A processor is provided having an instruction set with a sliding window non-linear convolution function. A processor obtains a software instruction that performs a non-linear convolution function for a plurality of input delayed signal samples. In response to the software instruction for the non-linear convolution function, the processor generates a weighted sum of two or more of the input delayed signal samples, wherein the weighted sum comprises a plurality of variable coefficients defined as a sum of one or more non-linear functions of a magnitude of the input delayed signal samples; and repeats the generating step for at least one time-shifted version of the input delayed signal samples to compute a plurality of consecutive outputs. The software instruction for the non-linear convolution function is optionally part of an instruction set of the processor. The non-linear convolution function can model a non-linear system with memory, such as a power amplifier model and/or a digital pre-distortion function.