Low Complexity FIR Filter Design Based On FRM Technique

Finite impulse response (FIR) filter is widely used in many application fields, such as image processing, communication, radar and speech signal processing, owing to its merits of stability and attainable strictly linear phase. The filter with narrow transition bandwidth is needed in some applications, for instance, eliminating code interference in multi-carrier communication. However, the narrower the transition bandwidth is, the larger the complexity of FIR filter is. Thus, how to design such a filter with low complexity becomes an impotant research issue.Frequency-response masking (FRM) is a new technique among various low complexity filter design methods. It receives great attention due to its capability of designing sharp cutoff FIR filters with arbitrary bandwidth. Its key idea involves obtaining narrow transition bandwidth via interpolation, and arbitrary bandwidth via magnitude complementation and frequency-response masking. Two new methods based on FRM are proposed to reduce the complexity of sharp cutoff FIR filters in this paper. Their efficiency is validated by experiments. The main works discussed is as follow.A transition band compensation technique for linear phase FIR filter design is proposed, which divides a single filter into three sub-filters. First, the compensating frequency response is formed by prototype filter and masking filter with masking technique. Then, a wide transition bandwidth filter is compensated by it. Lastly, a filter with narrow transition bandwidth is obtained. The search flow of the interpolation factor for prototype filter is given, and sub-filters'impact on overall filter's ripple is analysed. Experiments demostrate that, if an arbitrary prototype filter is adopted, its complexity is comparable to FRM filters; Otherwise, if a half-band filter is used, its complexity will be further reduced. Of course, a half-band filter can be designed with this method.Another method named TCIIS-FRM is proposed. On the basis of TCIIS structure and design algorithm studying, TCIIS structure is transformed into a folding form. Then, it is introduced into FRM for designing the masking filters. It shows that the amount of multiplers and adders can be reduced by this method, whos implementation cost is inversely proportional to transition bandwidth, the narrower the transition bandwidth is, the more the hardware saving percentage is. It can also be used to half-band filter design.Those design methods proposed for sharp cutoff FIR filters with low complexity, make theoretical sense to some extent, and possess practical application value.