1. Consider the z-transform X(z) whose pole-zero plot is shown below. a) Determine the ROC if it is known that the Fourier transform exists. For this case, determine whether the corresponding sequence is right-sided, left-sided, or two-sided. b) How many possible two-sided sequences have the pole zero plot shown below? c) Is it possible for the pole-zero plot to be associated with a sequence that is both stable and causal? If so, give the appropriate region of convergence. Im unit circle 0.5 1.5 3.0 Re

Part c only

Problem 4: Continuous-Time Fourier Transform Properties (a) Use your knowledge of the CTFT pairs and properties to calculate Jest * sin(2t) * cos3t|²dt, where the operator indicates continuous-time convolution. Your answer should be a real number.

The periodic signal x(t) is shown in the following figure. It is a rectangular pulse repeated every 4 seconds. a) Write the mathematical representation of x(t) b) What is the Fourier Transform of x(t)? c) Sketch X(@), showing the important parameters. Make sure you show the magnitude of X(@) at w = 0.

1-Find the Fourier-transform (FT), for the following signals: (a) x1(n) = -8(n + 1) + 8(n –- 1). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n)+8(n – 2). Calculate it in two ways, first directly, and second by relating it to the signal in the previous part, and then using the properties of the Fourier transform. (c) x3(n) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (–0.9)"-lu(n – 1), (e) v2(n) = (-0.9)"u(n – 1), (f) h(n) = 2[u(n) – u(n – 80)].

FIND DTFT ( NEED A NEAT HAND WRITING SOLUTION ONLY OTHERWISE WILL LEAVE A DOWNVOTE)