Even when no phase shift or amplitude change is present, the adaptive filter may offer computational efficincies over standard FIR filters, and certainly reduce the design costs of producing a filter. The ability of the filter to operate sucessfully lies in its ability to adapt to changes in phase an amplitude. This adaptation can only occur if there are sufficient samples in the filter such that the maximum phase shift at every frequency can be compensated for by the filter. The LMS filter does not respond well to very rapid changes in noise.
Large changes result in very steep gradients which result in very large filter weight adaptations.
The next few samples of input usually result in equally large gradients in the opposite direction. Samples processed with such widely varying filkter weights tend to pop. This behavior is evidenced by the last few seconds of our noise cancellation simulation, where the cymbals are removed imcompletely and leave an artifact as well. LMS adaptive filters work well for two of the four filter systems described above. By extension the Type II Inverse Filter should work as well as the Type I filter.