COMPARISION OF CONSTRAINT DESIGN OF FIR FILTER ON COMPLEX ERROR FUNCTION AND ON MAGNITUDE AND PHASE INDEPENDENTLY *RAGHVENDRA KUMAR, ** LILLIE DEWAN *M.Tech Student ** Asst. Professor Department of Electrical Engineering National Institute of Technology Kurukshetra INDIA e-mail: raghvendra_kumar80@rediffmail.com, l_dewanin@yahoo.com Abstract: An important feature of this paper is that both the algorithm presented in this paper allow for design constraints which often arise in practical filter design problems. Meeting required minimum stopband attenuation or a maximum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by both the methods compared here. Constraints designing can be done either by constraints on complex error function or constraints on magnitude and phase of error. This paper shows the comparison of these two techniques. Key Words: Constraints, Linear Quadratic ,Exchange Algorithm, Complex error function, Magnitude and Phase error 1. Introduction Digital filters are integral parts of many digital signal processing systems, including control systems, systems for audio and video processing, communication systems and systems for medical applications. Due to the increasing number of applications involving digital signal processing and digital filtering, the variety of requirements that have to be met by digital filters has increased as well. Consequently, there is a need for flexible techniques that can design digital filters satisfying sophisticated specifications. The design specifications are formulated in the frequency domain by choosing a complex desired frequency response which prescribes the desired magnitude and phase response. The complex function is defined on the domain of approximation. Which is a subset of the interval [0, 2 ) ( ω j e D ) ( ω j e D Ω π ]. In most cases the domain is the union of several disjoint frequency bands which are separated by transition bands where no desired response is specified. Ω The constraints designing of FIR Filter can be done by constraints on complex error function or by applying constraints on magnitude and phase of the error. These constraints can be put while using exchange algorithm as well. In this paper comparison of these two methods is discussed in detail. Cortezzao and Lightner [3] apply a multiple criterion optimization technique to a specification of both gain and group delay of FIR filter. But they state that their deign method requires considerable computing time and is reliable only for orders not higher than five for FIR filter. Chen and Parks [12] investigate an approach in which a large computer memory requirement and CPU time increases exponentially with increasing grid density, the complex valued response is converted into a real- valued function which is nearly equivalent to the complex function. They also state that their methods has using a linear programming technique the grid density governs the accuracy with which the solution approaches the optimum. Xiapoping Lai [13] applied PLS algorithm to the constrained least square design of FIR filter directly. But there was no method for non convex problem. The method presented here intends to solve the problem of computation time and memory requirement. The paper is organized as, after the brief introduction in section I, section II gives insight into Least square Approximation. Section IIIa deals with the Constrained Designing of filter with constraints on complex error function without using exchange approach while section III b deals exchange approach. Section IVa shows the constraints on magnitude and phase error independently without using exchange approach while IVb shows with using exchange approach. Section Vth gives the results obtained for the given example and section VIth deals conclusion followed by references. AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachusetts, USA, March 24-26, 2008 ISSN: 1790-5117 454 ISBN: 978-960-6766-47-3