Low precision finite impulse response filter for digital interpolation

TLDR: In this article, a low precision Finite Impulse Response filter (FIR) is provided for filtering in a digital interpolation operation, which includes two steps, a sampling rate conversion operation for interspersing zeroes between samples in an input sequence and a filtering step of filtering out images that result from this operation.

Abstract: A low precision Finite Impulse Response filter (FIR) is provided for filtering in a digital interpolation operation. The interpolation operation includes two steps, a sampling rate conversion operation for interspersing zeroes between samples in an input sequence and a filtering step of filtering out images that result from this operation. The filtering operation utilizes a FIR filter that utilizes low precision filter coefficients that are selected to tune the frequency response such that the low end frequency response including the pass band, the transition band, and the portion of the stop band immediately after the transition band provides a response equivalent to that commensurate with substantially higher precision FIR filter coefficients, with the high frequency end of the stop band gradually increasing. A second, low pass filter section is provided for filtering out the image energy that exists at the output of the FIR filter in the high frequency end of the stop band to provide an overall filter response that is commensurate to that utilizing substantially higher precision FIR coefficients in the filter section. The FIR filter coefficients utilized are restricted to the set of [-1, 0, +1] such that a multiplierless FIR filter can be realized. The FIR filter coefficients are obtained by processing the infinite FIR filter coefficients through a software delta-sigma quantizer which quantizes the output to the desired low precision FIR filter coefficients.