Windowing Design Method for Polynomial-Based Interpolation Filters

An efficient implementation for finding digitally the interpolated samples is the Farrow structure. It mimics digitally a hybrid system where a continuous-time (CT) signal is reconstructed using an analog reconstruction filter having a piecewise-polynomial impulse response. The interpolated samples are obtained by sampling reconstructed signal. This paper introduces a generalized design method for polynomial-based interpolation filters and Farrow structure. The proposed method also can be used to calculate the coefficients of Selva interpolator. In this approach, the ideal CT impulse response is truncated by using CT window functions. The obtained windowed impulse response is then approximated using the piecewise Taylor polynomial approximation. Length of the impulse response and degree of the approximating polynomial can be arbitrarily selected, and in this way the transition band width can be controlled. However, if CT fixed-window functions are used, the stopband attenuation is determined by window type and remains approximately constant with increase of length and order of the impulse response. The stopband attenuation can be controlled by using CT dynamic windows such as Kaiser window. The presented windowing design method is an effective tool for calculation of the Farrow structure coefficients, with filter performance that is comparable to the frequency domain design.