Design of IIR filters by optimization techniques

• Main Author: Wang, Zhe.
• Other Authors: Lin Zhiping
• Format: Final Year Project
• Language: English
• Published: 2011
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Electronic circuits
• Online Access: http://hdl.handle.net/10356/46038
• Institution: Nanyang Technological University

In this report, mainly two Minimax design techniques of Digital IIR Filters namely Sequential Constrained Least-Squares Method combined with Steiglitz-McBride (SCLS SM) and Sequential Minimization Procedure for Minimax Design of IIR Filter Based on Second-Order Factor Updates (SMSOF) are presented to solve the two optimization design issues on IIR filters, which refers to converting the non-convex optimization problem into the convex problem and the stability issue of IIR filters. Through simulation examples and comparisons between SCLS-SM and SM-based Direct Minimization Methods (Direct-SM), it was found that SCLS-SM has a higher possibility to obtain better results in our three examples’ case (High-Pass, Low-Pass and Band-Stop Filters), since SCLS-SM turning the non-convex optimization problem into a convex problem through combining Steiglitz-McBride (SM) Strategy. Two Positive Realness stability conditions were proposed to the SCLS-SM to ensure the stability of the IIR Filter. All-Pass Filter Example was also presented; however, SCLS-SM does not work better since it got an undesired maximum pole radius. Moreover, for SMSOF, a sufficient and necessary stability condition, i.e. stability triangle is taking into consideration: the IIR filter denominator in this method present in the form of a series of cascaded second-order factors, combining with Levy-Sanathanan-Koerner (L-SK), the minimax problem can be transformed into a semi-infinite-positive-definite QP problem. At each time, only the coefficients of the numerator and one second-order factor are optimized. Four simulation examples are presented showing that SMSOF generally does a good job even in the All-Pass Filters’ case, initialization scheme for SMSOF were also studied under different fed in conditions. Last but not least, a special IIR filter, namely Half-Band Filter (HBF) was designed through SOCP based All-Pass Filters’ Method, SCLS-SM, Direct SM and SMSOF Methods. By comparing among them, All Pass-Based HBF got overall best results.