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

Non-uniform wordlength delay lines for FIR filters

When FIR filters are designed floating point arithmetic is generally used. However when implemented on hardware such as ASICs, fixed point arithmetic must be used to minimise cost and power requirements. Research to minimise hardware costs has mainly focused on the quantization effects of fixed point wordlengths for the coefficients, multipliers and adders of FIR filters, but with the actual data delays assigned a uniform wordlength and essentially not optimised. This paper proposes that the wordlengths of the delay line can be non-uniform with a minimal increase in quantization noise for parallel implementation of FIR filters where there are differences in the magnitudes of the coefficients. A non-uniform delay line allows hardware savings in terms of delay register wordlengths, delay signal wordlengths and multiplier wordlengths. Results for an FIR design are presented which demonstrate the hardware savingswhen using a non-uniform wordlength delay lin

Efficient design of a class of multiplier-less perfect reconstruction two-channel filter banks and wavelets with prescribed output accuracy

The 11th IEEE Signal Processing Workshop on Statistical Signal Processing, Singapore, 6-8 August 2001This paper proposes a novel algorithm for the design and hardware reduction of a class of multiplier-less two-channel PR filter banks (FBs) using sum-of-powers-of-two (SOPOT) coefficient. It minimizes a more realistic hardware cost, such as adder cells, subject to a prescribe output accuracy taking into account of the rounding and overflow effects, instead of using just the SOPOT terms as in conventional method. Furthermore, by implementing the filters in the FBs using multiplier-block (MB), significant overall saving in hardware resources can be achieved. An effective random search algorithm is also proposed to solve the design problem, which is also applicable to PR IIR FBs with highly nonlinear objective functions.published_or_final_versio

Linear Phase FIR Low Pass Filter Design Based on Firefly Algorithm

In this paper, a linear phase Low Pass FIR filter is designed and proposed based on Firefly algorithm. We exploit the exploitation and exploration mechanism with a local search routine to improve the convergence and get higher speed computation. The optimum FIR filters are designed based on the Firefly method for which the finite word length is used to represent coefficients. Furthermore, Particle Swarm Optimization (PSO) and Differential Evolution algorithm (DE) will be used to show the solution. The results will be compared with PSO and DE methods. Firefly algorithm and Parks–McClellan (PM) algorithm are also compared in this paper thoroughly. The design goal is successfully achieved in all design examples using the Firefly algorithm. They are compared with that obtained by using the PSO and the DE algorithm. For the problem at hand, the simulation results show that the Firefly algorithm outperforms the PSO and DE methods in some of the presented design examples. It also performs well in a portion of the exhibited design examples particularly in speed and quality

Wordlength determination algorithms for hardware implementation of linear time invariant systems with prescribed output accuracy

This paper proposes two novel algorithms for optimizing the hardware resources in finite wordlength implementation of linear time invariant systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first algorithm formulates the design problem as a constrained optimization, from which an analytic closed-form solution of the internal wordlengths subject to a prescribed output accuracy can be determined by the Lagrange multiplier method. The second algorithm is based on a discrete optimization method called the Marginal Analysis method, and it yields the desired wordlengths in integer values. Both approaches are found to be very effective and they are well-suited to large scale systems such as software radio receivers. Design examples show that the proposed algorithms offer better results and a lower design complexity than conventional methods. © 2005 IEEE.published_or_final_versio

Particle Swarm Optimization with Quantum Infusion for the Design of Digital Filters

In this paper, particle swarm optimization with quantum infusion (PSO-QI) has been applied for the design of digital filters. In PSO-QI, Global best (gbest) particle (in PSO star topology) obtained from particle swarm optimization is enhanced by doing a tournament with an offspring produced by quantum behaved PSO, and selecting the winner as the new gbest. Filters are designed based on the best approximation to the ideal response by minimizing the maximum ripples in passband and stopband of the filter response. PSO-QI, as is shown in the paper, converges to a better fitness. This new algorithm is implemented in the design of finite impulse response (FIR) and infinite impulse response (IIR) filter

Multiplierless multirate FIR filter design and implementation

Ph.DDOCTOR OF PHILOSOPH