Delay-free Loops Research Articles

The LUD approach to switched-capacitor filter design

A new design method for switched-capacitor filters (SCF) is presented. It is based upon an LU matrix decomposition technique and has the distinct advantage of producing SC filter realizations containing no delay free loops. These are formed traditionally by capacitors and opamps in leapfrog realizations. It is demonstrated that this feature should render reduced dependence of the filter response to nonideal effects such as finite amplifier GB and switch resistance. Results from realistic leapfrog and LUD SC filter realizations confirm this.

Modified Realization Technique for Digital Filters Derived from Analog Counterparts

A simple realization scheme for one-dimensional and two-dimensional recursive digital filters derived from analog reference transfer functions is presented. The method is based on proper predistortion of the analog transfer function to obtain a new Hurwitz polynomial. Analog-to-digital transformations, such as the bilinear transformation, are then applied to the resulting predistorted reference transfer function to obtain the discrete version of the system. It is shown that a proper choice of the predistorting function will yield digital realizations which are free of the delay-free loops and in most cases are near minimal. To illustrate the simplicity and efficiency of the technique, examples of 1-D and 2-D cases are worked out. The proposed scheme can readily be extended to include the multi-dimensional case.

Voltage - current digital filters with zero magnitude sensitivity in attenuation zeros

A synthesis technique for 1-D and 2-D digital filters is described. In the filter attenuation zeros, the proposed structure exhibits zero magnitude differential sensitivity with respect to most of the coefficients. This structure is obtained from the voltage-current flow graph of the 1-D and 2-D doubly loaded analog lossless ladder prototype by the bilinear transformation of the variable s into z . The delay-free loops are removed using some manipulations, which are expressed in a very concise matrix form. In this way so called voltage-current digital filters, which exhibit excellent sensitivity and stability properties, are obtained.

Synthesis of new canonical digital ladder filters by continued fractions

Synthesis of digital filters by continued fractions is generally investigated. Several new canonic ladder realisations of a digital transfer function are presented, and the conditions for realisation are discussed. The new realisations are based on the applications of continued fraction expansions that proceed in terms of Ai + Bi2 and BjZ-1 + Aj on an alternating basis. The resulting structures avoid the presence of delay-free loops and achieve a relatively small range of multiplier values. They are more versatile than the existing structures, allowing one to synthesise functions more readily. Furthermore, it will be shown that existing structures can be generated as special cases of the presented structures. Illustrative examples are provided.

Low multiplier coefficient sensitivity block digital filters

Block ladder filters, based upon a ladder analog, are developed. A general procedure for removing delay free loops from digital filters is presented. Using the procedure, vector delay free loops of block ladder filters are eliminated. The multiplier coefficient sensitivities of the resulting block ladder based filters are considerably better than the corresponding sensitivities of previously developed block filters.

A new class of very low sensitivity and low roundoff noise recursive digital filter structures

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.

Variable digital filters

IIR prototype filters cannot be used for the design of variable filters through Schüssler's all-pass transformation because of the occurrence of delay-free loops; no such problem arises with FIR prototypes. In this paper, the drawbacks of the latter type, with regard to computational efficiency and output roundoff noise, have been brought out, An approach is suggested, wherein the delay-free loops with IIR prototypes are eliminated by modifying the coefficients of the first- and second-order sections of the prototype filter. The computation of modified coefficients In this approach requires fewer multiplications as compared to an existing method.

Synthesis of digital ladder filters from LC filters

Digital ladder filter networks may be realized by applying simple transformations to the flow-graph network representation of continuous domain resistively terminated <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</tex> two ports. It is shown that such methods have the disadvantage that there does not exist a transformation with the three requirements that the entire imaginary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -plane axis map to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -plane unit circle, that the resultant discrete network is stable and finally that the resultant discrete network be computationally realizable due to Its freedom from delay free loops. A synthesis technique is proposed for low sensitivity digital ladders. The conventional transformation that is applied to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</tex> filter prototype does lead to a stable structure with the required mapping property; the delay free loops are eliminated by straightforward flow-graph manipulation. The coefficient sensitivity of the magnitude transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|H(e^{f{\omega}T}|</tex> is low valued throughout the passband.

Detection, location, and removal of delay-free loops in digital filter configurations

Simple graph-theoretic methods for the detection and location of delay-free loops in a digital filter configuration are outlined along with a method to develop an equivalent realization without delay-free loops.

Low-sensitivity digital ladder filters

A class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter. The problem of unrealizability that is implied by delay-free loops in the discrete signal flow graph is overcome by using transformations that correspond to LC elements that exhibit finite Cube factors. The resultant deterioration in the passband of the transfer function is determined from the Blowstein LC ladder sensitivity theory and is, thereby, shown to be low valued at high sampling frequencies. The sensitivity properties of this class of digital ladder filters are directly analogous to the LC prototype because each LC element is replaced by a digital multiplier. Consequently, if maximum power transfer is approximately maintained throughout the passband of the LC prototype, then the first-order sensitivity of the corresponding digital transfer function to multiply a coefficient quantization is necessarily low valued.