# FIR low pass filter

V0.01 16-Aug-01
## Introduction

This document is designed to
explain the method used to design the coefficients for people who are already
familiar with DSP techniques. If you are not, then you probably will not
understand a great deal of this! There are many books abd web pages on the
subject, so I suggest if you want to get into DSP, have a look at these.

This is just one method to design a
Finite Impulse Response digital filter. It uses the Hamming window. I designed
this filter a bit "back to front" since I wanted the example to have
only 5 taps. In reality the number of taps is a *consequence* of the
design process, and is not a pre-requisite.

## Design parameters

First we must establish some parameters for
the design. These are fairly arbitrary in our case, but would normally be chosen
based on the processor, and task at hand.

Sampling frequency = 16Hz

Cutoff frequency = 1Hz

Transition width = 10Hz

This means that the filter will start falling off at 1Hz, and at 11Hz will be
fully attenuating. This design gives a stop-band attenuation of at least 51dB.

### Number of taps

The number of taps required is normally
calculated from the equation

This rather artificial setting gives us a filter with 5 taps.

### The filter coefficients

Once the number of taps is known, the
filter coefficients can be calculated. These are given by the equations:

For these equations, ‘n’ ranges from –2 to +2, giving the following values
for h(n):

h(-2) = 0.021

h(-1) = 0.096

h(0) = 0.146

h(1) = 0.096

h(2) = 0.021

These represent the a_{n} parameters of the digital filter: