Role of bandwidth in the quality of inversion of linear multirate systems with noise

A multirate system called the fractional sampling rate alteration system makes frequent appearance in many signal processing applications including fractionally spaced equalizers (FSE) and in multirate feedback control. In some applications it is necessary to invert this system, as in the example of a zero-forcing FSE. There is usually noise at the input of the inverse, and the noise amplification properties depend crucially on the bandwidth of the original system, as shown in this paper. Even though this effect is qualitatively known in FSE applications, the purpose of this paper is to provide the quantitative theoretical foundations for this effect. It will be shown that if the system has excess bandwidth, then the noise gain can be readily controlled, whereas unbounded noise amplification can result if there is no excess bandwidth.