2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
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<strong>2.</strong>6 Interconnection <strong>of</strong> <strong>LTI</strong> <strong>Systems</strong><strong>2.</strong> h 12 [n] is in series with h 3 [n] : h 123 [n] = h 12 [n] h 3 [n]h 123 [n] = (h 1 [n] + h 2 [n]) h 3 [n]Fig. <strong>2.</strong>21 (b).3. h 123 [n] is in parallel with h 4 [n] : h[n] = h 123 [n] h 4 [n]h[ n] ( h [ n] h [ n]) h [ n] h [ n],Fig. <strong>2.</strong>21 (c).1 2 3 4Thus, substitute the specified forms <strong>of</strong> h 1 [n] and h 2 [n] to obtainh [ ] [ ] [ 2] [ ]12n u n u n u nu [ n 2]Convolving h 12 [n] with h 3 [n] givesh [ n] u [ n 2] [ n 2]123u [ n][ ] 1 nh n u [ n ].<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>38
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