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(Solved): [10 points] Consider x_(1)(t)={(jt,0<=t<=1),(0, otherwise ):} and x_(2)(t)={(e^(-t),0<=t< ...



[10 points] Consider x_(1)(t)={(jt,0<=t<=1),(0, otherwise ):} and x_(2)(t)={(e^(-t),0<=t<=1),(0, otherwise ):}. (a) Find the optimum approximation hat(x)_(1)(t) of x_(1)(t) in terms of x_(2)(t). (b) Compute the energy of the error signal e_(1)(t). (c) Find the optimum approximation hat(x)_(2)(t) of x_(2)(t) in terms of x_(1)(t). (d) Compute the energy of the error signal e_(2)(t). Recommendation: use Appendix E. 7 in your textbook to compute the integrals.


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