| Digital IIR filters find wide applications in fields such as speech processing, image processing and noise/echo cancellation. In recent years, the design of linear phase IIR filter becomes a very hot issue of research interest.; As we know, FIR filters designed to approximate a magnitude response that has a narrow transition band between the passband and the stopband usually require a large number of multipliers and they have a large delay also. Hence we prefer to IIR digital filters that have less number of multipliers than their corresponding FIR counterparts but one of disadvantages is that an IIR filter cannot reach an exactly linear phase. The importance of the phase response linearity of a digital filter was recognized in early years' research and Finite Impulse Response (FIR) filters provided a perfect solution to this requirement. However, due to fundamental incompetence of FIR filters stated before, approximately linear phase IIR filters became the focus of research as a compromise between the implementation cost and the linearity of the phase response.; About twenty years ago, most of researches on digital filters and signal processing, when and if they discussed the design of digital filter, they treated mainly the approximation of the magnitude response, or else, dealt with magnitude and phase responses separately. For example, as we know, the one of the most well known methods for solving the problem of IIR filter phase linearity was based on the application of cascading the prototype IIR filter with an allpass phase equalizer.; In recent years, new methods have been proposed for the simultaneous approximation of both the magnitude and group delay of IIR digital filter. They have less number of multipliers than their corresponding FIR counterparts and yet provide the required phase response. This topic is covered all through this thesis. |
