which of the following sequences that the Fourier transform exists
$I x(n) = [(1/2)^{n} + 1]u(n) $
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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]
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]
Fourier transform from Laplace transform-The Fourier transform of finite support signals, which are absolutely integrable or finite energy, can be obtained from their Laplace transform rather than doing the integral. Consider the following signals 5.30 x3(t) - r(t + 1) - 2r(t) + r(t - 1) (a) Plot each of the above signals. (b) Find the Fourier transforms (X,(S2)) for1, 2, and 3 using the Laplace transform (c) Use MATLAB's symbolic integration function int to compute the Fourier transform of...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)] 2) (Fourier Transforms Using Properties)...
(a) (i) What is the relationship between DTFT (Discrete Fourier Transform) and the z- Transform?! (ii) x[n] = a[n-M + 1].u[-n] 1. Sketch x[n]. 2. Find the 2-transform X(z) of x[n]. 3. Find the DTFT X(w) of x[n]. 4. Sketch |X(w) vs w. Indicate all the important values on your diagram.
Find the Z-transform of the following sequences using the Z-transform properties table. Identify clearly the name of the properties that you use: a. x(n) = n(1/2)nu(n) b. x(n) = -n(1/3)nu(-n-1) c. x(n) = (-1)nu(n) d. x(n) = (-1)ncos(npi/3)u(n)
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Determine the z-transform of the following sequences and their ROCs: a) x(n) = (0.5)" for n> 5, and zero for all other values of n; b) x(n)= (0.5)"[u(n) - u(n-7)]; c) x(n)=(-1)"a"u(n), 0 <a<1.
2) (15pts) For medical imaging 2D Fourier Transform: show the Fourier Transform of 1 is equal to delta(u,v) le. If f(x,y) = 1, F(1) = δ(u,v), show all your steps.
3.10. Without explicitly solving for X (2), find the ROC of the z-transform of each of the following sequences, and determine whether the Fourier transform converges: (a) x[n] = [(y)"+(!)"]u[n – 10) J1, -10 <n<10, (b) xin] = 1 o. otherwise, (c) x[n] = 2"u[-n] (d) x[n] = |()*++ - (ja/331]u[n - 1] (e) x[n] = a[n+ 10] – u[n+ 50 (f) x[n]=()” [1] + (2+36)-24 – – 1).