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Signals and Systems by Smarajit Ghosh

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7.5 IMPORTANT PROPERTIES OF SYSTEMS

Figure 7.8 shows the two LTI systems having common input x(n). Their outputs are y1(n) and y2(n) respectively which are added to get the net output y(n). The systems are in parallel mode.

 

Replacement of parallel systems

 

Fig. 7.8 Replacement of parallel systems

 

y(n) = x(n)*h1(n) + x(n) *h2(n) = x(n)*[h1(n) + h2(n)]

 

Therefore, the parallel system can be replaced by a single system with impulse response [h1(n) + h2(n)].

Figure 7.9 shows the two systems which are in cascade i.e., in series.

 

Replacement of cascade systems

 

Fig. 7.9 Replacement of cascade systems ...

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