A 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 technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z/sup -1/). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation. >

A technique for realizing linear phase IIR filters

A technique for realizing linear-phase infinite impulse response (IIR) filters has been proposed by Powell and Chau (1991) and gives a real-time implementation of H(z/sup -1/)/spl middot/H(z), where H(z) is a causal IIR filter function. In their system, the input signal is divided into L-sample sections, time-reversed, section convolved with H(z), and time-reversed again. The signal is then filtered by H(z) to give the system output with a processing delay of 3L+1 samples. However, the group delay response of the system exhibits a minor sinusoidal variation superimposed on some constant value. This variation will degrade image quality in image processing and signal quality in signal transmission applications. Furthermore, the output of the system contains harmonic distortion for a sinusoidal input. The main drawbacks of Powell and Chau's technique are the large processing delay of 3L+1 samples and the accompanying phase and harmonic distortions. A smaller processing delay increases the phase and harmonic distortions, yet the amplitude response remains acceptable. Previously, the present authors presented a method of reducing the processing delay by shortening the section length by an integer factor N using a structure with increased number of paths for the time-reversed signal. The authors consider how to reduce the phase and harmonic distortions. We examined the operation of the sectioned convolution and analyzed it based on a state-space representation. Then, we found that the cause of the distortions is a periodic variation of the impulse response length in the sectioned convolution. To overcome this problem, a technique is devised to realize a recursive circuit having a truncated impulse response with a fixed-length L. A system applying this technique to the Powell-Chau system is demonstrated to exhibit perfect linear-phase characteristic and produce virtually no harmonic distortion. Therefore, the section length L can be reduced without limitation due to phase and harmonic distortions. Two methods for reducing the increased computational complexity of this technique assuming fixed L are developed, and simulations are performed for the proposed system to confirm the expected improvements.

A technique to truncate IIR filter impulse response and its application to real-time implementation of linear-phase IIR filters

Introduces efficient linear-phase FIR (finite-impulse response) filter structures using novel recursive subfilters. The novel filter structure is based on subfilters whose filter coefficients are related to each other recursively. A well-known structure that uses this method is the recursive running sum. The use of recursive subfilters is extended to cover the simple structures utilizing real and complex poles of radius r. The proposed linear-phase FIR filter structures result in computationally efficient implementations which require fewer general multipliers than conventional filters. This structure is beneficial for filters with narrow transition bands since the use of a single pole pair near the transition region lowers the required numerator order radically. Since the proposed filters have finite impulse responses, they can be realized efficiently using block processing. >

http://ieeexplore.ieee.org/iel2/706/573/00014927.pdf

Efficient linear phase FIR filter structures exploiting recursive subfilters

A technique is developed for indirectly realizing true time-reversed convolution for continuous inputs of infinite duration. This real-time technique is based on a novel extension of sectioned convolution methods using an infinite impulse response (IIR) filter and local time reversal using last-in, first-out (LIFO) memory stacks. This new architecture is shown to be free from zero input limit cycle and overflow oscillations even if the IIR filter on which it is based exhibits both. No constraints are placed on the magnitude or phase response characteristics of the IIR subfilter used in the time-reversed convolution scheme which permits the use of standard magnitude-only IIR filter design programs. Computer simulations are used to verify the expected magnitude and phase response. The conditions required for system time invariance are investigated both analytically and through computer simulations. The relationship between the number of samples per convolution section and the total harmonic distortion of the system is established through simulation. It is demonstrated that if the number of samples per section is greater than the number of samples required for the impulse response of the subfilter H(z) to decay below a threshold value, a stable, linear, time-invariant system results with noncausal transfer function H(z/sup -1/). >

Time reversed filtering in real-time

The idea of a multipurpose chip for the measurement of physiological signals is discussed here. First, the general idea of the chip consisting of an amplifier, a sigma-delta analog-to-digital converter (ADC) and a digital filter is presented. Then the possible implementation alternatives, specifications and, finally, the linear phase filters to maintain some important features in the signal are discussed. >

Multipurpose chip for physiological measurements

The authors introduce a modular VLSI architecture for a novel linear-phase FIR (finite impulse response) filter structure. The proposed linear-phase FIR filters have a highly reduced number of general multiplications per sample compared to conventional FIR filters. The novel filter structure is based on an IIR subfilter whose infinite impulse response is truncated into a finite one. Although the subfilter has a nonlinear phase response, it can be made exactly linear by reversing the data stream in time and using the same filter again. Another possibility is to use a maximum-phase version of the FIR filter in cascade. The choice between different realizations depends on the filter specifications. In the general case the filter coefficients cannot be represented with the simple shift-and-add procedure and the time reversal technique should be used. The authors prefer the maximum-phase FIR alternative. >

K.-P. Estola

Papers

A new modular VLSI filter architecture using computationally efficient recursive digital filter topology