intro

Introduction

In this experiment , we intend to design a "finite impulse response" filter or in short it is known as "FIR" and another one
is called "infinite impulse response" filter or also known as "IIR". The purpose of filters are to filter and change wave form , change its amplitude-frequency and phase frequency. The most common purpose of digital filters are to produce a better quality signal , to extract information from a signal or more combined signals. Application of filters on daily life are such as data compression , biomedical signal processing , digital audio , speech processing ,image processing , and etc. Digital filter is a mathematical alogarithm or routine implemented in hardware / software to perfom filtering.

Finete impulse response filter
FIR is characterized by the following mathematical equation ,
                                                               N-1
                                                    y(n) = S h(k)x(n-k)
                                                               k=0
where h(k) is the impulse response of the filter , x and y are the input and output respectively. The above impulse response if finite duration. Three distinct properties of a FIR filters :

it is always stable
it is always realizable
can always be disigned to have a linear phase

Digital FIR filter design process , these are the 5 stages in the design of a filter :
1) specification of the filter requirements
2) calculationof suitable filter coefficients based on the desired specification
3) Representation of the filter by a suitable structure (realization)
4) analysis of the effects of finite word length on the filter performace.
5) impletmentation of filter in software and or hardware

Infinte Impulse response filter
IIr filter is characterize by by the following mathematical equation ,
          ¥                                 N                      M
y(n) = S   h(k)x(n-k) = S a_kx(n-k) - S b_ky(n-k)
          k=0                              k=0                    k=1

where h(k) are impulse response of the filter and a_k and b_k are filter coefficients. According to this equation , the IIR filter response will have infinite duration.
One of the major advantage of the IIR filters is that it can achieve sharper transitions between passband abd stopband than FIR filters of the same order because of the "peaked" reponses created by poles. IIR filters have infinite duration impulse hence they can be matched to analog filters , all of which generally have infinitely long impulse responses. Therefore basic technique of the IIR filter design is by transformming well known analog filters into digital filters using complex value mappping. The advantage of this technique lies in the fact that both analog filter design (AFD) tables and the mappings are available extensively in the literature. This basic technique is called the analog to digital filter transformation The AFD table is only available for lowpass filter.

The IIR lowpass filter design technique involves the following steps :

design analog lowpass filters
study and apply filter transformation to obtain digital filters

The most common way of designing IIR filters is to trasformexisting analog filter to digital IIR filter.