Filters have a lot going for them. In the previous chapter we have seen that they are simple to design, describe and implement. So why bother devoting an entire chapter to the subject of systems that are not filters? There are two good reasons to study nonfilters-systems that are either nonlinear, or not time-invariant, or both. First, no system in the real world is ever perfectly linear; all ‘linear’ analog systems are nonlinear if you look carefully enough, and digital signals become nonlinear due to round-off error and overflow | Digital Signal Processing A Computer Science Perspective Jonathan Y. Stein Copyright 2000 John Wiley Sons Inc. Print ISBN 0-471-29546-9 Online ISBN 0-471-20059-X Nonfi Iters Filters have a lot going for them. In the previous chapter we have seen that they are simple to design describe and implement. So why bother devoting an entire chapter to the subject of systems that are not filters There are two good reasons to study nonfilters systems that are either nonlinear or not time-invariant or both. First no system in the real world is ever perfectly linear all linear analog systems are nonlinear if you look carefully enough and digital signals become nonlinear due to round-off error and overflow. Even relatively small analog nonlinearities can lead to observable results and unexpected major nonlinearities can lead to disastrous results. A signal processing professional needs to know how to identify these nonlinearities and how to correct them. Second linear systems are limited in their capabilities and one often requires processing functions that simply cannot be produced using purely linear systems. Also linear systems are predictable a small change in the input signal will always lead to a bounded change in the output signal. Nonlinear systems however may behave chaotically that is very small changes in the input leading to completely different behavior We start the chapter with a discussion of the effects of small nonlinearities on otherwise linear systems. Next we discuss several nonlinear filters a term that is definitely an oxymoron. We defined a filter as a linear and time-invariant system so how can there be a nonlinear filter Well once again we are not the kind of people to be held back by our own definitions. Just as we say delta function or talk about infinite energy signals we allow ourselves to call systems that are obviously not filters just that. The mixer and the phase locked loop are two systems that are not filters due to not being time-invariant. .
