Down and out in Swansea

The AVX instruction set uses CPU registers to perform SIMD (Single Instruction Multiple Data) operations, which can be used to significantly speed up mathematical operations. I recently decided to create a digital filter in C++, and starting with the basics I came across a Finite Impulse Response (FIR) filter. Mathematically a FIR filter outputs a weighted sum of the most recent input values of the signal. The mathematics of a FIR filter are outlined  here . In practice, we typically work on sections of a signal. This is quite simply because we can not hold the entire signal in RAM. Consider the following signal which has been split into three chunks each of size 6,                                                        $$ [012123][123332][123342] $$ and the following filter $b = [1,2]$. In the routines discussed in this blog the a...