Low-Complexity and High-Modularity Structure for Implementing Transient-Free Pascal-Delay Filter

The maximally flat variable-delay (VD) digital filter can be derived by using the discrete-Pascal-transform (DPT) and the DPT-based Pascal-polynomial interpolation. In this paper, we develop an efficient structure for the low-complexity and high-modularity implementation of this Pascal-type VD filter. As compared to other existing filter structures, this new structure greatly reduces the multiplication operations required in the filtering process. Roughly speaking, the proposed new structure can reduce the multiplication operations by almost one-third. Thus, this new filter structure has the lowest filter complexity among all the existing filter structures for the implementation of the maximally flat VD filter. As a result, signal interpolation can be efficiently performed through utilizing this new filter structure. As opposed to other existing structure with transient problem, we will show that the proposed new structure does not involve any transient problem. That is, it is a transient-free structure. Consequently, the proposed new filter structure can achieve more accurate signal-interpolation results than other structures that have the transient problem. Finally, we show that this proposed structure also has high modularity and it is suited for modularized hardware implementation.