1/f信號的積分多小波變換表示
Integral Multiwavelet Representation of 1/f Signal
-
摘要: 在積分多小波變換理論的基礎(chǔ)上，研究了1/f信號的積分多小波變換表示，給出了用積分多小波逆變換產(chǎn)生1/f信號(非近似1/f信號)的條件。并對1/f信號的積分多小波變換的統(tǒng)計特性進(jìn)行了研究，證明1/f信號的統(tǒng)計自相似性在多小波域內(nèi)可由積分多小波系數(shù)的自相關(guān)函數(shù)矩陣來表達(dá)?；趩涡〔ㄗ儞Q的1/f信號表示是其特例。
-
關(guān)鍵詞:
- 1/f信號; 自相似性; 積分多小波變換; 分形布朗運(yùn)動
Abstract: Based on the theory of integral multiwavelet transformation, the representation of 1/f signal (not near-1/f signal) is explored by inverse integral multiwavelet transforma-tion, and the conditions of representing 1/f signal are acquired. The statistical characteris-tics of integral multiwavelets transformation are studied, and it is proved that the self-similar characteristics of 1/f signal can be represented by the autocorrelation matrix of coefficients of integral multiwavelet in multiwavelet domain. The representation of 1/f signal by singular wavelet is only the special case of the representation. -
Wornell G. W. Signal Processing with Fractals: A Wavelet-Based Approach. New York: Prentice Hall PTR, 1996: 43-54.[2]劉峰,劉貴忠,張茁生.基于小波變換的1/f信號表示.中國科學(xué),2000,30(6):568-573.[3]Chui C K, Lian J. A study of orthonormal multi-wavelets[J].Appl. Numer. Math.1996, 20(3):273-298[4]Lebrun J. High-order banlanced multiwavelets: Theory, factorization, and design. IEEE Trans.on Signal Processing, 2001, SP-49(9): 1918-1930.[5]Flandrin P. Wavelet analysis and synthesis of fractional Browian motion. IEEE Trans. on Information Theory, 1992, IT-38(2): 910-917.[6]Tewfik A H, Kim M. Correlation structure of the discrete wavelet coefficients of fractional Brownian motion. IEEE Trans. on Information Theory, 1992, IT-38(2): 904-909.[7]Barton R J, Poor V H. Signal detection in fractional Gaussian noise. IEEE Trans. on Information Theory, IT-1988, 34(5): 943-959. -
計量
- 文章訪問數(shù): 2296
- HTML全文瀏覽量: 117
- PDF下載量: 694
- 被引次數(shù): 0
下載:
