欠采样信号恢复的几个定理

Theorems for Signal Restoration from Undersampled Samples

本文建立了从欠采样数据准确重建原始带限信号的方法,对带限信号f(t),若存在小于1的正有理数α,使f^n(t)带限,则f(t)可以从采样率大于Nyquist率α倍的采样数据无误差地恢复,计算结果与本文建立的理论符合得很好.

A method for bend-limited signal reconstruction from undersampled samples is developed here. It isshown that, for a band-limited signal, say f(t), if there exists a rational number α satisfying that f^n(t) is alsobend-limited, where 0<α<1, then f(t) can be precisely restorated from the points sampled with the fiequencyhigher than α times the Nyquist rate of f(t). Computing results agree with the theory perfectly.