A new realization of wave digital filters using GIC and fractional bilinear transform
01 Mar 2016-Engineering Science and Technology, an International Journal (Elsevier)-Vol. 19, Iss: 1, pp 429-437
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.
Citations
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TL;DR: The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LW DFOD a promising technique for the design of digital FODs.
Abstract: In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for Nth order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs.
34 citations
TL;DR: Post-implementation results show that implementation based on the radix-2r encoding is found to be more efficient than that of the CSD encoding and the design and implementation results are reported to highlight the improvements.
Abstract: This paper deals with the design and FPGA implementation of a fractional order digital differentiator. It is realized using computationally efficient lattice wave digital filter (LWDF) which requires minimum multipliers in comparison to the direct form structure. A nature inspired ant lion optimization (ALO) algorithm is utilized to compute optimal coefficients of the LWDF based digital differentiator. The proposed LWDF based digital differentiator is compared with the existing literature in terms of magnitude response, percentage magnitude error and root mean square magnitude error. LWDF structure comprises of constant coefficient multipliers, adders and delay units which are implemented on FPGA with the help of Xilinx system generator for DSP design tool. For efficient implementation of multipliers, multiplier-less logic through digit recoding techniques such as canonic signed digit (CSD) representation and radix-2r encoding are described through Verilog HDL and incorporated in the implementation model as black box. Post-implementation results show that implementation based on the radix-2r encoding is found to be more efficient than that of the CSD encoding. The design and implementation results are also reported to highlight the improvements.
9 citations
01 Dec 2015
TL;DR: In this article, a method to design and implement the comb lattice wave digital filter with only one multiplier, small area and low power dissipation is proposed, where a design level area optimization is done by converting constant multipliers into shifts and adds using canonical signed digit code (CSDC) technique.
Abstract: The minimum hardware and low power dissipation are the main concern for efficient filter implementation. A method to design and implement the comb lattice wave digital filter with only one multiplier, small area and low power dissipation is proposed. Lattice wave digital filter is used for filter realization due to its excellent properties. A design level area optimization is done by converting constant multipliers into shifts and adds using canonical signed digit code (CSDC) technique. The filter is implemented and successfully tested on Xilinx Spartan XC3s200-4ft256 field programmable gate array (FPGA) device. The effectiveness of the proposed design method is proven with an example.
8 citations
Journal Article•
TL;DR: In this paper, the roundoff-noise outputs from two transpose configurations, each for the cascade and parallel forms of a digital filter, are analyzed for the case of uncorrelated roundoff noise and fixed dynamic range.
Abstract: The roundoff-noise outputs from two transpose configurations, each for the cascade and parallel forms of a digital filter, are analyzed for the case of uncorrelated roundoff noise and fixed dynamic range. Corresponding transpose configurations are compared on the basis of the variance, or total average power, and the peak spectral density of the output roundoff noise. In addition to providing general computational techniques to be employed in choosing an appropriate configuration for the digital filter, these results also indicate useful \"rules of thumb\" relating to this choice of configuration. Included are indications of good (although not necessarily optimum) sequential orderings and pole-zero pairings for the second-order sections comprising the cascade form. Computational results are presented which indicate that the analysis is quite accurate and useful.
8 citations
01 Dec 2015
TL;DR: In this article, a wave digital equivalent of passive elements using wave theory and bilinear transform is formulated in yesteryear and two different transforms are used for analog to digital (A/D) conversion in order to overcome the limitation of the aforementioned transform.
Abstract: The wave digital equivalent of passive elements using wave theory and bilinear transform is formulated in yesteryear, but the bilinear transform produces large distortion in the mid and high frequency range. In this paper, a novel wave digital equivalents of analog passive elements are developed. Instead of bilinear transform, two different transforms are used for analog to digital (A/D) conversion in order to overcome the limitation of the aforementioned transform. The comparison of transforms along with the resultant wave digital equivalents of passive elements using these transforms and wave theory is introduced. In this paper, it is also considered that practically, analog elements are not ideal, but leaky. So, wave digital equivalents of leaky analog elements are also proposed.
4 citations
Cites background from "A new realization of wave digital f..."
...The discretization of these filters are not performed all together, but separately for each network element by the A/D transform [3] [4]....
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References
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TL;DR: This work presents a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay, focusing on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value.
Abstract: A fractional delay filter is a device for bandlimited interpolation between samples. It finds applications in numerous fields of signal processing, including communications, array processing, speech processing, and music technology. We present a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Various new approaches are proposed and several examples are provided to illustrate the performance of the methods. We also discuss the implementation complexity of the algorithms. We focus on four applications where fractional delay filters are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments.
1,014 citations
01 Feb 1986
TL;DR: Wave digital filters (WDFs) as discussed by the authors are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof, and have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions.
Abstract: Wave digital filters (WDFs) are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof. They have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions. A detailed review of WDF theory is given. For this several goals are set: to offer an introduction for those not familiar with the subject, to stress practical aspects in order to serve as a guide for those wanting to design or apply WDFs, and to give insight into the broad range of aspects of WDF theory and its many relationships with other areas, especially in the signal-processing field. Correspondingly, mathematical analyses are included only if necessary for gaining essential insight, while for all details of more special nature reference is made to existing literature.
937 citations
TL;DR: The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general.
Abstract: The interaction between the roundoff-noise output from a digital filter and the associated dynamic-range limitations is investigated for the case of uncorrelated rounding errors from sample to sample and from one error source to another. The required dynamic-range constraints are derived in terms of L p norms of the input-signal spectrum and the transfer responses to selected nodes within the filter. The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general. Two transpose configurations for the direct form of a digital filter are used to illustrate these results.
287 citations
18 Jun 1969
TL;DR: The realisation of negative-impedance convertors and invertors using the bridge-type circuit using the nullor to infinite-gain controlled sources is briefly surveyed and a relevant theorem concerning passivity is proved.
Abstract: The realisation of negative-impedance convertors (n.i.c.s) and invertors (n.i.i.s) using the bridge-type circuit is briefly surveyed. An equivalence relating the nullor to infinite-gain controlled sources is first proved, and is then used for the derivation of nullator-norator equivalent circuits for n.i.c.s and n.i.i.s. Some properties of networks containing singular elements, which are used in the realisation of gyrators, are investigated. Nullator-norator equivalent circuits for gyrators are derived by using the n.i.c.s and n.i.i.s. They are converted into physical networks by using the proved equivalence. Gyrator circuits are obtained by replacing nullors by operational amplifiers. A stability analysis of the gyrator circuits is produced and a relevant theorem concerning passivity is proved. The feasible Qfactors and the accuracy of the gyrator circuits are indicated by some experimental results. A generalised-impedance convertor (g.i.c.) is defined by generalising the n.i.c. theory, and it is shown that the gyrator circuits described can be used as g.i.c.s. The application of the gyrator and g.i.c. circuits in the synthesis of RC-active networks is considered. Finally, a highpass filter using gyrators and a bandpass filter using g.i.c.s are designed, and the experimental results are given.
252 citations
TL;DR: In this article, the roundoff-noise outputs from two transpose configurations, each for the cascade and parallel forms of a digital filter, are analyzed for the case of uncorrelated roundoff noise and fixed dynamic range.
Abstract: The roundoff-noise outputs from two transpose configurations, each for the cascade and parallel forms of a digital filter, are analyzed for the case of uncorrelated roundoff noise and fixed dynamic range. Corresponding transpose configurations are compared on the basis of the variance, or total average power, and the peak spectral density of the output roundoff noise. In addition to providing general computational techniques to be employed in choosing an appropriate configuration for the digital filter, these results also indicate useful "rules of thumb" relating to this choice of configuration. Included are indications of good (although not necessarily optimum) sequential orderings and pole-zero pairings for the second-order sections comprising the cascade form. Computational results are presented which indicate that the analysis is quite accurate and useful.
224 citations