離散時間分數維度布朗運動(discrete-time fractional Brownian motion, DFBM)和它的增量程序(increment process)，離散時間分數維度高斯雜訊(discrete-time fractional GaussianNoise, DFGN)經常廣泛地被運用在許多自然現象和醫學領域方面，這些訊號大都不是以前者就是以後者出現。此外，由於此類程序可由一個有限範圍(0,1)的赫斯特參數(Hurstparameter)來描述，使得原本看似複雜的程序顯得格外簡單與方便。在應用上，只要估測出赫斯特參數就能具體解析訊號間的差異。目前已有許多估測此一參數的有效方法，然而在應用上缺乏一個評估訊號是否適合使用的檢驗方式。本計畫的貢獻就是利用條件熵(conditional entropy)和共有訊息(mutualinformation)兩種方法來評估所關心的訊號是否可以使用，亦即判別訊號是決定性(deterministic)還是隨機性(random)的訊號。理論上，當兩個訊號來自同一個系統時則它們間的條件熵會較小，然而共有訊息會較大。由於此類訊號是隨機雜訊，因此它們的條件熵會較大，然而共有訊息會較小。透過這種驗證方式可以有效區分訊號是決定性或隨機性。
The discrete-time fractional Brownian motion (DFBM) and its increment process, discrete-time fractional Gaussian noise (DFGN), are often widely used in natural phenomena and medical field. These signals largely appear either the prior or the rear. Furthermore, the fact that these processes can be described by one Hurst parameter with limited range (0,1) makes the seemingly complicated processes simple and convenient. In application, we can concretely analyze the difference between different signals by estimating the Hurst parameter. At present there exist many effective methods to estimate this parameter. However, in application it lacks of an evaluation method for whether the interested signals are appropriate for use or not. In this project, we apply conditional entropy and mutual information to assess whether these signals are appropriate for use or not, i.e., judge these signals whether are deterministic or random signals. In theory, as two signals are coming from the same system, they have smaller conditional entropy, but larger mutual information. Since this kind of signals is random noise, they have larger conditional entropy, but smaller mutual information. We can effectively separate determinism from randomness on signals via this test and verification.
