Polynomial-based Interpolation Filters Research Articles

High-dynamics pulse-shaped signal simulation based on polynomial-based interpolation filters

High-dynamics pulse-shaped signal simulation based on polynomial-based interpolation filters

Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP) to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.

Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP) to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.

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.

Polynomial-Based Interpolation Filters—Part I: Filter Synthesis

This paper introduces a generalized design method for polynomial-based interpolation filters. These filters can be implemented by using a modified Farrow structure, where the fixed finite impulse response (FIR) sub-filters possess either symmetrical or anti-symmetrical impulse responses. In the proposed approach, the piecewise polynomial impulse response of the interpolation filter is optimized directly in the frequency domain using either the minimax or least mean square criterion subject to the given time domain constraints. The length of the impulse response and the degree of the approximating polynomial in polynomial intervals can be arbitrarily selected. The optimization in the frequency domain makes the proposed design scheme more suitable for various digital signal processing applications and enables one to synthesize interpolation filters for arbitrary desired and weighting functions. Most importantly, the interpolation filters can be optimized in a manner similar to that of conventional linear-phase FIR filters.

Polynomial-based filters with odd number of polynomial segments for interpolation

In many signal processing applications, it is beneficial to use polynomial-based interpolation filters. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. In the literature only polynomial-based filters having even number of polynomial pieces N have been considered. This letter presents a modification of the implementation form which allows realizing polynomial-based filters having an odd number of polynomial pieces. The condition that N must be even integer is not required any more. Further, a frequency-domain filter optimization method is developed, based on the methods for even-length filters. We illustrate through examples the performance of the odd-length polynomial-based filters.

Decimation by non-integer factor in software radio receivers

The sampling rate conversion is a critical functionality of the software radio receiver. Because the signals of different system standards have incommensurate symbol/sampling rates and a common Analog-to Digital Converter (ADC) is to be used for all supported standards, the decimation factor may become very difficult non-integer number. This paper gives overviews and comparisons of two efficient fractional decimator structures based on Cascaded Integrator-Comb (CIC) filters and low order polynomialbased interpolation filters.

A frequency-domain approach to polynomial-based interpolation and the Farrow structure

Interpolation filters are used to interpolate new sample values at arbitrary points between the existing discrete-time samples. One interesting class of these filters is the polynomial-based interpolation filters which can be efficiently implemented using the Farrow structure. This discrete-time filter structure has a time-varying impulse response. Therefore, it is usually modeled by a simple hybrid analog/digital (A/D) system which is based on the reconstruction of the continuous-time signal. In this work, an interesting frequency-domain relationship between the Farrow structure and the hybrid A/D model is derived. This result can be utilized to develop efficient design algorithms for polynomial-based interpolation filters.