ECET345 Signals and Systems Homework #6 Name of Student _________________________________________1. Find the z-transform x(z) of x(n) = . Hint: Follow the method used in the lecture for Week 6. Also, when evaluating the numerical value of a trig function, keep in mind that the arguments of trig functions are always in radians and not in degrees.2. Find the system transfer function of a causal LSI system whose impulse response is given byand express the result in positive powers of z. Hint: The transfer function is just the z-transform of impulse response. However, we must first convert the power of -0.5 from (n – 1) to (n – 2) by suitable algebraic manipulation.3. Express the following signal, x(n), in a form such that z-transform tables can be applied directly. In other words, write it in a form such that the power of 0.25 is (n-1) and the argument of sin is also expressed with a (n-1) multiplier. Hint: Express sin(n) as sin ((n-1+1)) = sin ((n-1) +) and then expand using use the trig identity for Sin(A+B).4. The transfer function of a system is given below. Find its impulse response in n-domain. Hint: First expand using partial fraction expansion and then perform its inversion using z-transform tables5. The transfer function of a system is given by .To such a system we apply an input of the type . Find the response of the system in n domain using MATLAB for obtaining the partial fraction expansion and then manually inverting the output using z-transform tables.6. A simulation diagram is shown below. We apply a unit impulse to such a system. Determine the numerical values of the first three outputs. You are free to use MATLAB where appropriate or do it entirely by hand.