Digital ladder structures and coefficient sensitivity

Recently, there has been a great deal of interest in the implementation of digital filter structures with low-coefficient word length. A conjecture has been made by Fettweis that if digital filter structures are modeled after analog ladder structures, which are known to have desirable coefficient sensitivity properties, then the digital ladder structures will also have these properties and could be implemented with low-coefficient word lengths. To investigate this conjecture, a seventh-order Chebyshev low-pass filter was realized as a digital ladder structure and the coefficient sensitivity was analyzed experimentally under coefficient rounding in floating-point representation. To serve as a comparison similar examples of cascade structures of direct and coupled form sections were also analyzed in the same manner. The conclusions drawn are that, indeed, the digital ladder structures in many cases can be implemented with lower coefficient word lengths than the conventional structures.