Normalized minimum norm digital filter structure: a basic building block for processing real and complex sequences

If a is a pole of a given transfer function, the complex first-order transfer function √(1-|a|²)/(z -a) represents a basic building block in various favorable realizations. The realization of this basic building block and its properties are investigated. It is shown that the structure is automatically scaled (normalized) and that it is a minimum norm structure (MNS) possessing low-sensitivity and low-noise properties. The structure is referred to as the normalized MNS. An elegant noise analysis of this structure is also given. As a direct application of the normalized MNS, a simple method is given to derive efficient structures for second-order filters. A particular second-order structure is suggested for very-low-sensitivity realization of classical filters