31 research outputs found

    IIR Digital Filter Design Using Convex Optimization

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    Digital filters play an important role in digital signal processing and communication. From the 1960s, a considerable number of design algorithms have been proposed for finite-duration impulse response (FIR) digital filters and infinite-duration impulse response (IIR) digital filters. Compared with FIR digital filters, IIR digital filters have better approximation capabilities under the same specifications. Nevertheless, due to the presence of the denominator in its rational transfer function, an IIR filter design problem cannot be easily formulated as an equivalent convex optimization problem. Furthermore, for stability, all the poles of an IIR digital filter must be constrained within a stability domain, which, however, is generally nonconvex. Therefore, in practical designs, optimal solutions cannot be definitely attained. In this dissertation, we focus on IIR filter design problems under the weighted least-squares (WLS) and minimax criteria. Convex optimization will be utilized as the major mathematical tool to formulate and analyze such IIR filter design problems. Since the original IIR filter design problem is essentially nonconvex, some approximation and convex relaxation techniques have to be deployed to achieve convex formulations of such design problems. We first consider the stability issue. A sufficient and necessary stability condition is derived from the argument principle. Although the original stability condition is in a nonconvex form, it can be appropriately approximated by a quadratic constraint and readily combined with sequential WLS design procedures. Based on the sufficient and necessary stability condition, this approximate stability constraint can achieve an improved description of the nonconvex stability domain. We also address the nonconvexity issue of minimax design of IIR digital filters. Convex relaxation techniques are applied to obtain relaxed design problems, which are formulated, respectively, as second-order cone programming (SOCP) and semidefinite programming (SDP) problems. By solving these relaxed design problems, we can estimate lower bounds of minimum approximation errors, which are useful in subsequent design procedures to achieve real minimax solutions. Since the relaxed design problems are independent of local information, compared with many prevalent design methods which employ local search, the proposed design methods using the convex relaxation techniques have an increased chance to obtain an optimal design

    Computer-Aided Design of Switched-Capacitor Filters

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    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

    DSP compensation for distortion in RF filters

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    There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality. In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated. In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance

    Low Latency Audio Processing

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    PhDLatency in the live audio processing chain has become a concern for audio engineers and system designers because significant delays can be perceived and may affect synchronisation of signals, limit interactivity, degrade sound quality and cause acoustic feedback. In recent years, latency problems have become more severe since audio processing has become digitised, high-resolution ADCs and DACs are used, complex processing is performed, and data communication networks are used for audio signal transmission in conjunction with other traffic types. In many live audio applications, latency thresholds are bounded by human perceptions. The applications such as music ensembles and live monitoring require low delay and predictable latency. Current digital audio systems either have difficulties to achieve or have to trade-off latency with other important audio processing functionalities. This thesis investigated the fundamental causes of the latency in a modern digital audio processing system: group delay, buffering delay, and physical propagation delay and their associated system components. By studying the time-critical path of a general audio system, we focus on three main functional blocks that have the significant impact on overall latency; the high-resolution digital filters in sigma-delta based ADC/DAC, the operating system to process low latency audio streams, and the audio networking to transmit audio with flexibility and convergence. In this work, we formed new theory and methods to reduce latency and accurately predict latency for group delay. We proposed new scheduling algorithms for the operating system that is suitable for low latency audio processing. We designed a new system architecture and new protocols to produce deterministic networking components that can contribute the overall timing assurance and predictability of live audio processing. The results are validated by simulations and experimental tests. Also, this bottom-up approach is aligned with the methodology that could solve the timing problem of general cyber-physical systems that require the integration of communication, software and human interactions

    Design and implementation of computationally efficient digital filters

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    Ph.DDOCTOR OF PHILOSOPH

    Optimisation of multiplier-less FIR filter design techniques

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    This thesis is concerned with the design of multiplier-less (ML) finite impulse response (FIR) digital filters. The use of multiplier-less digital filters results in simplified filtering structures, better throughput rates and higher speed. These characteristics are very desirable in many DSP systems. This thesis concentrates on the design of digital filters with power-of-two coefficients that result in simplified filtering structures. Two distinct classesof ML FIR filter design algorithms are developed and compared with traditional techniques. The first class is based on the sensitivity of filter coefficients to rounding to power-of-two. Novel elements include extending of the algorithm for multiple-bands filters and introducing mean square error as the sensitivity criterion. This improves the performance of the algorithm and reduces the complexity of resulting filtering structures. The second class of filter design algorithms is based on evolutionary techniques, primarily genetic algorithms. Three different algorithms based on genetic algorithm kernel are developed. They include simple genetic algorithm, knowledge-based genetic algorithm and hybrid of genetic algorithm and simulated annealing. Inclusion of the additional knowledge has been found very useful when re-designing filters or refining previous designs. Hybrid techniques are useful when exploring large, N-dimensional searching spaces. Here, the genetic algorithm is used to explore searching space rapidly, followed by fine search using simulated annealing. This approach has been found beneficial for design of high-order filters. Finally, a formula for estimation of the filter length from its specification and complementing both classes of design algorithms, has been evolved using techniques of symbolic regression and genetic programming. Although the evolved formula is very complex and not easily understandable, statistical analysis has shown that it produces more accurate results than traditional Kaiser's formula. In summary, several novel algorithms for the design of multiplier-less digital filters have been developed. They outperform traditional techniques that are used for the design of ML FIR filters and hence contributed to the knowledge in the field of ML FIR filter design

    Switched-capacitor filters and their application in data communications

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    There have been considerable developments in the field of switched-capacitor filter design over the past decade. Those developments which allow the operating frequency range of switched-capacitor filters to be extended are considered. The solution to the approximation and synthesis problems for l.d.i.-based switched-capacitor ladder filters discovered by Scanlan is explained. Computer software which implements his technique for low-pass filters is presented. A number of techniques for synthesising the network are investigated. It is shown that numerical difficulties limit the order of filter which can be synthesised. The sensitivity properties of switched-capacitor ladder filters are explored. A technique, which has been implemented in software, for evaluating the amplitude sensitivity of such filters is described. This program is used to demonstrate that the frequency variable terminations in the equivalent circuit of the switched-capacitor ladder filter adversely affect its sensitivity properties. Grcuit topologies which result in improved high frequency performance are considered, and a fully differential filter structure for high frequency operation is proposed. Circuits are presented for a digitally programmable switched-capacitor line equaliser and optimisation techniques for its design are investigated. The extension of the design to incorporate adaptive operation is discussed, and circuits based on the above designs which have been fabricated at the National Micro-electronics Research Centre (N.M.R.C.) in Cork are described

    Characterization and rejection of noise from in-cylinder pressure traces in a diesel engine

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    Diesel engine in-cylinder pressure analysis is important for engine research and diagnosis. It has been a subject of interest right from the inception of internal combustion engines. Engine cylinder pressure measurements provide insight into the combustion process and the accuracy of these measurements governs the quality of analyses of different combustion modes of the engine. Since the in-cylinder pressure increases abruptly after the start of combustion, non-flush mounting of the pressure transducer creates standing/resonant waves in the access passage which severely affect the recorded pressure fidelity by introducing undesired noise. The challenge is to get rid of these pressure pulsations and characterize the unaccounted noise which can lead to erroneous determination of different combustion parameters and characteristics. This work focuses on online filtering of the noisy pressure data so as to obviate the need of any post-processing for combustion and noise analysis. An online filtering algorithm is defined which is a combination of a five-point moving average filter and a forward and reverse Butterworth digital filter. The filter is tested for its robustness over different engine operating conditions such as engine load, speed, boost etc. The cut-off frequency of the filter is determined on a cycle-by-cycle basis using an algorithm based on the power spectral density of the pressure signal. The noise component is segregated from the pressure trace by means of pressure decomposition technique and the peak noise power is attributed to the access passage resonance frequency. Further development of this approach can be used to achieve optimal combustion control by means of the development of optimal injection strategies in order to fulfill emission reduction and performance requirements in Diesel engines
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