頻率估測之梯度搜尋法與其精度分析

Abstract

單頻訊號的頻率量測對於工程領域上是個很重要的技術，傳統的傅立葉轉換雖然可大約量測出頻率，但受到頻譜洩漏及雜訊的環境的影響，造成頻率量測值有誤差產生。其頻率誤差值過大情況下，在工程上不敷使用。

為了追求更高精度，並且增強對於雜訊的抵抗力以及解決頻譜洩漏的問題，一些頻率估測法因而產生，而梯度搜尋法更是眾多頻率估測法之一。論文中除了簡介梯度搜尋法外，最重要會加入此方法的誤差分析。分析中，推導出誤差邊界的方程式以及與Cromer Roa邊界的比較。文中最後也會藉由模擬方式與其他文獻中的方法做性能上的比較，凸顯出梯度搜尋法的優勢。

The frequency estimation for single-tone signal is an important technique for engineering area. DFT (or FFT) is a tradition method to measure the signal’s frequency approximately. However, the estimated frequency usually is not precise because of spectrum leakage and the noisy environment. So, the imprecise frequency is not enough for the application in the engineering area. To improve the precision of the estimated frequency and the robustness in the noisy environment, a lot of frequency estimators have been developed. Gradient search method (GSM) is one of the frequency estimators. In this thesis, the principle of GSM will be discussed first. And then, it is necessary to analyze the error bound for GSM. In this process, the error bound’s equation will be derived and compared with Cromer-Roa bound. The final chapter, GSM will be compared with the other estimators by simulation. It can show the advantages of GSM obviously by this comparison.