TABLE OF CONTENTS Our analysis of digital filters thus far has shown us that they can be designed with performances far exceeding those of linear analog types, respecting transition zone width, stop band attenuation and phase linearity. Moreover, the fact that it is possible to design real-time digital filters with arbitrary frequency response characteristics opens up new and almost undreamed of possibilities in both signal analysis and synthesis.
However, all of the filters discussed up to this point have been strictly linear, with frequency responses that are time invariant. In many cases this is fine, as attested by the myriad circumstances in which they are applied. But consider this problem: what if we had a broadband source, such as a speech or music signal, which was degraded by narrowband interference with a frequency within the bandwidth of the signal for example, a whistle? Simple, you might say just design a notch filter to remove it. This would work, as long as we could live with the fact that the filter would inevitably remove some of the signal. If the interference were more broadband in nature such as engine noise then the bandwidth of the filter required to remove it would suppress most of the signal, which of course would be unacceptable. Another situation that the linear filter could not handle would be narrowband interference that drifted across the spectrum of the audio source, such as a tone that rose or fell in pitch.
Ostensibly, these problems appear...
