1. Calculate Discrete-Fourier series coefficients for the following discrete-time signal x[n] 2A 0 Hints: You can use complex conjugate property of real signals to reduce the number of calculations 2. a) Find the impulse response of the following discrete-time system defined in z-Domain. H(z)= 3- b) The following input is applied to the system defined in a. Calculate the time-domain output using z-transform. x[n]=2"u[n] 3. Find the impulse response of the following discrete-time system defined in z-Domain. H()=- 1 4. Calculate the time domain response of the following system with initial condition and input. y[n]-[n-1]=x[n] x(t)=8[n] >[1]=2 Consider the discrete-time system where A= -1/6 c = [10]D=0 x(0)= and u(k)=-1(k) Find x(k) using (a) the frequency-domain method and (b) the time-domain method with Cayley-Hamilton (plug in and perform any multiplication or addition to achieve reasonably simplified answer, but the focus is not on the most simplified answer).