Time-variant CIC-filters for sample rate conversion with arbitrary rational factors

Abstract

Sample rate conversion (SRC) with rational factors can be realized by interpolation followed by decimation, where CIC-filters can be chosen for either. However, the necessary increase of the sample rate that goes with the interpolation is not feasible in most RF applications. Therefore a time-variant implementation of CIC-filters is presented which circumvents the high intermediate sample rate. This time-variant implementation results in a linear periodically time-variant system (LPTV) which is completely equivalent to its original linear time-invariant system (LTI) consisting of the interpolator and the decimator. Thus well-known methods of system analysis can be used by analysing the LTI system, while implementing the system as an LPTV system, avoiding the high intermediate sample rates of the LTI system. The advantage of CIC-filters not having stored the coefficients of the impulse response but rather the description of the impulse response, enabling an implementation which is independent of the interpolation- as well as the decimation-factor, is preserved with the LPTV system. In contrast to Lagrange interpolators cancelling only the image components of the interpolated signal, time-variant CIC-filters also cancel the aliasing components, which is important in applications, where antialiasing is more important than anti-imaging.