Find the z-transform of the following signals: (a) (b) x[n] = 0.5'u[n] (c) x[n]-[1482] (d) x[n]-[0...

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Find the z-transform of the following signals: (a) (b) x[n] = 0.5'u[n] (c) x[n]-[1482] (d) x[n]-[0 1 2 3 4] (e) x[n]=2(0.8) u[n] x[n]=u[n]-u[n-4] Problem 2) Plot the poles and zeros of the following transfer functions. Determine the stability. (Z-0.5) (z+0.75) (Z-0.5) (z-0.75) (z-0.5) (2+2) (d) H(₂)=- (e) H(2)= (1) H(z) = (2² -1.52-1) Problem 3) Express the following z-transform function as a sum of polynomials in 2¹ and a proper fraction. Determine ROC for stable and causal system 5+0.1z¹+0.3z +0.9z H(z)= (a) H(=)=- (b) H(z)=- (c) H(2)= (= -0.25) z(z-1) (2²-0.5z-0.5) 2+0.8z¹+0.2z² (8) H(2)=(-0.5)(2+0.5) (z²+z+0.74) (h) H(z)=(z-0.5)(2+0.5) (2²+2+4.25) Problem 4) Determine the inversez-transform using partial fraction expansion z²+3z H₁ (2)=- 2² +0.82-0.6 Problem 5) For the following given difference equation: y[n]+ayn-1]+ayn-2] = x[n]+ Bxn-1]+ ₂x[-2] a, 0.5, a=0.7, ß,=0.25, B₂ =3 1- Determine the impulse response using the z-transform method. 2- Calculate the time-domain output using the 2-transform method for the input x[n] = (0.15) u[n] Find the z-transform of the following signals: (a) (b) x[n] = 0.5'u[n] (c) x[n]-[1482] (d) x[n]-[0 1 2 3 4] (e) x[n]=2(0.8) u[n] x[n]=u[n]-u[n-4] Problem 2) Plot the poles and zeros of the following transfer functions. Determine the stability. (Z-0.5) (z+0.75) (Z-0.5) (z-0.75) (z-0.5) (2+2) (d) H(₂)=- (e) H(2)= (1) H(z) = (2² -1.52-1) Problem 3) Express the following z-transform function as a sum of polynomials in 2¹ and a proper fraction. Determine ROC for stable and causal system 5+0.1z¹+0.3z +0.9z H(z)= (a) H(=)=- (b) H(z)=- (c) H(2)= (= -0.25) z(z-1) (2²-0.5z-0.5) 2+0.8z¹+0.2z² (8) H(2)=(-0.5)(2+0.5) (z²+z+0.74) (h) H(z)=(z-0.5)(2+0.5) (2²+2+4.25) Problem 4) Determine the inversez-transform using partial fraction expansion z²+3z H₁ (2)=- 2² +0.82-0.6 Problem 5) For the following given difference equation: y[n]+ayn-1]+ayn-2] = x[n]+ Bxn-1]+ ₂x[-2] a, 0.5, a=0.7, ß,=0.25, B₂ =3 1- Determine the impulse response using the z-transform method. 2- Calculate the time-domain output using the 2-transform method for the input x[n] = (0.15) u[n]

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