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1. Determine the DTFT of each of the following sequences. a) X[n]=δ[n-1]+6[n-6] c) xt[n]= (-3)" (u[n-1]-u[n-10])...
Question 3]: Determine the DTFT of the following sequences over 0 SW S1, then plot the corresponding magnitude, angle, real part and imaginary part in one figure window. 1. x(n) = (0.3)"u(n) 2. x(n) = (0.5)"u(n-10) 3. x(n) = (0.9)" [u(n)-un-21)]
1. Determine the DTFT of each of the following sequences: TL (c) zelrnl - \o. otherwise
Determine the Discrete Time Fourier Transform (DTFT) of the following discrete-time signal. x[n]=n0.1" u(n) 1-0 1e112 0970.1e* 5) -0.12- e in 1-0.1e) C), ei (1+0.2e-in d) =-*+0.2e-10 e / +0.2012
Find the DTFT a. x1[n]=(.3)^nµ[n] b. x2[n]=(.3)µ[n-1] c. x3[n]=(.3)^n(µ[n]-µ[n-10]) d. x4[n]=(.3)^n(µ[n-1]-µ[n-10]) e. x5[n]=δ[n] f. x6[n]=δ[n-1] g. x7[n]=δ[n]+3δ[n-1]+7δ[n-3]
Suppose the signal x[n] = δ[n-1] + cos(nn/6+ π/4) is input to the LTI system described by the equation y[n][n] +r|n - 0.5yn -. Determine a closed-form expression for yn] Suppose the signal x[n] = δ[n-1] + cos(nn/6+ π/4) is input to the LTI system described by the equation y[n][n] +r|n - 0.5yn -. Determine a closed-form expression for yn]
Q.3) 120 Marks] [8 Marks] Determine the DTFT of the following DT signals i) x[n] = (0.5)" [u[n]-n(n-3)) a) ii) ? [n] = n (0.5)" u[n-2] b) [8 Marks] Consider the following CTFT pair: jw x(t) ?? (-v^2 + 5 i) e -/00t x(t) 6) using the CTFT properties determine the Fourier transform (CTFT) of: i x(3t-6) e) [4 Marks] Prove the Parseval's relationship for a CT signal x e
Question 4. (20 points) Compute the DTFT of the discrete-time signals, 1) x[n] = n(0.5)"u[n]. (opt) 2) x[n] = n(0.5)”cos(4n)u[n]. (opt) 3) x[n] = (0.5)" cos(4n)u[n]. (7pt)
1. The condition for signal x[n] to have DTFT is that x[n] is: (a) integratable, (b) differentiable, (c) summable, (d) compressible. 2. If X(92) is the DTFT of x[n], then the Fourier transform of x[-n) is (a) X(92)ej, (b) X(22)ein (c) X(32-1), (d) X(-22) 3. For 8-point computation of DFT, how many complex multiplications are involved? (a) 8, (b) 16, (c) 32, (d) 64. 4. For 32-point computation of FFT, how many complex multiplications are involved? (a) 32, (a) 325...
Question 1: (35 points: Consider the following sequences: x[n] = u[n] + 4" u[-n- 1] y[n] = x[n - 5) a) [10 points| Determine the Z-transform X(z) b) [10 points| Determine and draw the Region of Convergence (ROC) of x(n) c) [10 points] Determine the z-transform Y(z) d) [05 points) Determine the transfer function H(z)=Y(z)/X(z)
how to calculate the convolution Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence with u[n] is the sum of all the components (an integrator) 2. x[n]=仁1,-2-3-4) 1 vl n | =.xln|>k 11 | n | = 〈ー1, 2(00.-1,-3.-6.-10-10. Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence...