Effects of Multirate Systems on the Statistical Properties of Random Signals
Effects of Multirate Systems on the Statistical Properties of Random Signals
复制标题
多速率系统对随机信号统计特性的影响
DOI：
10.1109/tsp.1993.193133
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
P. Vaidyanathan
中科院分区：
文献类型：
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作者：
V. Sathe;P. Vaidyanathan
在多速率数字信号处理中，我们经常遇到时变线性系统，如抽取器、内插器和调制器。在许多应用中，这些构建块与线性滤波器互连以形成更复杂的系统。通常有必要了解信号在通过此类系统时的统计行为变化方式。虽然这方面的一些问题有一个明显的答案，但分析更多地涉及复杂的相互联系。例如，考虑这个问题：如果我们将周期为K的循环平稳信号通过分数采样率改变设备（由一个滤波器、一个非理想低通滤波器和一个抽取器实现），我们可以说输出的统计特性是什么？如果用理想的低通滤波器代替滤波器，性能会有什么变化？在本文中，我们回答这种性质的问题。作为一个应用，我们考虑一个新的自适应滤波结构，这是非常适合于带限信道的识别。这种结构利用了信道的带限特性，并将自适应滤波器嵌入到多速率系统中。优点是自适应滤波器具有较小的长度，并且以较低的速率执行自适应以及滤波。使用本文中开发的理论，我们表明，矩阵自适应滤波器（尺寸由抽取器和抽取器确定）提供了更好的性能，在较低的误差能量收敛比传统的自适应滤波器。即使矩阵自适应滤波器，在一般情况下，计算更昂贵，他们提供了一个性能的界限，可以作为一个衡量标准，以判断更实际的“标量多速率自适应”计划。
In multirate digital signal processing, we often encounter time-varying linear systems such as decimators, interpolators, and modulators. In many applications, these building blocks are interconnected with linear filters to form more complicated systems. It is often necessary to understand the way in which the statistical behavior of a signal changes as it passes through such systems. While some issues in this context have an obvious answer, the analysis becomes more involved with complicated interconnections. For example, consider this question: if we pass a cyclostationary signal with period K through a fractional sampling rate-changing device (implemented with an interpolator, a nonideal low-pass filter and a decimator), what can we say about the statistical properties of the output? How does the behavior change if the filter is replaced by an ideal low-pass filter? In this paper, we answer questions of this nature. As an application, we consider a new adaptive filtering structure, which is well suited for the identification of band-limited channels. This structure exploits the band-limited nature of the channel, and embeds the adaptive filter into a multirate system. The advantages are that the adaptive filter has a smaller length, and the adaptation as well as the filtering are performed at a lower rate. Using the theory developed in this paper, we show that a matrix adaptive filter (dimension determined by the decimator and interpolator) gives better performance in terms of lower error energy at convergence than a traditional adaptive filter. Even though matrix adaptive filters are, in general, computationally more expensive, they offer a performance bound that can be used as a yardstick to judge more practical "scalar multirate adaptation" schemes.