号的离散傅里叶变换(DFT)的计算问题,该信号在已知位置上只有k个非零DFT系数。我们说一组指标是谱的,如果存在一个DFT子矩阵(方阵),它的列在尺度上是酉的。当DFT支持集是谱的并且N是素幂时,我们证明了这可以在O(klogk)个操作中完成,使用k个样本提供DFT支持。这是对最近N是2的幂的类似结果的推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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