Design of low-sensitivity universal wave digital biquads
TL;DR: In this paper, a systematic procedure for the synthesis of low-sensitivity wave digital biquads is described, based on the strategy of using, as far as possible, multiplier coefficients that are machine representable, so as to decrease the dependence of the amplitude response on multiplier coefficients.
Abstract: A systematic procedure for the synthesis of low-sensitivity wave digital biquads is described. The procedure is based on the strategy of using, as far as possible, multiplier coefficients that are machine representable, so as to decrease the dependence of the amplitude response on multiplier coefficients that must be quantized. The procedure yields structures which can be stabilized with respect to zero- and constant-input limit-cycle oscillations. In addition, multiple-output structures can be obtained which realize simultaneously the standard second-order transfer functions. Experimental sensitivity wave digital biquad based on the three-amplifier RC-active configuration is less sensitive than other known low-sensitivity structures. Further, it is shown that by choosing the machine-representable coefficients, wave digital biquads can be obtained which are sensitivity-equivalent to other known low-sensitivity structures. >
Citations
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01 Apr 1991-Canadian Journal of Electrical and Computer Engineering-revue Canadienne De Genie Electrique Et Informatique
TL;DR: By replacing multipliers in conventional series and parallel adaptors by digital subnetworks comprising multipliers whose constants are as far as possible machine-representable, modified series as discussed by the authors is obtained whose operation is less dependent on multiplier constants that are not machine representable.
Abstract: By replacing multipliers in conventional series and parallel adaptors by digital subnetworks comprising multipliers whose constants are as far as possible machine representable, modified series and parallel adaptors are obtained whose operation is less dependent on multiplier constants that are not machine representable. Conventional and modified adaptors are then used to design several digital filters and the effects of coefficient quantization are investigated. The results obtained show that wave digital filters implemented with the modified adaptors are significantly less sensitive than filters implemented with conventional adaptors.
2 citations
Cites background or methods from "Design of low-sensitivity universal..."
...Compute the new values of ax and a2 from either Equation (4) or (5) using mXq and m2q....
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...From Equations (1) and (4), the relations for the modified series adaptors are obtained as...
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...Assign a particular combination of values from the permissible set of constants given in Equation (8) to the MR multiphers and obtain the values of the corresponding non-M^L multipliers mx and m2 using either Equation (4) or (5)....
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...Similarly, for the modified parallel adaptor, Equations (2) and (4) give Bx — (amx + bm2 + c)(Ax — A3) + (dmx + ew 2 + / ) X (Ai ~ A3) - Ax + 2A3 (7a) B2 = (amx + /?m2 + c)04i — A3) + (dw! + em2 4- / ) X (^ 2 A3) - A2 + 2A3 (7b) ....
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...More economical adaptors which use only four MR multipliers can readily be obtained by modifying Equation (4) as amx + bm2 (11a)...
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TL;DR: In this paper, the biquad function is realized in 165 forms using only one single second-order all-pass, and higher degree transfer functions are constructed modularly in different ways.
Abstract: Arbitrary time-discrete transfer functions are realized by simple wave digital filter structures. Systematic determination of appropriate coupling at few structures (so-called resonators) provides a lot of circuits; e.g. the biquad function is realized in 165 forms using only one single second-order allpass. Higher degree transfer functions are constructed modularly in different ways
References
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TL;DR: For poles close to the unit circle and near z = 1, the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise as mentioned in this paper.
Abstract: For poles close to the unit circle and near z = 1 , the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise. As the sampling rate is increased the poles approach z = 1 and the problems become more severe. For these situations several new digital filter structures are presented for which the above errors remain constant and generally insignificant as the sampling rate is increased. Results on sensitivity and the roundoff errors for these new structures are presented and compared with conventional realizations. Some numerical results are also presented showing order of magnitude improvements.
161 citations
TL;DR: It is shown that by minimizing this statistical word length, the actual coefficient word length upon rounding of the coefficients can generally be reduced as well.
Abstract: A statistical approach is proposed for estimating the necessary coefficient word length of a digital filter. With this statistical word length definition, an optimization procedure is then proposed for minimizing the statistical word length for a given filter structure and a given set of maximum error constraints. It is shown that by minimizing this statistical word length, the actual coefficient word length upon rounding of the coefficients can generally be reduced as well. Several examples are given and improvements of one to three bits in the actual coefficient word length are observed. The procedure does not necessarily lead to the actual global minimum coefficient word length.
86 citations
TL;DR: A simple method of calculating the steady-state value of the variance of the output noise of a digital filter due to the input quantization noise or internally generated noise from product round-off is presented.
Abstract: A simple method of calculating the steady-state value of the variance of the output noise of a digital filter due to the input quantization noise or internally generated noise from product round-off is presented. The output noise is expressed as a sum of simpler terms belonging to one of four basic groups. Explicit expressions have been developed for rapid evaluation of these terms in the expansion. The method is illustrated by means of examples.
42 citations
TL;DR: The application of the "branch and bound" technique for nonlinear discrete optimization, due to Dakin, to the problem of finding the coefficients of a recursive digital filter with prescribed number of bits, to meet arbitrary response specifications of the magnitude characteristic is investigated.
Abstract: The application of the "branch and bound" technique for nonlinear discrete optimization, due to Dakin, to the problem of finding the coefficients of a recursive digital filter with prescribed number of bits, to meet arbitrary response specifications of the magnitude characteristic, is investigated. Due to the fact that the objective function is nonlinear and the stability constraints are linear with respect to the parameter, the recent algorithm for nonlinear programming due to Best and Ritter is used. Based on the ideas presented, a general computer program has been developed. Numerical experience with the present approach is also presented.
41 citations