A TECHNIQUE FOR REALIZING LINEAR-PHASE IIR FILTERS

A new real-time IIR filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a novel technique using local time reversal and single pass sectioned convolution methods to realize a real-time recursive implementation of the noncausal transfer function H(z-1). When combined with a causal recursive filter, the precisely linear phase transfer function H(z) . H(z-1) results with fewer multiplies and significantly reduced storage requirements than previously reported noncausal recursive approaches. No constraints are placed on the magnitude or phase response characteristics of H(z). The new linear phase IIR filter can be designed using standard magnitude-only IIR filter design programs and can be made unconditionally free from parasitic zero-input limit cycle or overflow oscillations. The resulting group delay is typically constant to within 10(-5) of the average delay. For a given filter specification, the number of multiplies per sample is typically within a factor of two and the roundoff noise within one-half bit of a causal magnitude-only elliptic IIR implementation. Computer simulations are used to verify the expected phase linearity and magnitude response. A design approach is presented including a technique for establishing the number of samples per convolution section necessary to insure that a time invariant system results with linear phase and magnitude response equal to \H(z)\2. The relationship between the number of samples per convolution section and the total harmonic distortion of the system is also verified through simulation. A comparison to direct FIR implementations for nine example filter specifications is presented to demonstrate the computational advantage of the new linear phase IIR structure.