Problem 1.20 |Signals and Systems |Oppenheim |2nd ed.

Problem1.20 | Signals and Systems | Oppenheim | 2nd ed Problem 1.20 𝐴 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑡𝑖𝑚𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑠𝑦𝑠𝑡𝑒𝑚 𝑆 𝑤𝑖𝑡ℎ 𝑖𝑛𝑝𝑢𝑡 𝑥(𝑡)𝑎𝑛𝑑 𝑜𝑢𝑡𝑝𝑢𝑡 𝑦(𝑡)
𝑦𝑖𝑒𝑙𝑑 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑖𝑛𝑝𝑢𝑡 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑎𝑖𝑟𝑠:

                         𝑥(𝑡)=𝑒^𝑗2𝑡            𝑦(𝑡)=𝑒^𝑗3𝑡
                                     
                          𝑥(𝑡)=𝑒^(−𝑗2𝑡)            𝑦(𝑡)=𝑒^(−𝑗3𝑡)

   𝑎) 𝐼𝑓 𝑥_1 (𝑡)=cos⁡(2𝑡), 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑜𝑢𝑡𝑝𝑢𝑡 𝑦_1 (𝑡)  𝑓𝑜𝑟 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑆.
   𝑏) 𝐼𝑓 𝑥_2 (𝑡)=cos⁡(2(𝑡−1/2))  𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑜𝑢𝑡𝑝𝑢𝑡 𝑦_2 (𝑡)  𝑓𝑜𝑟 𝑠𝑦𝑠𝑡𝑒𝑚 𝑆.

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