Study on Design of Linear Phase IIR Filte Based on Hankel Norm Approximation and Its Application
|Course||Control Theory and Control Engineering|
|Keywords||linear phase IIR filter FIR filter optimal Hankel norm approximation data flow fuzzy control|
In signal process systems such as data transmission、radar receiving and image process, channels with linear phase are required. If the filter has good phase frequency characteristics then signal can’t cause angle excursion and phase distortion. So it’s benefit to improve transmission reliability and reduce bit error rate. Usurally finite impulse response (FIR) digital filter is adopted. It satisfies the magnitude specifications and has strict linear phase. However, for the same filter design index, the order of FIR filter is higher than infinite impulse response (IIR) filter five to ten times. It causes increasing cost and signal delay. IIR filter can get the higer selectivity with lower order. But its phase is nonlinear. For satisfying linear phase and amplitude frequency characteristics, we must add all-pass filter to revise phase. So it increases complexity and order of filter. This paper considers design of linear phase IIR digital filter. It satisfies not only the amplitude frequency characteristics but also the phase frequency characteristics. The important featuresof this method are the guaranteed L_∞error bound and the less computational load.We give its application on data flow fuzzy control. The main contribution lies in:The applications of model reduction theory to design of digital filter are presented. For discrete time system, all optimal Hankel norm approximation is proposed. For single input/single output (SISO) systeman independent proof is established and L_∞error bound is guaranteed. It provides theory for design of linear phase IIR digital filter.We re-examine the use of optimal Hankel norm approximation to linear phase IIR filter. The new algorithm involves computation of inversion matrices, which is substantially smaller than existing papers. Approximation error bound in terms of Chebyshev norm is established for the optimal Hankel norm approximation algorithm.Approach to the design of linear phase IIR filter is proposed. At first we design a linear phase FIR filter, second utilize optimal Hankel norm approximation and finally we get linear phase IIR filter. It has fewer computational load and linear phase.To illustrate the technique proposed in this paper, we simulate design of linear phase lowpass IIR filter and linear phase bandpass IIR filter based on the Hankel norm approximation. The results prove that the computational load is few. For higher order FIR filter, it has more superiority. The simulation proves the correctness of theoretical derivation.Data flow fuzzy control based on linear phase IIR filter is presented. Referring to utilize linear phase lowpass IIR filter to compute the average queuing length of buffer. Fuzzy controller is used to routing selection dynamically. We give the three kinds of simulations include random arriving rate、inconstant probability arriving rate and sudden event existing. Simulations show that after adopting the data flow fuzzy controller based on the linear phase IIR filter the average soujoum time is reduced. Network performance is improved. The fuzzy controller has high performance in conditions.