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
More filters
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).
Abstract: In this paper, 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). These second-order digital filter sections are used as building blocks in cascade synthesis. During the realization procedure, fractional bilinear transform is utilized for analog to digital conversion to get more competent digital filter sections. The noise performance of the proposed filter sections is compared with that of already known GIC second order digital filter sections. The proposed synthesis yields lowpass and highpass filters with ameliorated signal to noise ratio in comparison to that of the conventional GIC digital filters.
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
More filters
TL;DR: In this article, a delay replacement scheme was proposed for the recursive digital filter with poles near the unit circle, where delays at the proper places were inserted to avoid the delay-free loops.
Abstract: A class of new structures is proposed, for the realization of the recursive digital filter with poles near the unit circle, by introducing the particular type of delay replacement scheme in the existing digital filter structure and then, inserting, delays at the. proper places to avoid the delay-free loops. By applying the proposed method to the second-order direct form structures, new structures are found with very low magnitude transfer function sensitivities with respect to multiplier coefficients and low roundoff noises. Some numerical results are also presented.
36 citations
TL;DR: In this article, a systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS).
Abstract: A systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS). Collectively, these structures can realize any stable second-order transfer function. For every transfer function, a choice of at least two structures is available but, through a sensitivity analysis, the optimum one can always be identified. The paper concludes with sensitivity and roundoff-noise comparisons which show that the new structures are usually superior relative to corresponding direct canonic structures and also relative to the state-space section-optimal structure.
22 citations
TL;DR: In this paper, two distinct methods for the reduction of coefficient and product quantization effects in recursive digital filters are described, where a degree of freedom is introduced in the design by increasing the approximation order above the minimum.
Abstract: Two distinct methods for the reduction of coefficient and product quantization effects in recursive digital filters are described. A degree of freedom is introduced in the design by increasing the approximation order above the minimum. This is then used to increase the allowable margin for coefficient quantization error or to reduce the sensitivity to coefficient quantization. The two methods are used to design several sixth-order low-pass filters. The designs obtained are then compared with the corresponding minimum-order elliptic designs with respect to the effects of coefficient and product quantization. The results show that both methods lead to reduced wordlength for the implementation and also to reduced output quantization noise.
13 citations
TL;DR: An algorithm for designing IIR digital filters with short coefficient word lengths is presented, incorporating Crochiere's idea of equalizing passband and stopband statistical word lengths before applying the algorithm, which is capable of obtaining a further reduction in the overall word length.
Abstract: The paper presents an algorithm for designing IIR digital filters with short coefficient word lengths. The algorithm has the flexibility of obtaining a better design at the expense of investing more computational time. It was found that, by incorporating Crochiere's idea of equalizing passband and stopband statistical word lengths before applying the algorithm, we are capable of obtaining a further reduction in the overall word length when compared with that obtained by applying the algorithm alone. The principle of the algorithm and the concept of statistical word lengths equalization for further word length reduction applies to all IIR digital filters of different structures and passbands, with and without their transfer functions expressed in a closed form.
12 citations
TL;DR: The structures based on the summing four-amplifier biquad embody the simultaneous realization of a variety of filter transfer functions, namely, a low-pass, a bandpass, and a general biquadratic transfer function.
Abstract: A general method for deriving digital-filter structures from corresponding RC -active configurations is presented. The method is then used to derive digital-filter structures from various low-sensitivity RC -active configurations such as the three-amplifier state-variable biquad, and the corresponding summing four-amplifier biquad. The new digital structures are found to have the salient features of the reference configurations. For example, the structures based on the summing four-amplifier biquad embody the simultaneous realization of a variety of filter transfer functions, namely, a low-pass, a bandpass, and a general biquadratic transfer function. In addition, it is shown that in these structures, limit cycles can be eliminated by using a known technique based on magnitude truncation.
12 citations