Problem 2.22(a) |Linear Time-Invariant Systems |Oppenheim |2nd ed.

Problem 2.22 (a) 𝐹𝑜𝑟 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑤𝑎𝑣𝑒𝑓𝑜𝑟𝑚, 𝑢𝑠𝑒 𝑡ℎ𝑒 𝑐𝑜𝑛𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑦(𝑡)𝑜𝑓 𝑡ℎ𝑒 𝐿𝑇𝐼 𝑠𝑦𝑠𝑡𝑒𝑚 𝑤𝑖𝑡ℎ 𝑖𝑚𝑝𝑢𝑙𝑠𝑒 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 ℎ(𝑡)𝑡𝑜 𝑡ℎ𝑒 𝑖𝑛𝑝𝑢𝑡 𝑥(𝑡). 𝑆𝑘𝑒𝑡𝑐ℎ 𝑦𝑜𝑢𝑟 𝑟𝑒𝑠𝑢𝑙𝑡.

               𝑥(𝑡)=𝑒^(−𝛼𝑡)  𝑢(𝑡).
                  ℎ(𝑡)=𝑒^(−𝛽𝑡)  𝑢(𝑡).

𝐷𝑜 𝑡ℎ𝑖𝑠 𝑓𝑜𝑟 𝑏𝑜𝑡ℎ 𝑤ℎ𝑒𝑛 𝛼≠𝛽 𝑎𝑛𝑑 𝑤ℎ𝑒𝑛 𝛼=𝛽. 𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 :−
by… R.K. MTech (IIT Delhi)

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by… R.K. MTech (IIT Delhi) ... https://www.youtube.com/watch?v=5hR0yJfMpUc