12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5...
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given by 10 equally-spaced samples of X(e). Determine y[n]. Hint: N-point DFT of a sequence w[n] = 2-n (u[n]-u[n-N]) is W [k] = 1-22 1wk Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given...
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
Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First write the x[n] showed above as two pulse functions then take the DTFT using the equation given below Express discrete Fourier transform (DFT) of x[n] using DTFT X(Q). a. b. Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First...
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms of x[n] Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms...
12. Calculate the DFT of the following discrete-time signal with: x[0] = 1, x[1] = 2, x[2] =-3, x[3] = 0. The value of the DFT required for this question is X(1). (c) 4-j2, (d) not (a), not (b) and not (e). (6) 2-4, (a) 2 + j3, 13. Determine the finite length sequence, xfn] from the DFT sequence X[k]={10,15, 40,-5). Only the discrete-time signal value at x[0] is required for this question. (a) 6+j4 (b) 15, (c) 4+j4, (d)...
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)
5.25 LetX(eM) denote the DTFT of the length-9 sequence x[nl=[L -3, 4. -5, 7. -5. 4, -3. II (a) For the DFT sequence X1 k obtained by sampling X(em at uniform intervals of π/6 starting from ω 0, determine the IDFT x1(n) of X1[k] without computing X) and XiK]. Can you recover x In] from xilo (b) For the DFT sequence X|k] obtained by sampling X(e,") at uniform intervals of π/4 starting from ω ะ 0 determine the IDFT x2...
5. (4 pts) Let X(ej) be the DTFT of a signal x[n] which is known to be zero for n < 0 and n > 3. We know X(eja) for four values of N as follows. X(@j0) = 10, X(eja/2) = 5 – 5j, X(ejt) = 0, X(ej37/2) = 5 + 5j (a) (3 pts) Find x[n]. (Hint: Compute the IDFT) (b) (1 pts) Find X(ej?).
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...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...