HIGH PERFORMANCE PROTOTYPE FILTER DESIGN AND COST FUNCTION DETERMINATION

Abstract

Systems that highlight the specific features of a signal, reformat certain properties of a signal or change the signal to the desired property are called filters. Filters with finite impulse response are called FIR (Finite Impulse Response) filters. Systems that use multiple sampling rates in the processing of digital signals are called multirate digital signal processing systems. The two-channel filter bank is an essential part of the multirate filter bank and is referred to as the Quadrature MirrorFilter (QMF) Bank. In this study, a low-pass FIR filter, easy to design and having a high-performance is designed using the window based FIR filter design technique for the prototype of two channel QMF bank structures. For this purpose, with the help of two independent variables, the Kaiser window, which is widely used in the literature, is used for the window based FIR filter and for this window function the Beta parameter is optimized to obtain the best stop band ripple, pass band ripple and stop band gain. Optimization, in its most general meaning, is the process of determining the values that the decision variables will take in order to optimize the value of a defined objective function under certain constraints in a system. The aim of the optimization is to find the value of the parameter where the ripples are the lowest and the gain is the largest. In this study, for the optimization of Beta parameter, Artificial Bee Colony (ABC) algorithm based on swarm intelligence approach was used. ABC algorithm is an optimization algorithm based on the food search behavior of honeybees. The cost (objective) function is the cost-output relationship, which defines the cheapest or most efficient way of achieving a specific production level. This relationship is, for our work, found the which structure has the lowest error. In this study, Mean Square Error (MSE), Mean Absolute Error (MAE), Cross Entropy Errors (CEE) and Total Sum of these errors were used as cost function. Which cost function has the best performance is investigated. The data obtained are presented in tables. At the end of the study, a low pass FIR filter with high performance and low error rate has been obtained by optimizing only one parameter.