Averaged Lagrange Method for interpolation filter

Abstract

This paper presents a new method for Lagrange interpolation for reducing distortions without introducing any complexity. The aim is to improve the linearity of the phase and the gain responses of the interpolation filter by an averaging method. A first FIR interpolation filter of the second order computes the values between three successive samples of the input signal. At the same time, a second filter, identical to the first, computes the values between (xk–2 , xk–1 , xk ). Finally, the common values between (xk–2 , xk–1 ) provided by the two filters are averaged two by two. This double interpolation can be simply done with a single third order filter and with a Farrow structure filter. Compared to the usual Lagrange's third order interpolation filter, the behaviour of the filter we propose is more regular especially in the high frequencies of the Nyquist band. More, the filter coefficients are easier to calculate. The designed filter is tested on a FPGA of Altera. The results shows that the method significantly reduces distortions and improves quality of the frequency response.