https://www2.le.ac.uk/centres/csn/publications-1/Publications/past-present-and-future-of-spike-sorting-techniques

Past, present and future of spike sorting techniques

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.

Generalized digital Butterworth filter design

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 todays 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: 
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*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

Digital Signal Processing: A Computer Science Perspective

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.

Chromatic Dispersion Compensation Using Digital IIR Filtering With Coherent Detection

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.

/pdf/all-about-audio-equalization-solutions-and-frontiers-550t19t9nq.pdf

All About Audio Equalization: Solutions and Frontiers

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. >

S.R. Powell

Papers

A technique for realizing linear phase IIR filters