Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

Optimisation of multiplier-less FIR filter design techniques

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

A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters

International audienceMany applications of finite impulse response (FIR) digital filters impose strict format constraints for the filter coefficients. Such requirements increase the complexity of determining optimal designs for the problem at hand. We introduce a fast and efficient method, based on the computation of good nodes for polynomial interpolation and Euclidean lattice basis reduction. Experiments show that it returns quasi-optimal finite wordlength FIR filters; compared to previous approaches it also scales remarkably well (length 125 filters are treated in < 9s). It also proves useful for accelerating the determination of optimal finite wordlength FIR filters

Design Of Polynomial-based Filters For Continuously Variable Sample Rate Conversion With Applications In Synthetic Instrumentati

In this work, the design and application of Polynomial-Based Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis function coefficients. The frequency domain optimization of PBFs via linear programming has been proposed in the literature, however, the algorithm was not detailed nor were explicit formulas derived. In this contribution, a minimax optimization procedure is derived for the frequency domain optimization of a PBF with time-domain constraints. Explicit formulas are given for direct input to a linear programming routine. Additionally, accompanying Matlab code implementing this optimization in terms of the derived formulas is given in the appendix. In the literature, it has been pointed out that the frequency response of the Continuous-Time (CT) filter decays as frequency goes to infinity. It has also been observed that when implemented in SRC, the CT filter is sampled resulting in CT frequency response aliasing. Thus, for example, the stopband sidelobes of the Discrete-Time (DT) implementation rise above the CT designed level. Building on these observations, it is shown how the rolloff rate of the frequency response of a PBF can be adjusted by adding continuous derivatives to the impulse response. This is of great advantage, especially when the PBF is used for decimation as the aliasing band attenuation can be made to increase with frequency. It is shown how this technique can be used to dramatically reduce the effect of alias build up in the passband. In addition, it is shown that as the number of continuous derivatives of the PBF increases the resulting DT implementation more closely matches the Continuous-Time (CT) design. When implemented for SRC, samples from a PBF impulse response are computed by evaluating the polynomials using a so-called fractional interval, µ. In the literature, the effect of quantizing µ on the frequency response of the PBF has been studied. Formulas have been derived to determine the number of bits required to keep frequency response distortion below prescribed bounds. Elsewhere, a formula has been given to compute the number of bits required to represent µ to obtain a given SRC accuracy for rational factor SRC. In this contribution, it is shown how these two apparently competing requirements are quite independent. In fact, it is shown that the wordlength required for SRC accuracy need only be kept in the µ generator which is a single accumulator. The output of the µ generator may then be truncated prior to polynomial evaluation. This results in significant computational savings, as polynomial evaluation can require several multiplications and additions. Under the heading of applications, a new Wideband Digital Downconverter (WDDC) for Synthetic Instruments (SI) is introduced. DDCs first tune to a signal\u27s center frequency using a numerically controlled oscillator and mixer, and then zoom-in to the bandwidth of interest using SRC. The SRC is required to produce continuously variable output sample rates from a fixed input sample rate over a large range. Current implementations accomplish this using a pre-filter, an arbitrary factor resampler, and integer decimation filters. In this contribution, the SRC of the WDDC is simplified reducing the computational requirements to a factor of three or more. In addition to this, it is shown how this system can be used to develop a novel computationally efficient FFT-based spectrum analyzer with continuously variable frequency spans. Finally, after giving the theoretical foundation, a real Field Programmable Gate Array (FPGA) implementation of a novel Arbitrary Waveform Generator (AWG) is presented. The new approach uses a fixed Digital-to-Analog Converter (DAC) sample clock in combination with an arbitrary factor interpolator. Waveforms created at any sample rate are interpolated to the fixed DAC sample rate in real-time. As a result, the additional lower performance analog hardware required in current approaches, namely, multiple reconstruction filters and/or additional sample clocks, is avoided. Measured results are given confirming the performance of the system predicted by the theoretical design and simulation

A minimax approach for the joint design of acoustic crosstalk cancellation filters

Journal ArticleAbstract-This paper presents a method for jointly designing immersive audio rendering filters for a single listener using loudspeakers. The filters for crosstalk cancellation are assumed to have finite impulse responses and are designed using the minimax criterion. In addition to the traditional Atal-Schroeder crosstalk canceler structure, this paper explores an alternate topology that requires the approximation of a single filter. In general, the minimax approach provides improved low-frequency performance leading to a better overall separation of the direct-path and cross-path transfer functions than least-squares designs. The performance of the single-filter structure is better than that of the traditional crosstalk cancellation structure

Design and Realization of Fully-digital Microwave and Mm-wave Multi-beam Arrays with FPGA/RF-SOC Signal Processing

There has been a constant increase in data-traffic and device-connections in mobile wireless communications, which led the fifth generation (5G) implementations to exploit mm-wave bands at 24/28 GHz. The next-generation wireless access point (6G and beyond) will need to adopt large-scale transceiver arrays with a combination of multi-input-multi-output (MIMO) theory and fully digital multi-beam beamforming. The resulting high gain array factors will overcome the high path losses at mm-wave bands, and the simultaneous multi-beams will exploit the multi-directional channels due to multi-path effects and improve the signal-to-noise ratio. Such access points will be based on electronic systems which heavily depend on the integration of RF electronics with digital signal processing performed in Field programmable gate arrays (FPGA)/ RF-system-on-chip (SoC). This dissertation is directed towards the investigation and realization of fully-digital phased arrays that can produce wideband simultaneous multi-beams with FPGA or RF-SoC digital back-ends. The first proposed approach is a spatial bandpass (SBP) IIR filter-based beamformer, and is based on the concepts of space-time network resonance. A 2.4 GHz, 16-element array receiver, has been built for real-time experimental verification of this approach. The second and third approaches are respectively based on Discrete Fourier Transform (DFT) theory, and a lens plus focal planar array theory. Lens based approach is essentially an analog model of DFT. These two approaches are verified for a 28 GHz 800 MHz mm-wave implementation with RF-SoC as the digital back-end. It has been shown that for all proposed multibeam beamformer implementations, the measured beams are well aligned with those of the simulated. The proposed approaches differ in terms of their architectures, hardware complexity and costs, which will be discussed as this dissertation opens up. This dissertation also presents an application of multi-beam approaches for RF directional sensing applications to explore white spaces within the spatio-temporal spectral regions. A real-time directional sensing system is proposed to capture the white spaces within the 2.4 GHz Wi-Fi band. Further, this dissertation investigates the effect of electro-magnetic (EM) mutual coupling in antenna arrays on the real-time performance of fully-digital transceivers. Different algorithms are proposed to uncouple the mutual coupling in digital domain. The first one is based on finding the MC transfer function from the measured S-parameters of the antenna array and employing it in a Frost FIR filter in the beamforming backend. The second proposed method uses fast algorithms to realize the inverse of mutual coupling matrix via tridiagonal Toeplitz matrices having sparse factors. A 5.8 GHz 32-element array and 1-7 GHz 7-element tightly coupled dipole array (TCDA) have been employed to demonstrate the proof-of-concept of these algorithms

Designs of Digital Filters and Neural Networks using Firefly Algorithm

Firefly algorithm is an evolutionary algorithm that can be used to solve complex multi-parameter problems in less time. The algorithm was applied to design digital filters of different orders as well as to determine the parameters of complex neural network designs. Digital filters have several applications in the fields of control systems, aerospace, telecommunication, medical equipment and applications, digital appliances, audio recognition processes etc. An Artificial Neural Network (ANN) is an information processing paradigm that is inspired by the way biological nervous systems, such as the brain, processes information and can be simulated using a computer to perform certain specific tasks like clustering, classification, and pattern recognition etc. The results of the designs using Firefly algorithm was compared to the state of the art algorithms and found that the digital filter designs produce results close to the Parks McClellan method which shows the algorithm’s capability of handling complex problems. Also, for the neural network designs, Firefly algorithm was able to efficiently optimize a number of parameter values. The performance of the algorithm was tested by introducing various input noise levels to the training inputs of the neural network designs and it produced the desired output with negligible error in a time-efficient manner. Overall, Firefly algorithm was found to be competitive in solving the complex design optimization problems like other popular optimization algorithms such as Differential Evolution, Particle Swarm Optimization and Genetic Algorithm. It provides a number of adjustable parameters which can be tuned according to the specified problem so that it can be applied to a number of optimization problems and is capable of producing quality results in a reasonable amount of time

Time-Interleaved Analog-to-Digital Converter (TIADC) Compensation Using Multichannel Filters

Published methods that employ a filter bank for compensating the timing and bandwidth mismatches of an M-channel time-interleaved analog-to-digital converter (TIADC) were developed based on the fact that each sub-ADC channel is a downsampled version of the analog input. The output of each sub-ADC is filtered in such a way that, when all the filter outputs are summed, the aliasing components are minimized. If each channel of the filter bank has N coefficients, the optimization of the coefficients requires computing the inverse of an MN times MN matrix if the weighted least squares (WLS) technique is used as the optimization tool. In this paper, we present a multichannel filtering approach for TIADC mismatch compensation. We apply the generalized sampling theorem to directly estimate the ideal output of each sub-ADC using the outputs of all the sub-ADCs. If the WLS technique is used as the optimization tool, the dimension of the matrix to be inversed is N times N. For the same number of coefficients (and also the same spurious component performance given sufficient arithmetic precision), our technique is computationally less complex and more robust than the filter-bank approach. If mixed integer linear programming is used as the optimization tool to produce filters with coefficient values that are integer powers of two, our technique produces a saving in computing resources by a factor of approximately (100.2N(M- 1)/(M-1) in the TIADC filter design.published_or_final_versio