Construction of periodic analytic signals satisfying the circular Bedrosian identity
Construction of periodic analytic signals satisfying the circular Bedrosian identity
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DOI：
10.1093/imamat/hxq001
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发表时间：
2010-04
影响因子：
1.2
通讯作者：
L. Tan;Lihua Yang;D. Huang
中科院分区：
文献类型：
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作者：
L. Tan;Lihua Yang;D. Huang
圆Bedrosian恒等式对于非平稳周期信号的处理具有重要意义。迄今为止，关于圆Bedrosian恒等式的所有已知结果几乎都是在频域中给出的。本文利用后移不变子空间的知识，在时域上建立了这一恒等式的一些新的充分必要条件。作为应用，构造了一类满足循环Bedrosian恒等式的周期解析信号。结果表明，这些信号具有非负的瞬时频率，且在Lp（∞）中是稠密的，1 ≤ p ≤ ∞。
The circular Bedrosian identity has considerable importance for the non-stationary periodic signal processing. Up to now, almost all the known results for the circular Bedrosian identity are given in the frequency domain. In this paper, based on the knowledge of backward shift invariant subspace, some new necessary and sufficient conditions for this identity are established in the time domain. As an application, a class of periodic analytic signals satisfying the circular Bedrosian identity are constructed. It is shown that these signals have non-negative instantaneous frequencies and are dense in Lp(𝕋), 1 ≤ p ≤ ∞.