3.10. Without explicitly solving for X (2), find the ROC of the z-transform of each of...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
Q1-20 points) a) Find the transform of the following signals and plot the ROC. 1 x(n)=(-0,357u(n-4)+(0.25?u(n+2) IL- x(n)=-cu-n-1) b) Find the Inverse Z-transform of: z(2-1.5) for (2-0.33)(2-0.5) ROC: z>0.5
need help solving thank you Fourier Transforms • Find the Fourier transform of et if -a<x<a 0 otherwise. • Find the Fourier transform of S f(0) = 3 10 if - 1<x<1 otherwise
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Problem 4: (a) and (b): Find the z-transform including the ROC for each of the following waveforms: [n] 3(금)"u[n] Xa | 지 = (c) Find the z-transfor by m of the impulse response hn] of an LTI system, when h[n] is given h[n] = 5(을)"u[n]. (d) and (e): Using z-transforms, find the responses (yan] and yb[n]) of the system described in part (c) to the inputs (an andn] described in parts (a) and (b
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot and indicate the region of convergence. Indicate whether or not the discrete-time Fourier transform of the sequence exists. (a) 8[n +5] (b) (-1)"u[n] (c) (-3)”u[-n – 2] (d) 27u[n] +(4)”u[n – 1]
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2) a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
10. Find the ROC of the Z-transform of x[n] (a) [:l> (6) 31 (0)1> (a) not (a), not (b) and not () 11. Calculate the DFT of the following discrete-time signal with: x[0] = 2, x[1] = -1, x[2] = 3, x[3] = -2. The value of the DFT required for this question is X(0). (a) 2 + j3. (b) 2-4, (c) 6, (d) not (a), not (b) and not e
3. The signal x[n] =-(b)”u[-n – 1]+ (0.5)”u[n], a) find the z-transform X(z) [5] b) plot the ROC. [3] С
(24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4) (24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4)