Give only right answers and workings for these very challenging questions.

1.How can you solve for the unit sample response given by 2(0.5)ⁿu(n).

2.What does counter integration, expansion into a series of terms and partial fraction expansion have in common?

3.Solve using inverse method the inverse{1,3/2,7/4,15/8,31/16,....} and give a condition necessary for the reverse to be efficient.

4.x(n)=(-1)n+1a is the inverse z transform of a log function in the conditions that n1; x(n)=0, n0. Determine the log function and illustrate.

5.Given 5+7z^-1+z^-3 as a one sided z- transform X⁺(z), solve for the signal x(n)

6.Solve and illustrate for x(n)=(n-k) the 1- sided z- transform.

7.1/(1-a) isn's system's step response. Solve for an LTI system the impulse response.

8.Define the difference equation and the conditions that result in the unit step response[1.099+1.088(0.9)ⁿ.cos(/3n5.2^o)]u(n)

9.A transient response occurs when p_k, k=1,2,...N are the poles of the system and |p_k| < 1 for all k. True or false?

10. When do we say that the rate of decay in a signal is rapid?