Windowing Design Method for Polynomial-Based Interpolation Filters
- PDF / 696,263 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 91 Downloads / 248 Views
Windowing Design Method for Polynomial-Based Interpolation Filters Djordje Babic
Received: 14 June 2011 / Revised: 26 August 2012 © Springer Science+Business Media, LLC 2012
Abstract An efficient implementation for finding digitally the interpolated samples is the Farrow structure. It mimics digitally a hybrid system where a continuoustime (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. Keywords Polynomial-based filters · Filter design · Taylor polynomial approximation · Window functions · Kaiser window · Prolate window 1 Introduction In many digital-signal processing (DSP) applications, there is a need to evaluate the discrete-time signal at time instants between the existing sample values. In recent D. Babic () School of Computing, University Union, Knez Mihailova 6/6, Belgrade, Serbia e-mail: [email protected]
Circuits Syst Signal Process
years, the most interesting class of interpolation filters has been the polynomial-based interpolation filters [4, 5, 7–9, 14–18]. The polynomial-based interpolation filters have a piecewise-polynomial impulse response. The most attractive feature of these filters is that they can be efficiently implemented using the Farrow structure [8, 17, 18] or its modifications [4, 5]. This discrete-time filter structure consists of several parallel FIR filters having fixed coefficient values making it a suitable structure for digital signal processor and VLSI implementations. According to the sampling theorem, the new samples at arbitrary time instants can be generated using the non-realizable sinc interpolation. A method to model this ideal interpolation is to use a hybrid analog/digital system where a continuous-time signal is reconstructed by using a digital-to-analog (D/A) converter and a reconstruction filter [18]. The reconstructed signal is then sampled at the desired time instants to obtain the desired inte
Data Loading...
