A technique for realizing linear phase IIR filters
TL;DR: 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.
Abstract: 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. >
Citations
More filters
TL;DR: This work reviews the basic concepts of spike sorting, including the requirements for different applications, together with the problems faced by presently available algorithms, and proposes a roadmap stressing the crucial points to be addressed to support the neuroscientific research of the near future.
361 citations
Cites background from "A technique for realizing linear ph..."
...In these cases, nearly linear phase IIR filters can be used (Nongpiur et al., 2013; Powell and Chau, 1991)....
[...]
TL;DR: This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter.
Abstract: This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closed-form expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonic) square magnitude frequency responses are maximally flat at /spl omega/=0 and at /spl omega/=/spl pi/. Another result of the correspondence is that for a specified cutoff frequency and a specified number of zeros, there is only one valid way in which to split the zeros between z=-1 and the passband. This technique also permits continuous variation of the cutoff frequency. IIR filters having more zeros than poles are of interest because often, to obtain a good tradeoff between performance and implementation complexity, just a few poles are best.
212 citations
Book•
01 Jan 2000
TL;DR: The author walks readers through a variety of advanced topics, clearly demonstrating how even such areas as spectral analysis, adaptive and nonlinear filtering, or communications and speech signal processing can be made readily accessible through clear presentations and a practical hands-on approach.
Abstract: From the Publisher:
Get a working knowledge of digital signal processing for computer science applications
The field of digital signal processing (DSP) is rapidly exploding, yet most books on the subject do not reflect the real world of algorithm development, coding for applications, and software engineering. This important new work fills the gap in the field, providing computer professionals with a comprehensive introduction to those aspects of DSP essential for working on todays cutting-edge applications in speech compression and recognition and modem design. The author walks readers through a variety of advanced topics, clearly demonstrating how even such areas as spectral analysis, adaptive and nonlinear filtering, or communications and speech signal processing can be made readily accessible through clear presentations and a practical hands-on approach. In a light, reader-friendly style, Digital Signal Processing: A Computer Science Perspective provides:
*A unified treatment of the theory and practice of DSP at a level sufficient for exploring the contemporary professional literature
*Thorough coverage of the fundamental algorithms and structures needed for designing and coding DSP applications in a high level language
*Detailed explanations of the principles of digital signal processors that will allow readers to investigate assembly languages of specific processors
*A review of special algorithms used in several important areas of DSP, including speech compression/recognition and digital communications
*More than 200 illustrations as well as an appendix containing the essential mathematical background
143 citations
TL;DR: Digital infinite impulse response (IIR) filtering is proposed as a means for compensating chromatic dispersion in homodyne-detected optical transmission systems with subsequent digital signal processing.
Abstract: Digital infinite impulse response (IIR) filtering is proposed as a means for compensating chromatic dispersion in homodyne-detected optical transmission systems with subsequent digital signal processing. Compared to finite impulse response (FIR) filtering, IIR filtering achieves dispersion compensation (DC) using a significantly smaller number of taps. DC of 80 and 160 km in a 10-Gb/s binary phase-shift-keying is experimentally compared for the two filtering schemes. IIR filtering can achieve performance similar to the FIR filtering scheme.
96 citations
Cites methods from "A technique for realizing linear ph..."
...studied for noncausal filtering achieving linear phase response using IIR filters [8]....
[...]
TL;DR: Digital signal processing techniques for modifying the spectral balance in audio signals and applications of these techniques are reviewed, ranging from classic equalizers to emerging designs based on new advances in signal processing and machine learning.
Abstract: Audio equalization is a vast and active research area. The extent of research means that one often cannot identify the preferred technique for a particular problem. This review paper bridges those gaps, systemically providing a deep understanding of the problems and approaches in audio equalization, their relative merits and applications. Digital signal processing techniques for modifying the spectral balance in audio signals and applications of these techniques are reviewed, ranging from classic equalizers to emerging designs based on new advances in signal processing and machine learning. Emphasis is placed on putting the range of approaches within a common mathematical and conceptual framework. The application areas discussed herein are diverse, and include well-defined, solvable problems of filter design subject to constraints, as well as newly emerging challenges that touch on problems in semantics, perception and human computer interaction. Case studies are given in order to illustrate key concepts and how they are applied in practice. We also recommend preferred signal processing approaches for important audio equalization problems. Finally, we discuss current challenges and the uncharted frontiers in this field. The source code for methods discussed in this paper is made available at https://code.soundsoftware.ac.uk/projects/allaboutaudioeq.
90 citations
Cites methods from "A technique for realizing linear ph..."
...Powell and Chau’s real-time linear phase IIR filters [115] used a modification of a well-known time reversal technique....
[...]
References
More filters
TL;DR: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented, which obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands.
Abstract: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented. The algorithm obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands, and is capable of designing very long filters. This approach allows the exact specification of arbitrary band-edge frequencies as opposed to previous algorithms which could not directly control pass- and stopband locations and could only obtain (N - 1)/2 different band-edge locations for a length N low-pass filter, for fixed \delta_{1} and \delta_{2} . As an aid in practical application of the algorithm, several graphs are included to show relations among the parameters of filter length, transition width, band-edge frequencies, passband ripple, and stopband attenuation.
806 citations
TL;DR: The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general.
Abstract: The interaction between the roundoff-noise output from a digital filter and the associated dynamic-range limitations is investigated for the case of uncorrelated rounding errors from sample to sample and from one error source to another. The required dynamic-range constraints are derived in terms of L p norms of the input-signal spectrum and the transfer responses to selected nodes within the filter. The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general. Two transpose configurations for the direct form of a digital filter are used to illustrate these results.
287 citations
TL;DR: Explicit formulas for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev and Cauer parameter responses, were derived in this paper.
Abstract: Explicit formulas are derived for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev, inverse Chebyshev, and Cauer parameter (elliptic) filter responses. Using these formulas a direct top down design method is obtained and most of the practical design problems can be solved without special knowledge of filter synthesis methods. Since the formulas are simple enough also in the case of elliptic filters, the design process is sufficiently simple to serve as basis in the first part (filter design from specs to algorithm) of silicon compilers or applied to high level programmable digital signal processors.
259 citations
TL;DR: In this article, a solution obtained by a direct approximation procedure in the z plane is presented, where the denominator of the transfer function turns out to be a Gaussian hypergeometric function, connected with the Legendre functions.
Abstract: A well-known limitation of the recursive digital filter, when compared to the nonrecursive filter, is its incapability of having a strictly linear phase characteristic; thus it may only approximate a constant group delay. For the analog filters the choice of the maximally flat criterion leads to the use of the Bessel polynomials. Yet digital approximations of these continuous filter functions are inadequate to yield the true maximally flat delay approximation of the recursive filters. Our purpose is to provide for the problem at hand a solution obtained by a direct approximation procedure in the z plane. The denominator of the transfer function turns out to be a Gaussian hypergeometric function, more particularly connected with the Legendre functions. The stability of the filters is discussed and some numerical results in regard to the amplitude and phase responses as well as the pole loci are given.
247 citations
TL;DR: An algorithm that can be used to design finite impulse response (FIR) digital filters with linear phase with Fortran IV listing of the program is presented.
Abstract: This paper presents an algorithm that can be used to design finite impulse response (FIR) digital filters with linear phase. The presentation is in the form of a block diagram together with the Fortran IV listing of the program.
169 citations