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![Conventional bandpass digital filter section [5].](profile/Richa-Barsainya/publication/283940782/figure/fig13/AS:296518285316112@1447706876434/Conventional-bandpass-digital-filter-section-5_Q320.jpg)
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...
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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...
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In the present work, we investigate the dipion transitions between ϒ(5S) and ϒJ(1D) with J=1, 2, 3. Our analysis indicates that the dominant sources of the anomalously large widths of ϒ(5S)→ϒJ(1D)π+π− should be Zb(′), i.e., the dipion transitions occur via the cascade decays ϒ(5S)→Zb(′)±π∓→ϒJ(1D)π+π−. With the assumption that all the short ranged d...
Citations
... These wave digital equivalents were shown to overcome the nonlinear effects of the conventional wave digital equivalents. Furthermore, the fractional GIC wave digital filter sections using wave characterization and fractional bilinear transform were proposed in [12]. These fractional GIC filters are evinced to have better inband signal to noise ratio than the conventional GIC structure proposed in [5]. ...
... Hitherto, bilinear transform and fractional bilinear transform is used to derive the GIC digital structure [5,12]. In this paper, Al-Alaoui transform and wave characterization are utilized to obtain a new GIC digital structure from an analog GIC configuration. ...
... where jH F ðxÞj -0 only in case of the bandstop section. S m ðxÞ is the PSD of the noise produced by one multiplier and is given by S m ðxÞ ¼ d 2 12 , where d is the quantization step [5]. It is important to note that the noise generated by the two multipliers m 1 and m 2 will get attenuated at low as well as high frequencies in new GIC sections, as in [5]. ...
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.
... Every WDF is derived from its reference analog filter [1] [2]. The discretization of these filters are not performed all together, but separately for each network element by the A/D transform [3] [4]. The WDF transfer function is obtained from its reference filter, just like infinite impulse response (IIR) filters, by applying the transformation method. ...
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-2 r 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-2 r 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.
This study aims towards the efficient design of arbitrary-band and halfband lowpass (LP) filter based on lattice wave digital filter (LWDF) structure with the usage of minimal number of multipliers in its structural realisation. The designing of the LP filter is formulated as an optimisation problem where coefficients of LWDF transfer function are iteratively optimised by the evolutionary algorithms. The potential of four optimisation algorithms, real-coded genetic algorithm, particle swarm optimisation, differential evolution algorithm, and cuckoo search algorithm, are explored for determining the optimal LWDF coefficients by minimising the error objective function. The structural realisation of LP using LWDF structure enhances the design accuracy as the usage of multiplier prominently reduces. The simulation and statistical results of the proposed lattice wave digital lowpass filter (LWDLF) and bireciprocal lattice wave digital lowpass filter (BLWDLF) design show significant improvement in the mean square error, passband ripples, transition bandwidth, stopband attenuation, rate of convergence, and execution time. To manifest the efficient design of the proposed LWDLF and BLWDLF, the results are compared with the designed arbitrary-band, halfband canonic-LP filters and previous published works.
This paper deals with the application of lattice wave digital filter (LWDF) (3rd and 5th order) for obtaining an efficient design of a Fractional Delay Filter (FDF). The Real Coded Genetic algorithm (RCGA) and Cuckoo Search Algorithm (CSA) have been used in order to determine the optimal coefficient values of LWDF in order to meet the ideal frequency response characteristics. The simulation of FDF using LWDF structure improves the accuracy of design because of its excellent properties and also it needs only N number of multiplier coefficients for N th order FDF. The simulation results of lattice wave digital Fractional delay filter (LWDFDF) are compared with infinite impulse response-fractional delay filter (IIR-FDF), also designed using RCGA and CSA and it is seen that LWDF based FD filter is superior to the IIR design.
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.
The purpose of this paper is to identify unknown IIR systems using a reduced order adaptive lattice wave digital filter (LWDF). For the system identification problem, LWDF structure is utilized, as it mocks-up the system with a minimal coefficient requirement, less sensitivity and robustness. The modelling technique is based on minimizing the error cost function between the higher order unknown system and reduced order identifying system. Two optimization algorithms, namely, genetic algorithm (GA) and gravitational search algorithm (GSA) are utilized for parameter estimation. By means of examples, it is shown that LWDF offers various advantages in system identification problem such as requirement of minimum number of coefficients, low mean square error (MSE), variance and standard deviation. The results demonstrate that better system identification performance is achieved by LWDF structure compared to adaptive canonic filter structure.
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.
