Bounded Complex and Lossless Bounded Complex Transfer Functions and their Applications

Abstract

The concepts of structural boundedness and structural losslessness are known to be the keys behind the realization of low passband sensitivity digital filters implemented using real arithmetic. A generalization of these concepts leads to bounded complex and lossless bounded complex transfer functions, which are shown to play a similar role in the realization of low passband sensitivity digital filters with complex coefficients. Various filter realization strategies are pointed out, which involve the interconnection of complex lossless building blocks, thereby assuring the structural passivity property in the realization. Some design examples are included to verify the low sensitivity properties.

Indexing terms:

• Digital filter
• Bounded complex transfer function