In this paper, we propose three grid-based nonuniform interpolation techniques to find the AUC of the convolution operation of a digital alias-free FIR filter. Up to the authors’ knowledge, these techniques were not addressed in literature before. We call them composite 3-nonuniform-sample (C3NS), composite 4-nonuniform-sample (C4NS) and composite 5-nonuniform-sample (C5NS) rules. They are named after the traditional composite Simpson’s 1/3 rule which is usually used in second-order polynomial interpolation of equally-spaced sampling points. The proposed new rules shows better estimated results than the uniform-based ones when the number of sampling points doesn’t match the required Nyquist rate. Moreover, we prove that composite Simpson’s 1/3 rule is more accurate than composite Simpson’s 3/8 rule mathematically and by simulation.