3. Evaluation of z-transforms and inverse z-transforms and their application to the derivation of time sequences and discrete-time Fourier transforms. (a) Using the z-transform, determine the output of an LTI system with impulse response h[n] = {1,2,-1,0,3} for the input x[n] = {1,2,-1} (b) Compute the z-transform and ROC of the signal: x(n) (2) u(-n)-2"u(-n-1) Plot the pole-zero pattern. (c) Mathematically explain how the discrete-time Fourier transform (DTFT) is related to the z-transform. C Please do in Discrete Mathematics or Computing Mathematics abababababababababababababa (a) Show that for all integers 1