A Simplified Structure for FIR Filters with an Adjustable Fractional Delay

This paper introduces an efficient filter structure for implementing finite-impulse response (FIR) filters with an adjustable fractional delay. In this structure the first two subfilters are the same as in the modified Farrow structure, whereas the remaining ones are generated by properly combining these two subfilters with some additional very short filters, pure delay terms, adders, and multipliers. For significantly reducing the number of multipliers, the three-step synthesis scheme proposed by Yli-Kaakinen and Saramaki in the case of the modified Farrow structure is followed. First, the number of subfilters and their orders are determined such that the given criteria are sufficiently exceeded. Second, an initial filter is determined using a simple design scheme. This filter serves as a start-up solution for further optimization being performed using a constrained nonlinear optimization algorithm. Third, those coefficient values of the subfilters having a negligible effect on the overall system performance are fixed to be zero-valued. Both the performance and complexity of the proposed adjustable digital filters are compared with those of some existing adjustable FIR filters proposed in the literature. This comparison shows that, in the case of stringent amplitude and phase delay specifications, the number of multipliers for the proposed filters is less than 80 percent when compared with the corresponding optimized modified Farrow structure.

[1]  Ewa Hermanowicz,et al.  On designing a wideband fractional delay filter using the farrow approach , 2004, 2004 12th European Signal Processing Conference.

[2]  T. Saramaki,et al.  Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay , 2006 .

[3]  Craig A. Rahenkamp,et al.  Modifications to the McClellan, Parks, and Rabiner computer program for designing higher order differentiating FIR filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[4]  Chien-Cheng Tseng,et al.  Design of 1-D and 2-D variable fractional delay allpass filters using weighted least-squares method , 2002 .

[5]  T. Saramaki,et al.  Interpolation filters with arbitrary frequency response for all-digital receivers , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[6]  C. W. Farrow,et al.  A continuously variable digital delay element , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[7]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[8]  T. Saramaki,et al.  Optimization and efficient implementation of FIR filters with adjustable fractional delay , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

[9]  Tapio Saramäki,et al.  An algorithm for the optimization of adjustable fractional-delay all-pass filters , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[10]  Tapio Saramäki,et al.  Multiplier-free polynomial-based FIR filters with an adjustable fractional delay , 2002, 9th International Conference on Electronics, Circuits and Systems.

[11]  Vesa Välimäki,et al.  Efficient tunable IIR and allpass filter structures , 2001 .