頁籤選單縮合
題 名 | Applications of the Fractional Fourier Transform in Geophysics=分數傅立葉轉換在地球物理上的應用 |
---|---|
作 者 | 謝秋雰; | 書刊名 | 中國地質學會會刊 |
卷 期 | 42:3 1999.08[民88.08] |
頁 次 | 頁465-475 |
分類號 | 353.1 |
關鍵詞 | 分數傅立葉轉換; 複數訊號; 泛雜音; 反射訊號; Fractional fourier transform; Complex signal; Random noise; Reflected signals; |
語 文 | 英文(English) |
中文摘要 | 由量子光學所發展的分數傅立葉轉換(FRFT),是一種新的數學觀念,它可以將函 數轉換到u-域。以訊號處理的角度而言,u-域是頻率和時間的結合。FRFT可以在時間和頻 率軸之間選任何角度做轉換,但傳統傅立葉轉換(FT)只限制在π╱2。是故FRFT可視為泛 化傅立葉轉換,而FT可視為其特例。FRFT的潛在應用性尚未出現於地球物理文獻,本研 究對其在地球物理上的可能應用做起始探討。首先將訊號經由希伯特轉換為複數訊號後,再 透過FRFT轉換到u-域。三種處理項目包括(1)泛雜音之消除,(2)分離頻率域重疊的訊號, 及(3)在頻率-波數域重疊的反射訊號。處理結果顯示,泛雜音可以更有效的在u-域將其壓 抑,在頻率或頻率-波數域重疊的訊號,於選取適當角度之FRFT後也可分離。 |
英文摘要 | The fractional Fourier transform (FRFT) is a mathematical concept borrowed from quantum optics that can transform a function into the u-domain. In the context of signal processing, thc u-domain is a combination of frequency and time. FRFT can be adapted to any angle between frequency and time, while the conventional Fourier transform (FT) is limited to π/2. For this reason, FRFT can be considered as the generalized Fourier transform and FT as a particular case of FRFT. As potential applications of FRFT have not been published in any geophysical literature, this study initiates a discussion of its possible implications in the geophysical community. We first obtained a complex signal through the Hilbert transform, and then used FRFT to transform it into the u-domain. Three processes were included: (1) random noise elimination, (2) isolation of overlap signals in the frequency domain, and (3) mixed reflections in the frequency-wave number domains. The processed results how that the random noise can be suppressed more effectively in the u-domain than in the frequency domain, and that the overlapping coherent signals in the frequency domain and the mixed reflections in the frequency-wave number domains are separable by selecting a proper transform angle. |
本系統中英文摘要資訊取自各篇刊載內容。