Design of Digital IIR filters with the Advantages of Model Order Reduction Technique

In this paper, a new model order reduction phenomenon is introduced at the design stage of linear phase digital IIR filter. The complexity of a system can be reduced by adopting the model order reduction method in their design. In this paper a mixed method of model order reduction is proposed for linear IIR filter. The proposed method employs the advantages of factor division technique to derive the reduced order denominator polynomial and the reduced order numerator is obtained based on the resultant denominator polynomial. The order reduction technique is used to reduce the delay units at the design stage of IIR filter. The validity of the proposed method is illustrated with design example in frequency domain and stability is also examined with help of nyquist plot. Keywords—Error index (J), Factor division method, IIR filter, Nyquist plot, Order reduction. I.INTRODUCTION N important step in the development of a digital filter is the determination of a realizable transfer function G(z) approximating the given frequency response specifications. If an IIR filter is desired, it is also necessary to ensure that G(z) is stable. The process of deriving the transfer function G(z) is called digital filter design. After G(z) has been obtained, the next step is to realize it in the form of a suitable filter structure. There are two major issues that need to be answered before one can develop the digital transfer function G(z). The first and foremost issue is the development of a reasonable filter frequency response specification from the requirements of the overall system in which the digital filter is to be employed. The second issue is to determine whether an FIR or IIR filter is to be designed. The order reduction technique is then introduced to obtain an equivalent reduced IIR linear phase filter. The mathematical models obtained from the theoretical criteria those relevant with the given system normally results as a higher order model. Such systems are difficult to be analyzed and also the design of controller becomes too difficult. Obviously, there is a need for smaller models. Smaller models are models that describe the behavior of a system accurately, without the disadvantage of unnecessary K.Ramesh is Lecturer with the Department of Electrical and Electronics Engineering, Velalar College of Engineering and Technology, Erode, Tamilnadu, India-638012. (e-mail: [email protected]) A.Nirmalkumar is Professor and Head with the Department of Electrical and Electronics Engineering, Bannari Amman institute of Technology, Sathyamangalam, Tamilnadu, India-638401. G.Gurusamy is Dean with the Department of Electrical and Electronics Engineering, Bannari Amman institute of Technology, Sathyamangalam, Tamilnadu, India-638401. detail. This enables the modeling of coupled complex phenomena in a reasonable time. First of all, these models should be smaller than the original model, meaning that they are computationally less demanding. Their behavior must in at least one way be comparable to the behavior of the original model. Preferably, the smaller models are physically as well as mathematically motivated. This makes the models interpretable and efficient. The host of mathematical processes to derive smaller models forms the field of what we call Model Order Reduction (MOR). The reason for the name is that the model is reduced in size by some technique. The model is assumed to be already present, being derived by physical laws and assumptions. Sometimes the methods are abusively called Reduced Order Modeling., which should then account for the task of modeling in such a way that the derived models are smaller right away. In many cases it is very well possible to reduce the size of a model. We already saw that mathematical rules of discretization may lead to models which are too large and have too much detail for the required precision. Also the final output of the model has some flexibility in the required accuracy. In applications a small error is often admissible. This flexibility gives room for smaller approximations and faster methods. Furthermore, we are often only interested in certain states of the model, for instance only in the output due to a certain input. This, while the model contains information of inputs that are never imposed. Model Order Reduction tries to quickly capture the essential features of a structure. This means that in an early stage of the process, the most basic properties of the original model must already be present in the smaller approximation. At a certain moment the process of reduction is stopped. At that point all necessary properties of the original model must be captured with sufficient precision. The order reduction of a linear time invariant system is applied in almost all fields of electrical engineering. The use of order reduced models for test simulations of complex systems is a lot easier than utilizing full order models. This is due to the fact that the lower order transfer function can be analyzed more easily. Therefore, order reduction algorithms are standard techniques in the integrated circuits community for analysis, approximation and simulation of models arising from interconnect and electromagnetic structure analysis. Conventional reduction methods are available in literature for reducing the order of large-scale linear MIMO systems in frequency domain [1–4]. Some of the existing methods are based on the global properties of G(s) have been proposed in the literature amongst which the frequency domain method using the continued-fraction expansion of G(s) and the classical Pade approximations are well known for their computational simplicity and matching of few initial timeA World Academy of Science, Engineering and Technology 28 2009