An Improved Criterion for Induced Stability of Fixed-Point Digital Filters with Saturation Arithmetic

Abstract

<p>This paper establishes a criterion for the induced stability of fixed-point state-space digital filters with saturation nonlinearities and external interference. The criterion is established in a linear matrix inequality (LMI) setting, and therefore, computationally tractable. The criterion turns out to be an improvement over a previously reported criterion. A comparison of the presented criterion with existing criterion is made. Numerical examples are given to demonstrate the usefulness of the proposed approach.</p>

Analysis of Memory Effects in Digital Filters with Overflow Arithmetic

“…for all Equation (11) can be expressed as (13) Note that, owing to (2), 2  given by (13) is nonnegative. From (12), it is clear that (14) if (4b) holds true. From (14), it follows that…”

“…Due to the presence of such nonlinearities, the implemented filter may exhibit undesired zero-input oscillations [2][3]. The problem of stability of digital filters with finite wordlength nonlinearities has been studied extensively [2][3][4][5][6][7][8][9][10][11][12][13][14]. Several stability results to reduce the effects of nonlinear phenomenon have appeared recently [10][11][12][13][14][15][16].…”

“…The analysis of undesired memory effects in digital filters with finite wordlength nonlinearities is an important problem. The criteria in [3][4][5][6][7][8][9][10][11][12][13][14][15] cannot be used to measure the memory effects in digital filters. Recently, the Hankel norm performance criterion for the reduction of memory effects of digital filters with saturation arithmetic has been established in [16].…”

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

“…In the realization of digital filters on finite wordlength machine, nonlinearities namely, quantization and overflow, are usually unavoidable (Ahn, 2011; Antoniou, 2006; Butterweck et al, 1988; Chen, 2009; Diksha et al, 2016; Kandanvli and Kar, 2008, 2009, 2011, 2013; Kar and Singh, 2004; Kokil and Arockiaraj, 2016, 2017; Kokil and Kar, 2012; Kokil and Shinde, 2015; Kokil et al, 2012, 2018a, 2018c; Li et al, 2012; Rehan et al, 2018; Schlichtharle, 2001; Singh, 1985; Tadepalli et al, 2014, 2018). The presence of these nonlinearities may lead digital filters to become as nonlinear systems.…”

“…Saturation, two’s complement, triangular and zeroing are various forms of overflow nonlinearity correction techniques and on account of their catastrophic effects on the digital filters behavior, they have been addressed in literature (Arif et al, 2017; Butterweck et al, 1988; Kandanvli and Kar, 2008, 2009, 2013; Kar, 2007; Kar and Singh, 2004; Kokil and Arockiaraj, 2017; Kokil et al, 2018a, 2018b, 2018c, Kumar et al, 2019; Lee et al, 2012; Li et al, 2012, Singh, 2006). As it is evident from literature that the saturation overflow arithmetic produces the smallest deviation from the linear operation (Butterweck et al, 1988), the stability analysis of digital filters with saturation overflow has been considered as a forefront research problem (Ahn, 2011; Amjad et al, 2017; Arif et al, 2017; Kandanvli and Kar, 2009, 2013; Kar and Singh, 2004; Kokil and Arockiaraj, 2016; Kokil and Kar, 2012; Kokil and Shinde, 2015; Kokil et al, 2012; Lee et al, 2012; Parthipan et al, 2018; Singh, 1985; Tadepalli et al, 2014).…”