Synthesis of low-sensitivity orthogonal digital filters

✍ Scribed by Abo-Zahhad, M.; Fahmy, M. F.

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 274 KB
• Volume: 25
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/(sici)1097-007x(199711/12)25:6<503::aid-cta972>3.0.co;2-#

✦ Synopsis

A novel method is proposed for the synthesis of low-sensitivity digital filters meeting any prescribed transfer function. The method is based on extracting an orthogonal matrix from the filter state matrix, resulting in structures that need n Givens rotations and at most n#1 multipliers. Thus the proposed realization is canonic in the sense that it has the same degrees of freedom as the original transfer function. It is also shown that when the filter transfer function is a reciprocal reactant bounded function, it can be decomposed into allpass functions that need only Givens rotations for their realization. As the basic module in the realization is the Givens rotation, the CORDIC computation algorithm can be applied directly. This means considerable savings in computation time and complexity. It also results in structures that are less sensitive to the effects of finite word length. Illustrative examples, including the design and synthesis of linear phase selective filters, are given to show the extremely low sensitivity with respect to finite word length of the resulting realizations when compared with other methods.