Parallel realizations of digital interpolation filters for increasing the sampling rate

Digital interpolators can be used to increase the sampling rate of a sampled waveform when the limitations of analog to digital converter circuitry may prevent obtaining directly the increased sampling rate. As Schafer and Rabiner have shown [1], the interpolation process can be viewed as a linear filtering operation which produces output samples at a rate different from the input rate. In this paper, the interest is in the case where the output rate is an integral multiple of the input. The interpolating filter can be realized in a transversal or serial form in which the output samples are obtained in serial form. However, by rearranging the delays, weights, and outputs, the output samples may be obtained in parallel form. The reason for seeking parallel outputs is that parallel arithmetic may be performed without the need for commutators, and at a slower rate than serial arithmetic. If the sampling rate is to be increased by a factor L, L parallel outputs are obtained. By means of specific examples, the various methods for obtaining parallel outputs are shown. The examples are 3-point interpolators (i.e., each interpolated value is a linear combination of three input sample values) used for tripling the sampling rate. Generalizations to higher order interpolators are given and an example shows a 4-point interpolator for quadrupling the sampling rate. The Appendix gives the numerical values of digital impulse responses for various Lagrangian interpolators.