It is known that all resolution IV regular 2 designs of run size N = 2 where 5N/16 < n < N/2 must be projections of the maximal even design with N/2 factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even 2 design and that of its complement in the maximal even design. Using these identities, we identify some (we...

This paper presents an approach to the wordlength allocation and optimization problem for linear digital signal processing systems implemented as custom parallel processing units. Two techniques are proposed, one which guarantees an optimum set of wordlengths for each internal variable, and one which is a heuristic approach. Both techniques allow the user to tradeoff implementation area for ari...

Many digital signal processing algorithms are first developed in floating point and later converted into fixed point for digital hardware implementation. During this conversion, more than 50% of the design time may be spent for complex designs, and optimum wordlengths are searched by trading off hardware complexity for arithmetic precision at system outputs. We propose a fast algorithm for sear...

This paper investigates the problem of global asymptotic stability of fixed-point statespace two-dimensional (2-D) digital filters described by the Roesser model in the presence of finite wordlength nonlinearities. The class of nonlinearities under consideration captures the combined effects of quantization (except value truncation) and overflow arithmetic employed in practice. A new criterion ...

Identities about the wordlength patterns of regular s designs and their complementary designs are established through a first-order differential equation satisfied by a structure function. The identities are then generalized to s designs with multiple groups of factors. An advantage of using the structure function and partial differential equation is that it can easily adapt to some structural ...

This paper describes a novel resource binding technique for use in multiple-wordlength systems implemented in FPGAs. It is demonstrated that the multiple-wordlength binding problem is significantly different for addition and multiplication, and techniques to share resources between several operations are examined for FPGA architectures. A novel formulation of the resource binding problem is pre...

A novel iterative quantization procedure for the design of finite wordlength linear phase FIR filters of high order and minimum frequency domain error is proposed: a one by one increased number of filter coefficients is quantized where the augmented frequency domain error is re-minimized in each case. This new approach achieves a smaller frequency domain error than rounding of the optimal non-q...

This paper proposes a realization method of high accuracy 2-D variable IIR digital filters with real coefficients. The proposed method uses the reduced-dimensional decomposition form as a prototype structure of 2-D variable digital filters to suppress the degradation of tuning accuracy due to the linear approximation of variable coefficients. Furthermore, the 1-D subfilters of the prototype fil...