Digital Signal Processing ( IF 2.9 ) Pub Date : 2021-05-21 , DOI: 10.1016/j.dsp.2021.103089 Eric Grivel , Roberto Diversi , Fernando Merchan
In signal processing, ARMA processes are widely used to model short-memory processes. In various applications, comparing or classifying ARMA processes is required. In this paper, our purpose is to provide analytical expressions of the divergence rates of the Kullback-Leibler divergence, the Rényi divergence (RD) of order α and their symmetric versions for two Gaussian ARMA processes, by taking advantage of results such as the Yule-Walker equations and notions such as inverse filtering. The divergence rates can be interpreted as the sum of different quantities: power of one ARMA process filtered by the inverse filter associated with the second ARMA process, cepstrum, etc. Finally, illustrations show that the ranges of values taken by the divergence rates of the RD are sensitive to α, especially when the latter is close to 1.
中文翻译:
高斯平稳ARMA过程的Kullback-Leibler和Rényi发散率比较
在信号处理中,ARMA 过程被广泛用于模拟短记忆过程。在各种应用中,需要对 ARMA 过程进行比较或分类。在本文中,我们的目的是通过利用 Yule 等结果,为两个高斯 ARMA 过程提供 Kullback-Leibler 散度、α阶 Rényi 散度 (RD)及其对称版本的散度率的解析表达式-Walker方程和概念,例如逆滤波。发散率可以解释为不同数量的总和:一个 ARMA 过程的幂由与第二个 ARMA 过程关联的逆滤波器过滤,倒谱等。 最后,插图显示了由 ARMA 过程的发散率取值的范围RD对α敏感,尤其是当后者接近 1 时。