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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 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. Keywords: Digital filter, Al-Alaoui transform, Generalized immittance converter, Wave equations

In this paper, an interpolation method based on discrete cosine transform (DCT) is employed for digital finite impulse response-fractional order differentiator (FIR-FOD) design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR) system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF) interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

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.

In this paper, an optimal design of linear phase digital finite impulse response (FIR) highpass (HP) filter using the L1-norm based real-coded genetic algorithm (RCGA) is investigated. A novel fitness function based on L1 norm is adopted to enhance the design accuracy. Optimized filter coefficients are obtained by defining the filter objective function in L1 sense using RCGA. Simulation analysis unveils that the performance of the RCGA adopting this fitness function is better in terms of signal attenuation ability of the filter, flatter passband and the convergence rate. Observations are made on the percentage improvement of this algorithm over the gradient-based L1 optimization approach on various factors by a large amount. It is concluded that RCGA leads to the best solution under specified parameters for the FIR filter design on account of slight unnoticeable higher transition width.