對於多射頻訊號尋找最小取樣頻率之有效率遞迴演算法

Abstract

我們提出一個有效率的遞迴演算法來針對多射頻訊號尋找其最小取樣頻率，這在軟體無線電(Software Radio)上有重要的應用，我們可以同時對多射頻訊號做不重疊失真取樣來降低成本。首先我們同時對兩個射頻訊號取樣，提出新的條件來達到不失真取樣，並且這些條件僅需要少量的運算。藉由遞迴增加取樣頻率來滿足所有的不失真條件，我們可以找到最小的不失真取樣頻率。我們可以將演算法擴充到同時取樣多個射頻訊號，並且在取樣後於不同的射頻訊號間加上保護頻帶(Guard Band)。模擬的結果顯示，我們提出的演算法能較之前的方法有效地降低運算量。

In this thesis, we propose an efficient iterative algorithm for finding the minimum sampling frequency for a signal that consists of multiple bandpass signals. This finds important application in software radio where it is desirable to downconvert multiple bandpass signals simultaneously. We will derive a new set of conditions for alias-free sampling for signals that contain two bandpass signals. The conditions can be easily examined with few computations. The minimum sampling frequency can be found by iteratively increasing the sampling frequency to meet the alias-free conditions. We will show how the algorithm can be extended to find the minimum sampling frequency for signals that consist of more than two bandpass signals. Furthermore we will generalize the result to the case when a guard band is required between different bandpass signals after sampling. The simulations demonstrate that the proposed method has a much lower complexity than existing algorithms.