Conversion of Analog Filter into Digital Filter

CONVERSION OF ANALOG FILTER INTO DIGITAL FILTER

Let the system function of analog filter is n

Ha(s)= Σ_K+1 Ck / s-pk (1) k=1

where pk are the poles of the analog filter and ck are the coefficients of partial fraction expansion. The impulse response of the analog filter ha(t) is obtained by inverse Laplace transform and given as

The unit sample response of the digital filter is obtained by uniform sampling of ha(t). h(n) = ha(nT)

n=0,1,2. ………….

System function of digital filter H(z) is obtained by Z transform of h(n).

Using the standard relation and comparing equation (1) and (4) system function of digital filter is given as

STANDARD RELATIONS IN IIR DESIGN

EXAMPLES - IMPULSE INVARIANCE METHOD