Low-sensitivity digital-filter structures which are amenable to error-spectrum shaping

Abstract

A/~ract -A systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS). Collectively, these structures can realize any stable second-order transfer function. For every transfer function, a choice of at least two structures is available but, through a sensitivity analysis, the optimum one can always be identified. The paper concludes with sensitivity and roundoff-noise comparisons which show that the new structures are usually superior relative to corresponding direct canonic structures and also relative to the state-space section-optimal structure.

Evolutionary synthesis of low-sensitivity digital filters using adjacency matrix

“…More complex filters require high computational effort to be evaluated by the symbolic mathematical package. In order to accelerate the fitness computation, a new procedure using the relative sensitivity criterion [39] is employed:…”

“…A given structure may require a large number of multipliers and yet be relatively insensitive to the coefficients quantization errors while another one with fewer elements may generate parasitic oscillations when signals are quantized [37]. Thus, low-sensitivity is related to the filter topology and it is expected that the evolutionary synthesis methods that are able to explore large solutions spaces can find better solutions than the deterministic approaches [38][39][40][41] which are bounded to a limited set of filter structures.…”

“…In the first example, a second-order filter is used to compare the results of the proposed method with other results found in the literature [36,39,46]. This is justified by the fact that classical design techniques will realize higherorder transfer functions by cascading second and first-order sections to minimize the coefficient quantization effects [37].…”

Evolutionary synthesis of low-sensitivity equalizers using adjacency matrix representation

“…The multipliers values ( 1 0.50 m = , 2 1.00 m = − , 3 0.50 m = − ) are obtained by solving the system of equations that results from equating the coefficients in (20) and (21). If this system has no real solution, zero fitness is assigned to the individual.…”

“…A given structure may require a large number of multipliers and yet be relatively insensitive to the coefficients quantization errors while one with fewer elements may generate parasitic oscillations when signals are quantized [18]. Thus, low-sensitivity is related to the filter topology and it is expected that the evolutionary synthesis methods could find better solutions than the deterministic approaches [19][20][21][22] which are bounded to a limited set of filter structures.…”