Analog-digital systems for adaptive measurements and parameter estimation of noisy processes

Design and analysis of algorithmic multi-pass A/D converters with the theoretically highest resolution and rate of conversion

“…After n cycles, the conversion result--estimate b V ðmÞ n is routed to addressee, and the cycle of the next ðm þ 1Þ sample conversion starts. A possibility of introducing the mathematical methods of the analysis and optimisation into MP ADCs design appears due to the usage of the adaptive statistically fitted observation conception and extended algorithms presented in [1][2][3][4][5][6]. Application of these algorithms to the sub-optimal MP ADC design requires their modifications, because they were derived for the case of piecewise linear ( Fig.…”

“…2a) does not permit direct mathematical analysis of the MP ADC and derivation of optimal conversion algorithms nor direct application of extended algorithms [1][2][3][4][5][6]. Below we present briefly the principles of the sub-optimal extended conversion algorithms derivation using the approach and algorithms presented in [1][2][3][4][5][6].…”

“…The particular feature of the algorithms presented in [1][2][3][4][5][6] is that they take into account and adjust the parameters of the analogue observation elements in the way excluding their saturation at each cycle of estimates calculation. That is just what creates a principal possibility of application of these algorithms to MP ADCs optimisation.…”

“…The ''sub-optimal'' algorithm used the samples y k processing has the same form as a scalar version of algorithm presented in works [1][2][3][4][5][6] (see also [14][15][16][17], the only difference is the internal noise variance should be replaced by the quantisation noise power r 2 n ¼ D 2 =12). Under assumption that the first approximation of distribution of sample V values at the MP ADC input is Gaussian with the mean value V 0 and variance…”

“…2) and its limited input range cause unconquerable mathematical difficulties while trying to resolve optimisation task--the basis for synthesis of optimal algorithms for data processing. To omit these difficulties, the extended algorithms presented in works [1][2][3][4][5][6] can be used.…”