Unformatted text preview: f systems S1
and S2 as shown in Fig. P2.21(a).
Denote the output of S1 as:
w[k]=x[k]2x[k1]+x[k2]
Denoting the output of S2 as y[k] (given that the input is w[k]):
y[k]=w[k]+w[k1]2w[k2]
Substituting the first equation into the second one we’ll have:
y[k]=(x[k]2x[k1]+x[k2])+(x[k1]2x[k2]+x[k3])2(x[k2]2x[k3]+x[k4])
So
y[k]=x[k]x[k1]3x[k2])+5x[k3]2x[k4]
(iii) Calculate the inputoutput relationship for the parallel configuration of systems S1
and S2 as shown in Fig. P2.21(b).
The outputs of systems in parallel are added:
y[k]=2x[k]x[k1]x[k2]
(iv) Show that the series and parallel configurations of systems D1 and S2 are LTI
systems.
Since both represent linear, constant coefficient differential equations then both systems
are LTI systems....
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This document was uploaded on 03/06/2014 for the course EE 341 at NMT.
 Fall '09
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