Two's complement quantization in periodic digital filters

The stability of periodically shift variant (PSV) filters are studied when implemented with two's complement truncation (TCT) quantization. Block form and standard (nonblock) form implementations are considered, and two sufficient conditions are established for stability. As a special case, second-order coupled-form PSV filters are then investigated under TCT quantization. Stability regions are established within the parameter space for block implementations. Examples are given to illustrate the results     

Two's complement quantization in two-dimensional state-spacedigital filters

Two-dimensional (2-D) state-space digital filters are investigated for stability with and without quantization. A sufficient condition is obtained for the stability of the linear Fornasini-Marchesini (1976) state-space model. The same model is then studied for stability when implemented using two's complement truncation quantization, and a sufficient condition for asymptotic stability of the nonlinear filter is obtained. In the process, a theorem is proved which gives a sufficient condition for the stability of a one-dimensional (1-D) state-space digital filter under the same type of quantization     

Decoupling of the overflow and quantization phenomena in orthogonal biquad recursive digital filters

In digital communication networks, a special class of complex biquad recursive digital filters called orthogonal filters is increasingly being used. The separate effects of the overflow and quantization nonlinearities on these orthogonal filters' responses have been investigated [5], [6]. In this paper we examine the zero-input stability properties of the actual orthogonal filter having both overflow and quantization nonlinearities. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic. The quantization techniques used may be roundoff, magnitude, or value truncation. An example demonstrates the adverse coupling effect between the overflow and quantization nonlinearities. Two criteria are therefore derived to ensure asymptotic overflowstability of the filter in the presence of quantization. These criteria have been translated to the coefficient plane; various regions corresponding to different minimum wordlengths required to ensure decoupling of the overflow and quantization phenomena have been derived.This work was supported in part by a Monash Graduate Scholarship and Telecom Australia under Contract No. 64515.     

Elimination of limit cycles due to two's complement quantization innormal form digital filters

Normal form digital filters are attractive due to their desirable properties when implemented in finite wordlength arithmetic. These filters are free from all overflow limit cycles and quantization limit cycles when magnitude truncation is used, However, when two's complement truncation (TCT) quantization is used, limit cycles can still exist. In this paper, it is shown that when block structures are used, normal form digital filters can be made free of limit cycles due to TCT quantization. It is shown that this can be done with a small block size. An algorithm is also presented to find the minimum block size required for a given filter. Some examples are given to illustrate the results     

Determination of quantization error in two-dimensional digital filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the following computation J = Σm=0^∞Σn=0^∞y²(m, n). In this paper general method for the evaluation of J based on Laurent expansion of the integrand is presented. Illustrative example for such a computation is given. Notations: We denote with V^-2= {(z1, z2): |z1| ≤ 1, |z2| ≤ 1} the closed unit bidisc, with V²= {(z1, z2): |z1| < 1, |z2| < 1} the open unit bidisc, and with T2= {(z1, z2): |z1| = 1, |z2| = 1} the distinguished boundary of the unit bidisc.     

Stability of digital filters implemented with two's complementtruncation quantization

The stability of digital filters implemented with two's complement truncation quantization is investigated. Both the direct-form and normal-form realizations are considered and regions in the parameter plane are obtained where the filters are globally asymptotically stable. Regions within the stability triangle of a direct-form digital filter are also studied where limit cycles of period one and two are possible. The results are illustrated with several examples     

Structural design of current-mode biquad filters

This work describes how to generate and design a novel current-mode biquad filter model using tunable multiple-output operational transconductance amplifiers and grounded capacitors (MO-OTA-Cs) for synthesizing both transmission poles and zeros. Transfer functions of low-pass, band-pass, high-pass, notch and all-pass are realized based on the filter model. The theory focuses mainly on establishing a relationship between the cascaded MO-OTA-Cs and the multiple-loop feedback matrix, which makes the structural generation and design formulas. All the filter architectures contain only grounded capacitors, which can absorb parasitic capacitances and require smaller chip areas than floating ones. The simulation results are also presented to confirm the theoretical analysis.     

Universal biquad filters using low-voltage current mirrors

Novel Single Input Multiple Output (SIMO) and Multiple Input Single Output (MISO) current-mode universal biquad topologies are introduced in this paper. The proposed topologies have been realized by employing low-voltage current mirrors as active elements. As a result, an absence of resistors is achieved in the derived filter topologies; also only grounded capacitors are required. The resonant frequency of the filters can be electronically controlled by an appropriate dc current. In addition, the derived filters offer the feature of orthogonal adjustment between the resonant frequency and Q factor. The behavior evaluation of the proposed filters has been performed through a test chip prototype fabricated in AMS 0.35 μm CMOS technology.     

Second-order OTA-C filters derived from Nawrocki-Klein biquad

Based on the Nawrocki and Klein biquad and using different input and output techniques, many new filter structures and functions are developed from both voltage- and current-mode viewpoints. For example, it is found that the basic five operational transconductance amplifier (OTA) structure has the LP, BP, HP, BS and AP functions without the use of capacitor injection and component matching, a feature shared by no other existing two integrator loop OTA-capacitor (OTA-C) circuit, including the original NK biquad. Various BS, LPN, HPN, AP and universal architectures are obtained, which require fewer OTAs and may be more useful than the original biquad. This research shows that the NK biquad is one of the most important second-order OTA-C filters at least from the viewpoint of filter architectures and functions, and thus should receive attention in continuous-time filter design     

Design formulas for active RC filters using operational-amplifier biquad

Complete design formulas for realising any biquadratic voltage transfer function are given. The configuration uses ten or fewer resistors, two capacitors and four single-ended operational amplifiers. The realisation achieves extremely low sensitivity and can readily be used in realising stable high Q factor active filters up to 100kHz.     

New universal biquad filters using only two unity-gain cells

New current-mode and voltage-mode universal biquad filters are presented using only two unity-gain cells (one current follower and one voltage follower) in each configuration. The proposed filters employ one less follower than in the literature to date. The filters can realize highpass, bandpass, lowpass, notch and allpass responses without any changes in the circuit topology. The circuits enjoy the following advantages: minimum number of active elements, no component-matching condition and low active and passive sensitivities.     

Design criterion for zero-input asymptotic overflow-stability of recursive digital filters in the presence of quantization

This paper investigates the zero-input stability properties of the exact second-order recursive digital filter having both overflow and quantization non-linearities. Two examples demonstrate the adverse influence of quantization on the overflow-stability property of the filter. Three sets of conditions are presented to ensure asymptotic overflow-stability in the presence of quantization. Using these criteria, various regions in the coefficient plane corresponding to different minimum internal wordlengths required to ensure the non-interaction of overflow and quantization are derived. These results thus form a useful design criterion.This work was supported in part by a Monash Graduate Scholarship (awarded to P.K. Sim) and Telecom Australia under Contract No. 64514.     

A systematic realization of current mode universal biquad filters

A family of current mode universal biquads has been proposed. The biquad filters employ multiple output floating nullor (MOFN) configured as multiple output current conveyors (MOCC). The five-MOFN-based biquad has the property of independently tunable gain, bandwidth, and cut-off frequency without having any passive component matching constraint. Although the four/three MOFN-based universal biquads offer limited tunability of different parameters they do not have any parameter matching constraint on them and in addition, they offer the advantage of reduction in the number of MOFNs and resistances. The workability of all the proposed circuits has been verified using PSPICE simulations based CMOS MOFNs implemented in 0.35?µ CMOS technology.     

Two's complement extension of a parallel binary division by ten

A division of binary numbers by ten is extended to negative numbers in a two's complement form. The analysis of these negative remainder cases has allowed a more uniform, general approach to the remainder detection problem and should permit an extension to division by other constants.     

Asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow nonlinearities

A novel criterion for the global asymptotic stability of fixed-point state-space digital filters under various combinations of quantization and overflow nonlinearities is presented. The criterion is compared with a previously reported criterion.     

A new on-line bandwidth tuning approach for biquad OTA-C filters

A new and general bandwidth (BW) tuning strategy for biquad OTA-C filters is presented. We have taken benefit of the advantages of the classical Phase-Locked Loop (PLL) scheme to on-line tune the central frequency f_o and we have applied it to tune also the bandwidth BW of biquad filters. The proposed design procedure uses only two different sizes of OTAs. This methodology has been applied to five biquad band-pass OTA-C filters, allowing f_o-tuning and BW-tuning in an independent way. Furthermore, the influence of OTA non-idealities is discussed by including compact and general expressions for f_o and BW for all these filters. Simulation results validate our proposal with excellent BW-tuning accuracies: an rms error of 0.73% with respect to the bandwidth desired.     

Design formulas for biquad active filters using three operational amplifiers

A circuit configuration and its design formulas are presented for the realization of all the useful forms of a biquadratic voltage transfer function. The circuit employs three single-ended operational amplifiers, two capacitors, and at most eight resistors. With an additional resistor, it can realize any biquadratic voltage transfer function.     

On the realization of two's complement overflow limit cycle free state-space digital filters

A frequency-domain criterion for the overflow stability of a class of state-space digital filters is presented. The result is derived using a Lyapunov technique and the associated MKY machinery. Some consequences of the present derivation are discussed.     

A note on the orthogonal realization of allpass digital filters andtheir finite wordlength performance

In this correspondence, a direct method to obtain an orthogonal realization of an allpass transfer function from the entries of the Jury table or the Schur-Cohn test is presented. The performance of this orthogonal realization using fixed- or floating-point implementation is discussed. Based on this formulation, simple formulae for the coefficient sensitivity and output roundoff noise variances are obtained. The results are illustrated with an example