Search of Optimal s-to-z Mapping Function for IIR Filter Designing without Frequency Pre-warping

ABSTRACT

Bilinear transformation is one of the most popular s-to-z mapping functions and widely used to design digital filters, disregarding its susceptibility to “frequency warping”. Although “frequency pre-warping” is used to counter the warping effect, it cannot be applied uniformly in all the cases. Moreover, the pre-warping technique is unable to remove the warping-effect completely. It is a general convention that the higher-order s-to-z transform gives more linear mapping than the lower order counterparts. Surprisingly, the 1st-order bilinear transformation is still preferred over higher-order s-to-z mapping functions. An investigation has been performed to develop a generalized criterion for selecting optimal s-to-z mapping function so that IIR filters can be designed without the need of “frequency pre-warping”. A couple of IIR filters (integer and fractional order) have been designed using several s-to-z mapping schemes, without applying the frequency pre-warping technique. MATLAB and Simulink responses have been given to support and validate the developed generalized criterion, for selecting optimal s-to-z mapping function.

KEYWORDS:

• Bilinear transformation
• Fractional-order filters
• IIR filters
• s-to-z mapping
• Simulink
• Warping effect

Additional information

Notes on contributors

Shalabh K. Mishra

Shalabh K Mishra holds Master of Technology degree in signal processing from Netaji Subhas Institute of Technology, University of Delhi, India. He is studying for a PhD at the Netaji Subhas Institute of Technology, University of Delhi. His research interests include digital and analog signal processing.Email: [email protected]

Dharmendra K. Upadhyay

Dharmendra Kumar Upadhyay holds Bachelor of Engineering degree in electronics and communication engineering from Kumaon University, Nainital and Master of Technology in communication and information systems from Aligarh muslim. University, Aligarh, UP. He obtained PhD from Uttarakhand Technical University, Dehradun, Uttarakhand. He is currently working as professor in Division of Electronics and Communication Engineering, Netaji Subhas Institute of Technology, University of Delhi, New Delhi. His research interests include digital signal processing, microwave filter and antenna designs. He has published several papers in various International Journals including IET, Electronics Letters. He is a life member of ISTE. He is also the reviewer of several reputed International Journals namely IEEE Transactions on Circuits and Systems-I; Circuits and Systems-II; Signal Processing; Circuits Systems and Signal Processing- Springer, ETRI Journal, etc.Email: [email protected]

Maneesha Gupta

Maneesha Gupta received BE and ME in electronics & communication engineering from Government Engineering College, Jabalpur in 1981 and 1983, respectively and PhD in electronics engineering from Indian Institute of Technology, Delhi in 1990. She is currently working as a professor in electronics & communication engineering Department of Netaji Subhas Institute of Technology, New Delhi since 2000. Her teaching and research interests are switched capacitors circuits and analog signal processing. She has co-authored over 120 research papers in the above areas.