FIR Filter

A FIR filter is a type of digital interpolating filter. We will be looking at its use to both distort and interpolate a digital signal as in a CD Player. Mathematically this this is done by the following convolution:

$\sum _{l=-\infty }^{\infty }h({\frac {lT}{2}})\delta (t-{\frac {lT}{2}})*\sum _{k=-\infty }^{\infty }x(kT)\delta (t-kT)$.

So how do we do an infinite sum in a computer? Well we can't because we can't fit an infinite amount of data in a computer, so we have to trim it down.