Optimal design of state - space digital filters by simultaneous minimization of sensitivity and roundoff noise

Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters

“…In the literature on synthesis of filter structures [13][14][15][16][17][18][19][20][21][22][23][24][25], it is shown that the two Gramians and the second-order modes play central roles in analysis and optimization of filter performance such as the roundoff noise and the coefficient sensitivity. In other words, given the transfer function of a digital filter, we can formulate some cost functions with respect to the aforementioned filter performance in terms of the two Gramians (K, W ), and a filter structure of high performance can be obtained by constructing the two Gramians appropriately in such a manner that they optimize or sub-optimize the corresponding cost functions.…”

“…An example of high-performance digital filter structures is the balanced form [15,16,18,23,25]. This form consists of the two Gramians given by…”

“…In other words, few results have been reported about the relationship between the frequency transformation and the internal properties. As is well-known, the internal properties of filters are closely related to the problem of how we should construct a filter structure of a given transfer function, and this problem must be carefully considered in order to obtain analog filters of high dynamic range and low sensitivity [6][7][8][9][10][11][12] or digital filters of high accuracy with respect to finite wordlength effects [13][14][15][16][17][18][19][20][21][22][23][24][25]. Hence it is worthwhile to investigate the frequency transformation from the viewpoint of the internal properties, and to extend the results to some practical applications.…”

Statistical sensitivity and minimum sensitivity structures of 2-D separable-denominator digital filters

“…The problems of quantization effects have been studied in detail by the state-space approach for 1-D digital filters [1][2][3][4][5] and 2-D digital filters [6][7][8]. The state-space approach has been attempted for digital filters from the view point of frequency domain [2,7,8] and time domain [4,9].…”

“…The state-space approach has been attempted for digital filters from the view point of frequency domain [2,7,8] and time domain [4,9].…”