科研之友
微信
新浪微博
Facebook
分享链接
摘要
A novel method of linear approximation of a matrix is proposed for designing the linear-phase and non-linear-phase extrapolated impulse response (EIR) filters. There are zero-valued and one-valued coefficients in the scale vectors of the proposed EIR filters. These zero-valued coefficients do not require multipliers or adders, and these one-valued coefficients do not require multipliers, in the filter implementation. Additionally, the optimal design of the EIR filters in the mini-max sense and the least-square sense by the iterative gradient searching (IGS) technique is investigated. In implementing the IGS technique, the original EIR filter, the principal component analysis based EIR filter and the proposed EIR filter are set as the initial solutions, separately. If the proposed EIR filter is set as the initial solution, the IGS technique can synthesize the prototype finite impulse response (FIR) filter satisfactorily, with the lowest hardware implementation complexity. Further, experimental comparison of the proposed EIR method with the two most popular non-EIR low-complexity FIR filter design methods also indicates some superiority of the proposed EIR method. Finally, the proposed method of linear approximation of a matrix may also be useful in other areas of signal processing.
