利用非均勻取樣不穩定信號並重建

Abstract

利用信號的非均勻取樣點來重建它，在很多應用上是個重要的議題，尤其是在處理非頻帶限制(non-band-limited)的信號。我們引用Brueller et al. [6] 所提出之疊代演算法，對信號做時頻分析並有效地估測其瞬時頻寬，進而利用此結果，在使原信號變成頻帶限制的情況下，計算出時間軸的變形函數，並可重組原信號。根據這技術，此變形函數是累加的，每次疊代以補償和前一次的瞬時頻寬之不同為目標，最後這演算法會收斂並且在變形的時間軸上得到一個固定的瞬時頻寬。而此法在觀念上是最佳，因為它是利用最小取樣率來正確地重建信號，即在含有低頻成份的區域，則用較小的取樣密度，反之亦然。

In many applications, it is an important task to reconstruct a signal from their samples at non-uniformly distributed instants, especially in processing a non-band-limited signal. We refer to an iterative algorithm proposed by Brueller et al. [6]. This method is based on time-frequency analysis to availably estimate instantaneous bandwidth, further uses the result to calculate the time-distortion function, under which the original signal becomes band-limited and thus can be reconstructed. According to this approach, the time-distortion function is accumulated, and each iteration is aimed at compensating for differences in the instantaneous bandwidth after previous iteration. The final results of this algorithm converge to a constant instantaneous bandwidth over the distorted time axis. This method is optimal in the sense that it requires the minimal sampling rate for correct reconstruction of the signal. In other hand, it needs lower sampling density in the regions where there are low frequency components than in the other regions where there are higher frequency components and vice versa.