Using 2-transform tables (page 776 of text or equivalent), find the z-transform of (a) x(n) = 2 (0.1")u(n) 2 (0.1")u(n)-(-0.5"-1)u(n-1) (b) x(n) = (1/3)- u(n-2) (c) x (n) = cos (n) u(n). and express it in positive powers of z. When computing the value of trigonometric functions, keep in mind that the arguments are always in radians and not in degrees. (d) x (n) = (0.5)" sin (n) u(n) and express it in positive powers of z Find the inverse z-transform, x(n), of the following functions by bringing them into a form such that you can look up the inverse z-transform from the tables. This will require some algebraic and /or trigonometric manipulation/calculation. You will also need a table of z-transforms (page 776 of text or equivalent). When computing the value of trigonometric functions, keep in mind that the arguments are always in radians and not in degrees. Find the inverse 2-transform, x(n), of the following functions by bringing them into a form such that you can look up the inverse z-transform from the tables. This will require some algebraic and /or trigonometric manipulation/calculation. You will also need a table of z-transforms (page 776 of text or equivalent). When computing the value of trigonometric functions, keep in mind that the arguments are always in radians and not in degrees. (2Z-0.5) (Z+0.5) then use the z-transform tables. Having found the inverse z-transform, determine its numerical value at n = 2. (a) x(z) = = atb (c) Hint: Use the algebraic identity = + to bring the expression into a form where you can use the tables. Note that if the inverse z-transform of x(z) is x(n), then the inverse z-transform of Z-kx(z) is x(n-k), i. e, replace n by (n- k) in the inverse transform since zk is a delay by k samples. ,-k (b) Using partial fraction expansion, find the inverse z-transform of 3 (z - 0.2) (z + 0.4) (c) Using the tables, find the inverse z-transform of 2 z - 0.7071 z z - 1.41 z +1 (d) Using the tables, find inverse z-transform of .2165 z z - 0.25z + 0.0625 Signal 1. 8[n] 2. u[n] 3.-u[-n-1) 4.8[n-m] 5. a'u[n] SOME COMMON Z-TRANSFORM PAIRS 6. -a u[-n-1] 7. na u[n] 8.-na u[-n-1] 9. [cos won]u[n] 10. [sinaron]u[n] 11. [cos aon]u[n] 12. [ sin aon]u[n] Transform at az az (1-az-) 1-[cos w] 1-[2 cos w]2 +2 [sin] 1-[2 cos ]2+g 1-[r cosa] 1-[2r cos ]z + [r sin we]2 1-[2r cos an]2 + All : ROC |d 0) or (if m < 0) ld > lal | < |al