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This paper introduces realizations of a reconfigurable finite-impulse-response (FIR) filter for simultaneous equalization and lowpass filtering. The main advantage of the proposed solutions is computational complexity reduction compared to existing solutions for a given performance, which leads to reduced hardware complexity. The proposed structures employ properties of both a variable bandwidth (VBW) filter and a variable equalizer (VE) with variable coefficients. The overall transfer function of the proposed reconfigurable lowpass equalizer (RLPE) is a weighted linear combination of fixed subfilters where the weights are directly determined by the bandwidth and one or several parameters of the channel needed to be equalized. The paper provides design procedures based on minimax optimization and introduces a fast design method for the filter with several variable parameters that can substantially decrease the design time. Filter order estimation expressions as well as complexity expressions are presented for all proposed realizations. Design examples include comparison of the RLPE structures and a common approach of using a regular FIR equalization filter requiring online redesign when the bandwidth or channel characteristics are changed. It is shown that the number of general multiplications can be reduced up to 91% using the proposed RLPE. • Three low-complexity realizations of variable FIR filters with simultaneously variable bandwidth and equalization. • No need for online design when the bandwidth or channel characteristics are modified. • Design procedure to obtain the overall filter with the lowest complexity. • Design procedure to obtain the overall filter with the lowest complexity for reduced design time. [ABSTRACT FROM AUTHOR]

In this paper, the power series expansion of exponential function is used to transform the design problem of variable fractional delay (VFD) filter into the designs of digital differentiators with various orders such that conventional digital differentiators can be applied to implement VFD filter efficiently. The proposed method is flexible because the VFD filter can be designed by making the trade-off among the storage requirement of filter coefficients, computational complexity and delay of filter. Finally, some numerical examples are demonstrated to show the effectiveness and flexibility of the proposed design methods. [ABSTRACT FROM PUBLISHER]

In this paper, the design of fractional order digital differentiator is investigated. First, the radial basis function interpolation method is described. Then, the non-integer delay sample estimation of discrete-time sequence is derived by using the radial basis function interpolation approach. Next, the Grünwald-Letnikov derivative and non-integer delay sample estimation are applied to obtain the transfer function of fractional order digital differentiator. Finally, the applications in digital image sharpening and parameter estimation of fractional noise process are studied to demonstrate the usefulness of this new design approach. [ABSTRACT FROM AUTHOR]

In this paper, the design of digital differentiator is investigated. First, the relation between fractional delay filter and first-order differentiator is established such that the differentiator can be obtained from fractional delay filter by using the computation of limit. Then, conventional finite-impulse response (FIR), all- pass and Farrow-based fractional delay filters are directly applied to design first-order differentiator. Next, the proposed method is extended to design high-order differentiators. Finally, several design examples are illustrated to demonstrate the effectiveness of this new design approach. [ABSTRACT FROM AUTHOR]

Abstract: The Savitzky–Golay (SG) filters are generally used for smoothing and differentiation in many fields. The properties of the SG smoothing filters have been well studied. However, the properties of the SG differentiation filters or SG digital differentiators (SGDD, for the first order differentiation) are not developed well somehow, although they have been widely used. In the paper, the properties of the SGDD are discussed in detail. The effects of the SGDD on a noise-free single Gaussian line and a noise-free Gaussian doublet are studied via simulation. The results indicate that the contrast and resolution loss of the SGDD depends on the ratio of the width of signal derivative and filter length. The linear SGDD is not preferable for preserving small details of signal derivative from this study. The cubic and quintic SGDD with the choice of appropriate filter length are recommended in order to maintain the resolution of signal derivative. [Copyright &y& Elsevier]