# Digital Signal Processing/FIR Filter Design

## Filter designEdit

The design procedure most frequently starts from the transfer function amplitude.

From the filter specification, the amplitude response is found with the help of various methods. The inverse Laplace transform provides the impulse response in the form of sampled values starting at time zero and ending after a given number of samples. The length of the impulse response is also called the filter order.

## Filter structureEdit

A Finite Impulse Response (FIR) filter's output is given by the following sequence:

${\displaystyle y[n]=b_{0}x[n]+b_{1}x[n-1]+\cdots +b_{N}x[n-N]}$

The following figure shows the direct implementation of the above formula, for a 4th order filter: