BASICS OF ANALOG FILTER DESIGNS?

       
QUESTION#1 . NATURE OF FILTERS

A designer designs either finite impulse response filter or infinite impulse response filter.The design techniques for both are almost different with respect to their nature of design and other designing requirements as well.As we are discussing analog filter designing techniques one point should be observed that graphical representation of analog parameters is displayed on s-plane and furthermore our poles should be on the left half plane as well.But this representation is with different way in digital filters where plane of representation is z-plane and here all poles should lie inside the unit circle.

structure of analog filter

QUESTION#2. WHY LOW PASS FILTER IS DESIGNED FIRST

All filters can be designed by various different techniques.But normally low pass filter is initially designed due to the interesting practice that this low pass filter can be modified in all other forms of filters high pass,band limited,band rejected and other various filters of our desired features and characteristics.One precaution in designing filters either analog or digital should be examined and practiced that before going to final design we must prepare the software design of the required filter this will ensure us that if we design required hardware then wanted results can be obtained accurately.



             

low pass filter configuaration

QUESTION#3. MATURITY OF ANALOG DESIGNING DOMAIN

Analog filter techniques are full time mature and well furnished with all needs of designing parameters.If we want to design a digital filter then firstly it will be designed in analog domain then will be converted to the desired digital domain.The reason for tackling analog domain only while designing filters and then conversion to other forms like discrete or digital is simply that analog domain is old and full of efficiently designing features as many scientists and observers examined all the aspects of analog filters in the past and digital filters as compared with analog filters are not so much mature and efficient result producer as compared with analog so designing in analog domain is preferred due to maturity of analog domain mainly.

QUESTION#4. BENEFITS OF CONVERSION FROM ANALOG TO DIGITAL

While converting from analog to digital domain after full examination of nature of outputs obtained at the end of both domains we come to know that required characteristics of both analog as well as digital like stability,response all are almost the same.

 Design of IIR Filers From Analog Fitters 

2. T he left-half plane (L H P) o f the 5-plane should m ap into the inside o f the

unit circle in the z-plane. Thus a stable analog filter w ill be converted to a

stable digital filter.

W e m entioned in the preceding section that physically realizable and stable

IIR filters cannot have linear phase. R ecall that a linear-phase filter m ust have a

system function that satisfies the condition

H( z) = ± z ~ n H ( z ~ 1) (8.3.4)

w here z ~ N represents a delay o f N units o f tim e. But if this w ere the case, the

filter w ould have a m irror-im age p ole outside the unit circle for every p ole inside

the unit circle. H en ce the filter w ould be unstable. C onsequently, a causal and

stable IIR filter cannot have linear phase.

If the restriction on physical realizability is rem oved, it is possible to obtain

a linear-phase IIR filter, at least in principle. This approach involves perform ing a

tim e reversal o f the input signal x ( n ), passing x ( —n) through a digital filter H(z),

tim e-reversing the output o f H(z), and finally, passing the result through H(z)

again. This signal processing is com putationally cum bersom e and appears to offer

no advantages over linear-phase F IR filters. C onsequently, when an application

requires a linear-phase filter, it should be an F IR filter.

In the design o f IIR filters, w e shall specify the desired filter characteristics

for the m agnitude response only. This does not m ean that w e consider the phase

response unim portant. Since the m agnitude and phase characteristics are related,

as indicated in Section 8.1, we specify the desired m agnitude characteristics and

accept the phase response that is obtained from the design m ethodology.

8.3.1 IIR Filter Design by Approximation of Derivatives

O ne o f the sim plest m ethods for converting an analog filter into a digital filter is to

approxim ate the differential equation in (8.3.3) by an equivalent difference equation.

This approach is often used to solve a linear constant-coefficient differential

equation num erically on a digital com puter.

For the derivative d y { t ) / d t at tim e t — n T , w e substitute the bac k wa rd difference

^ (n T ) — y ( n T — l ) ] / 7 \ Thus

dy( t )

dt

y ( n T) - y i n T - T)

(g.3.5)

w here T represents the sam pling interval and y(n) = y { nT) . T he analog differentiator

w ith output d y ( t ) / d t has the system function H( s ) = s, w hile the digital

system that produces the output [y(n) — >-(n — 1 ) ]/T has the system function

H ( z ) = (1 —z ~ y) / T . Consequently, as show n in Fig. 8.29, the frequency-domain.