Investigation into digital audio equaliser systems and the effects of arithmetic and transform errors on performance

Merged with duplicate record 10026.1/2685 on 07.20.2017 by CS (TIS)Discrete-time audio equalisers introduce a variety of undesirable artefacts into audio mixing systems, namely, distortions caused by finite wordlength constraints, frequency response distortion due to coefficient calculation and signal disturbances that arise from real-time coefficient update. An understanding of these artefacts is important in the design of computationally affordable, good quality equalisers. A detailed investigation into these artefacts using various forms of arithmetic, filter frequency response, input excitation and sampling frequencies is described in this thesis. Novel coefficient calculation techniques, based on the matched z-transform (MZT) were developed to minimise filter response distortion and computation for on-line implementation. It was found that MZT-based filter responses can approximate more closely to s-plane filters, than BZTbased filters, with an affordable increase in computation load. Frequency response distortions and prewarping/correction schemes at higher sampling frequencies (96 and 192 kHz) were also assessed. An environment for emulating fractional quantisation in fixed and floating point arithmetic was developed. Various key filter topologies were emulated in fixed and floating point arithmetic using various input stimuli and frequency responses. The work provides detailed objective information and an understanding of the behaviour of key topologies in fixed and floating point arithmetic and the effects of input excitation and sampling frequency. Signal disturbance behaviour in key filter topologies during coefficient update was investigated through the implementation of various coefficient update scenarios. Input stimuli and specific frequency response changes that produce worst-case disturbances were identified, providing an analytical understanding of disturbance behaviour in various topologies. Existing parameter and coefficient interpolation algorithms were implemented and assessed under fihite wordlength arithmetic. The disturbance behaviour of various topologies at higher sampling frequencies was examined. The work contributes to the understanding of artefacts in audio equaliser implementation. The study of artefacts at the sampling frequencies of 48,96 and 192 kHz has implications in the assessment of equaliser performance at higher sampling frequencies.Allen & Heath Limite

Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

Chromatic Dispersion Compensation Using Filter Bank Based Complex-Valued All-Pass Filter

A long-haul transmission of 100 Gb/s without optical chromatic-dispersion (CD) compensation provides a range of benefits regarding cost effectiveness, power budget, and nonlinearity tolerance. The channel memory is largely dominated by CD in this case with an intersymbol-interference spread of more than 100 symbol durations. In this paper, we propose CD equalization technique based on nonmaximally decimated discrete Fourier transform (NMDFT) filter bank (FB) with non-trivial prototype filter and complex-valued infinite impulse response (IIR) all-pass filter per sub-band. The design of the sub-band IIR all-pass filter is based on minimizing the mean square error (MSE) in group delay and phase cost functions in an optimization framework. Necessary conditions are derived and incorporated in a multi-step and multi-band optimization framework to ensure the stability of the resulting IIR filter. It is shown that the complexity of the proposed method grows logarithmically with the channel memory, therefore, larger CD values can be tolerated with our approach

Available Techniques for Magnetic Hard Disk Drive Read Channel Equalization

This paper presents an extensive, non-exhaustive, study of available hard disk drive read channel equalization techniques used in the storage and readback of magnetically stored information. The physical elements and basic principles of the storage processes are introduced together with the basic theoretical definitions and models. Both read and write processes in magnetic storage are explained along with the definition of simple key concepts such as user bit density, intersymbol interference, linear and areal density, read head pulse response models, and coding algorithm

Theory and Methodology of Integrated Ladder Filter Design

This thesis presents a systematic study of integrated ladder filter design. A theoretical model of ladder structures is first established in terms of a family of symmetric matrix polynomial systems (SMPS's). It is shown that SMPS's are a natural mathematical abstraction of ladder circuits. The properties of stability, canonical (or minimal) realisation, low-sensitivity and low-noise, are proved for SMPS's under certain very simple conditions. A design methodology is then presented for active-RC, SC and digital ladders. The basic principle is that a SMPS can be decomposed by means of matrix factorisation into several linear systems, which can then be easily realised by active or digital circuits. It is shown that many existing methods, such as leapfrog or coupled biquads, result from some special decompositions. It is further shown that LU and UL factorisations drawn from numerical methods can be used to develop several novel structures (so-called LUD and ULD structures) which demonstrate significant improvments over existing ones regarding sensitivity, component area and dynamic range. This is confirmed by examples and statistical investigations. Besides the matrix methods applicable to standard lowpass and bandpass cases, further research is undertaken for bandstop, highpass and allpass filter designs. It is demonstrated that frequency transformations can be used to reduce the hardware cost in many classical filtering cases. A novel building block, the so called TWINTOR, is introduced in bandstop design to reduce the switching rate. Active-RC and SC allpass ladders are constructed and proved to have significant advantages over the existing biquad circuits. Matrix methods also provide an efficient vechicle for the development of a filter design software package called PANDDA. Its many outstanding features are described. Finally measured results from two fabricated LUD SC filters are presented. They confirm the high quality of the novel circuit structures developed by this research

An investigation into the real-time manipulation and control of three-dimensional sound fields

This thesis describes a system that can be used for the decoding of a three dimensional audio recording over headphones or two, or more, speakers. A literature review of psychoacoustics and a review (both historical and current) of surround sound systems is carried out. The need for a system which is platform independent is discussed, and the proposal for a system based on an amalgamation of Ambisonics, binaural and transaural reproduction schemes is given. In order for this system to function optimally, each of the three systems rely on providing the listener with the relevant psychoacoustic cues. The conversion from a five speaker ITU array to binaural decode is well documented but pair-wise panning algorithms will not produce the correct lateralisation parameters at the ears of a centrally seated listener. Although Ambisonics has been well researched, no one has, as yet, produced a psychoacoustically optimised decoder for the standard irregular five speaker array as specified by the ITU as the original theory, as proposed by Gerzon and Barton (1992) was produced (known as a Vienna decoder), and example solutions given, before the standard had been decided on. In this work, the original work by Gerzon and Barton (1992) is analysed, and shown to be suboptimal, showing a high/low frequency decoder mismatch due to the method of solving the set of non-linear simultaneous equations. A method, based on the Tabu search algorithm, is applied to the Vienna decoder problem and is shown to provide superior results to those shown by Gerzon and Barton (1992) and is capable of producing multiple solutions to the Vienna decoder problem. During the write up of this report Craven (2003) has shown how 4th order circular harmonics (as used in Ambisonics) can be used to create a frequency independent panning law for the five speaker ITU array, and this report also shows how the Tabu search algorithm can be used to optimise these decoders further. A new method is then demonstrated using the Tabu search algorithm coupled with lateralisation parameters extracted from a binaural simulation of the Ambisonic system to be optimised (as these are the parameters that the Vienna system is approximating). This method can then be altered to take into account head rotations directly which have been shown as an important psychoacoustic parameter in the localisation of a sound source (Spikofski et al., 2001) and is also shown to be useful in differentiating between decoders optimised using the Tabu search form of the Vienna optimisations as no objective measure had been suggested. Optimisations for both Binaural and Transaural reproductions are then discussed so as to maximise the performance of generic HRTF data (i.e. not individualised) using inverse filtering methods, and a technique is shown that minimises the amount of frequency dependant regularisation needed when calculating cross-talk cancellation filters.EPRS

Switched-current filtering systems: design, synthesis and software development

Allpass filters are commonly employed in many applications to perform group delay equalisation in the passband. They are non-minimum phase by definition and are characterised by poles and zeros in mirror-image symmetry. SI allpass filters of both cascade biquad and bilinear-LDI ladder types have been in existence. These were implemented using Euler based integrators. Cascade biquads are known to have highly sensitive amplitude responses and Euler integrators suffer from excess phase. The equalisers that are proposed here are based on bilinear integrators instead of Euler ones. Derivation of these equalisers can proceed from either the s-domain, or directly from the z-domain, where a prototype is synthesised using the respective continued-fractions expansions, and simulated using standard matrix methods. The amplitude response of the bilinear allpass filter is shown to be completely insensitive to deviations in the reactive ladder section. Simulations of sensitivities and non-ideal responses reveal the advantages and disadvantages of the various structures. Existing DI multirate filters have to date been implemented as direct-form FIR and IIR polyphase structures, or as simple cascade biquad or ladder structures with non-optimum settling times. FIR structures require a large number of impulse coefficients to realise highly selective responses. Even in the case of linear phase response with symmetric impulse coefficients, when the number of coefficients can be halved, significant overheads can be incurred by additional multiplexing circuitry. Direct-form IIR structures are simple but are known to be sensitive to coefficient deviations and structures with non-optimum settling times operate entirely at the higher clock frequency. The novel SI decimators and interpolators proposed are based on low sensitivity ladder structures coupled with FIR polyphase networks. They operate entirely at the lower clock frequency which maximises the time available for the memory cells to settle. Two different coupling architectures with different advantages and disadvantages are studied

Database of audio records

Diplomka a prakticky castDiplome with partical part

Analogue filter networks: developments in theory, design and analyses

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