带限函数的无符号采样重建
Reconstruction of Bandlimited Functions from Unsigned Samples
AI总结：
研究从可能非均匀采样的绝对值中恢复实值带限函数，证明采样率超过奈奎斯特率两倍时重建总是可行，并提出了基于FFT的指数收敛算法。
摘要：
我们考虑从可能非均匀采样的样本绝对值中恢复实值带限函数。我们证明，如果函数以超过其奈奎斯特率两倍的速率采样，则这种重建总是可能的；而如果采样率低于奈奎斯特率的两倍，则可能无法实现。在均匀采样的情况下，我们还描述了一种基于FFT的算法来执行重建。我们证明该算法在使用的样本数量上呈指数收敛，并在一些测试案例中检验了其数值行为。
英文摘要：
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
