A technique for realizing linear phase IIR filters

Abstract

A new real-time IIR filter s t r u c t u r e is presented t h a t possesses exact phase linearity with 10 -1000 times fewer general multiplies t h a n conventional FIR filters of similar performance a n d better magnitude characteristics t h a n equiripple o r maximally flat g r o u p delay IIR filters. This s t r u c t u r e is based on a novel technique using local time reversal a n d single pass sectioned convolution methods to realize a real-time recursive implementation of the noncausal t r a n s f e r function H ( 2 -l ) . When combined with a causal recursive filter, the precisely line a r phase t r a n s f e r function H(z) . H ( 2 -I ) results with fewer multiplies a n d significantly reduced storage requirements t h a n previously reported noncausal recursive approaches. No constraints a r e placed on t h e magnitude o r phase response c h a racteristics of H(z). T h e new linear phase IIR filter can be designed using s t a n d a r d magnitude-only IIR filter design programs a n d c a n be m a d e unconditionally f r e e f r o m parasitic zero-input limit cycle or overflow oscillations. T h e resulting g r o u p delay is typically constant to within of the average delay. F o r a given filter specification, t h e n u m b e r of multiplies per sample is typically within a factor of two a n d the roundoff noise within one-half bit of a causal magnitude-only elliptic IIR implementation. C o m p u t e r simulations a r e used to verify t h e expected phase linearity a n d magnitude response. A design a pproach is presented including a technique f o r establishing t h e n u m b e r of samples per convolution section necessary to i n s u r e t h a t a time invariant system results with linear phase a n d magnitude response equal to ! H(z)/'. T h e relationship between t h e n u m b e r of samples per convolution section a n d t h e total h a rmonic distortion of t h e system is also verified through simulation. A comparison to direct FIR implementations f o r nine example filter specifications is presented to demonstrate t h e computational advantage of the new linear phase IIR s t r u c t u r e .

All About Audio Equalization: Solutions and Frontiers

“…However, several approaches exist for linear phase IIR filter design. Powell and Chau's real-time linear phase IIR filters [115] used a modification of a well-known time reversal technique. Willson and Orchard described a variation on this approach that yields higher performance (more stopband loss, less passband ripple and/or narrower transition band) [116].…”

Time-domain realisation of model-based rendering for 2.5D local wave field synthesis using spatial bandwidth-limitation

“…Latter behaviour can also be achieved by time-inverting the allpass' input signal and timeinverting the resulting output signal, again. An online, blockbased approach for backward filtering is given in [22].…”

Sample delay reduction of linear phase IIR filters by shortening section length of signals

“…filters [5] In order to time reverse the signal sequence at each section in the circuit in Fig. 4, let us consider the case in which the time reversal block is replaced with an L-sample LIFO buffer (Last In First Out: the shift register with the operation in Fig.…”

“…13, which is a filter satisfying the following design specifications given in Ref. 5: [behavior for undn].…”

“…These methods, however, could not be realized in real time. A real-time realization has been proposed by Powell and Chau [5]. The method consists of the following five steps.…”