Impulse invariance

Creator
Creator
Seonglae Cho
Created
Created
2023 Nov 3 7:55
Editor
Edited
Edited
2023 Nov 30 16:54
Refs
Refs

Continuous to discrete means sampling

When we are given a desired CT system that we wish to implement is. If Hc(jΩ)H_c(j\Omega) is band-limited (BL), Heff(jΩ)=Hc(jΩ)=Hc(jω/T)=H(ejω)H_{eff}(j\Omega) = H_c(j\Omega) = H_c(j\omega/T) = H(e^{j\omega}) because of
FT of Impulse Train
is
impulse train
and h[n]=hc(nT)h[n] = h_c(nT) (definition)
that’s FT is H(ejω)=1THc(jω/T)H(e^{j\omega}) = \frac{1}{T} H_c(j\omega/T) so we need to multiply TT
 
 

LPF

h[n]=sin(πn)πnh[n] =\frac{sin(\pi n)}{\pi n}
 
 
 
 
 
 

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