Optimal filtering in fractional Fourier domains
Optimal filtering in fractional Fourier domains
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DOI：
10.1109/icassp.1995.480329
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发表时间：
1995-05
期刊：
影响因子：
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通讯作者：
M. Kutay;Haldun M. Özaktas;O. Arikan;L. Onural
中科院分区：
文献类型：
--
作者：
M. Kutay;Haldun M. Özaktas;O. Arikan;L. Onural
普通傅立叶变换最适合于分析和处理时不变信号和系统。当我们处理时变信号和系统时，在分数傅立叶域中的滤波可以使我们以较小的最小均方误差（MSE）估计信号。我们推导出最佳的分数傅立叶域滤波器，最大限度地减少MSE给定的非平稳信号和噪声统计，和随时间变化的失真内核。我们提出了一个例子，其中的MSE减少了50倍，作为在分数傅立叶域中的滤波的结果，与传统的傅立叶或时域中的滤波相比。我们还讨论了分数傅里叶变换如何可以计算在O（N log N）的时间，使性能的改善，实现了很少或没有增加计算复杂度。
The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum mean square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.