Chien-Cheng Tseng

Improved design of digital fractional-order differentiators using fractional sample delay

In this paper, a digital fractional-order differentiator (FOD) is designed by using fractional sample delay. To improve the design accuracy of conventional fractional differencing and Tustin design methods at high frequency regions, the integer delay is replaced by fractional sample delay. By using the well-documented finite-impulse-response Lagrange, infinite impulse response allpass, and Farrow fractional delay filters, the proposed FOD can be implemented easily even though the fractional sample delay is introduced. Several design examples are illustrated to demonstrate the effectiveness of the proposed method.

Design of Fractional Order Digital Differentiator Using Radial Basis Function

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.

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.

Digital differentiator design using fractional delay filter and limit computation

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), allpass 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.

Digital IIR Integrator Design Using Richardson Extrapolation and Fractional Delay

In this paper, a new design of digital integrator is investigated. First, the trapezoidal integration rule and differential equation are applied to derive the transfer function of the digital integrator. The Richardson extrapolation is then used to generate high-accuracy results while using low-order formulas. Next, the conventional Lagrange finite-impulse response fractional delay filter is directly applied to implement the designed integrator. Two implementation structures are studied: direct substitution and polyphase decomposition. Finally, numerical comparisons with conventional digital integrators are made to demonstrate the effectiveness of this new design approach.

Design of Fractional Delay Filter Using Hermite Interpolation Method

In this paper, the design of fractional delay (FD) filters using the Hermite interpolation is investigated. First, the transfer function of fixed FD filters is obtained from the Hermite interpolation formula by using variable substitution. Then, two implementation methods for the Hermite-based FD filters are presented. One is the derivative sampling scheme using an analog differentiator, the other is the Shannon sampling scheme with an auxiliary digital differentiator. Next, the proposed method is applied to design wide-range variable fractional delay (VFD) filters and some extensions are made. Finally, several numerical examples are demonstrated to show the effectiveness of the proposed Hermite interpolation design method.

Design of Wideband Fractional Delay Filters Using Derivative Sampling Method

In this paper, the design of wideband fractional delay filter is investigated. First, the reconstruction formula of derivative sampling method is applied to design wideband fractional delay filter by using index substitution and window method. The filter coefficients are easily computed because closed-form design is obtained. Then, the weighted least squares method is used to design fixed and variable wideband fractional delay filters. Finally, numerical examples are demonstrated to show that the proposed method has smaller design error than the conventional fractional delay filter without sampling the derivative of signal.

Designs of Discrete-Time Generalized Fractional Order Differentiator, Integrator and Hilbert Transformer

In this paper, the design of a generalized fractional order differentiator (FOD) whose magnitude and phase responses can be controlled independently is investigated. First, a relation between conventional FOD and generalized FOD is studied such that the design tools of conventional FOD in the literature can be used to design variable generalized FOD directly. Then, the similar method is applied to design generalized fractional order integrator (FOI). Next, the proposed generalized FOD and FOI are used to generate a secure single side band (SSB) signal for saving the transmission bandwidth. The parameters of variable generalized FOD and FOI can be used as the secure keys for construction and reconstruction. Finally, the relation between fractional Hilbert transformer and generalized FOD is studied and the edge detection application is demonstrated to show the flexibility and effectiveness of the proposed generalized FOD.

Closed-Form Design of Half-Sample Delay IIR Filter Using Continued Fraction Expansion

In this paper, the closed-form design of half-sample delay infinite-impulse response (IIR) filter is presented. First, the continued fraction expansion (CFE) and its recursive computation are reviewed briefly. Then, the CFE of square root function is applied to design half-sample delay IIR filters with various orders. The comparisons with conventional maximally flat half-sample delay all-pass and Lagrange filters are made and implementation issue is also addressed. Next, the designed half-sample delay filter is used to reduce the approximation error of the conventional IIR Simpson integrator, to design half-band and diamond shaped filters, and to magnify the digital image. Finally, several numerical examples are illustrated to demonstrate the effectiveness of the proposed design method

Efficient Design and Implementation of Variable Fractional Delay Filters Using Differentiators

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.