增進稀疏快速傅立葉轉換效能之方法及其理論分析

Abstract

在本論文中，我們提出了一種基於稀疏傅立葉技術重建訊號頻譜的新估計方法。這種新的估計方法可以比常規方法更精確地重建結果。同時，我們分析了重建性能並導出所提方法的數學式。 這些導出的結果考慮了稀疏乾擾，窗函數和噪聲，並且適合用於硬體實現。分析結果有助於確定SFFT中的參數，而不用進行繁瑣的蒙特卡羅模擬測試，因為在SFFT中有很多參數，包括FFT大小，稀疏，窗口函數的數量，SNR，所需的恢復率等。提供模擬結果以顯示導出結果的準確性以及所提出的方法相對於常規方法的性能優越性。

In this thesis we proposes a new estimation method to reconstruct the FFT samples based on the sparse FFT techniques. This new estimation method can more accurately reconstruct the results than the conventional methods. Also, we analyze the recovering rate performance and derive closed-form expressions for the proposed method. These derived results consider inter sparse interference, windowing function and noise, and are suitable to use for practical implementations. The derived analytical results helps in determining the parameters in SFFT without conducting cumbersome Monte Carlo simulations, because there are so many parameters in SFFT including FFT size, number of sparse, windowing functions, SNR, required recovering rate, etc. Simulation results are provided to show the accuracy of the derived results as well as the performance superiority of the proposed method over the conventional methods.