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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TL;DR: Methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides are explored and attention is paid to simplicity of parametric control.
Abstract: Wave digital filters (WDFs) were originally developed for robust discrete-time simulation of analog filters, but recently they have been applied successfully to modeling of physical systems such as musical instruments and to model-based sound synthesis. While basic WDF elements are sufficient to implement arbitrary passive lumped-element models, the computational efficiency of such models is not optimal. In this paper, we explore methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides. In addition to efficiency, attention is paid to simplicity of parametric control. A modeling and sound synthesis case study of the bell is presented to demonstrate the performance obtained by the consolidated approach.
18 citations
TL;DR: In this article, a new class of second-order digital filters is developed by using the concept of wave characterization, fractional bilinear transform and generalized immittance converter (GIC).
10 citations
TL;DR: In this article, a sensitivity measure for determining the optimum set of machine-representable multiplier constants in the derivation of low-sensitivity digital biquadratic filters was proposed.
Abstract: A sensitivity measure is proposed for determining the optimum set of machine-representable multiplier constants in the derivation of low-sensitivity digital biquadratic filters. A comparison of this measure with two other sensitivity measures of this class is then undertaken using four different design examples. The four sixth-order filters considered are a Butterworth low-pass, a Chebyshev high-pass, an elliptic bandstop, and an elliptic bandpass filter. It is shown that the three sensitivity measures usually give slightly different low-sensitivity designs and that the new sensitivity measure often gives the best design. >
8 citations
TL;DR: It is shown that the required details of the resulting filter structure, namely, the organization of the different adaptors and the values of the multiplier constants can be obtained directly from the specified discrete transfer function.
Abstract: A simple and straightforward procedure for the realization of multidimensional digital filters which are based on the concept of generalized immittance converter is presented. It is known that these digital filters possess many salient features such as low noise, low sensitivity, absence of limit cycles and capability of realizing multiple transfer functions. Unlike the other known methods, which use analog transfer function as the basis, the method proposed in this paper uses the discrete transfer function directly for realization. It is shown that the required details of the resulting filter structure, namely, the organization of the different adaptors and the values of the multiplier constants can be obtained directly from the specified discrete transfer function.
7 citations
TL;DR: In this paper, a new digital generalized immittance converter (GIC) structure is proposed which is capable of realizing all the standard second-order digital filter sections by using the concepts of wave characterization, Al-Alaoui transform and GIC.
Abstract: By using the concepts of wave characterization, Al-Alaoui transform and generalized immittance converter (GIC), a new digital GIC structure is proposed which is capable of realizing all the standard second-order digital filter sections. The Al-Alaoui transform is utilized for reference circuit discretization, leading to development of second-order digital filter sections which possess better noise properties than the conventional GIC and GIC discretized using the fractional bilinear transform. The proposed second-order digital filter sections are used as building blocks in cascade synthesis of filter. Two design examples are considered to analyze the effectiveness of the proposed filter sections and their comparison with the other filter sections is performed in terms of quantization noise and approximation to analog filter response. The proposed synthesis yields lowpass and highpass filters that have a better signal to noise ratio and better approximation of the analog filter frequency response than the conventional GIC digital filters and fractional GIC digital filters.
2 citations
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