Design of fractional order differentiator using type-III and type-IV discrete cosine transform

Abstract

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.

Keywords

• Fractional order differentiator
• Fractional derivative
• Finite impulse response
• Discrete cosine transform
• Discrete sine transform
• Discrete Fourier transform