Translations:Inverse filters/20/en

How can a stable filter approximate an unstable filter? The foregoing stability analysis is fine and good, but what if we demand a feedback filter with feedback-loop amplification - that is, ${|}c{|>}1$? What weapon do we have to make such a filter stable? The only weapon we have is time delay. We must delay the filter’s output to obtain a semblance of stability in our system. Thus, by demanding feedback-loop amplification ${|}c{|>}1$, the factors of stability and output delay must be balanced against each other. With no delay in the output, the feedback filter is necessarily unstable. However, the longer we are willing to delay the filter’s output, the greater is the chance we have for constructing a stable filter that does approximately the same job as the unstable one (Treitel and Robinson, 1966).