The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1)...
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm is an efficient way to compute the values X Now consider a finite-length sequence xin] whose length is N samples.We want to evaluate X(z) the z-transform of the finite-length sequence, at the following points in the z-plane where ris a positive number. We have available an FFT algorithm (a) Plot the points z in the z-plane for the case N-8...
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...
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...
ASSIGNMENT 2 (C4,_CO2, PO1) 1. Calculate DFT of the following discrete-time sequence, x(n) using DFT technique x(n) = {72,-56, 159) (C4, CO2,PO1) 2. Calculate the 8-point DFT of the following discrete-time sequence, x(n) using Decimation In Time Fast Fourier transform (DIT-FFT) algorithm. Show the sketch and label all parameters on a signal flow graph/butterfly diagram structure in your answer. (1-3<ns3 x(n) = 0 elsewhere
5.34 Let xIn],0sns N-1, be a length-N sequence with an N-point DFT XIk],0sksN-1. (a) sa symmetric sequence satisfying the condition x n] = 지(N 1 n)N] show that X [N/2] 0 for N even. (b) Ifx[n] is a antisymmetric sequence satisfying the condition x[n] = rKN-1-n)N], show that X[0] = 0 (c) If x[n] is a sequence satisfying the condition x[n] =-x[(n + M〉N] with N = 2M, show that X[21] = 0 for I=0, 1, ,M-1 5.34 Let xIn],0sns...
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples from X(eu): g[n] CH 0 for n<0and n > 4 = x(e,2 ) for k = 0, 1, 2,3,4 = Find g(0] and gl1]. 12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples...
Consider a finite length DT sequence of length N -16 described below. 1, 0<n< 2 Use MATLAB built-in function dftmtx (N), and compute X[k] command and create stem plots for the following: DFT(X[k]. Use subplot (a) x n] vs n; (b) X[k] vs k; (c) angle (X [k) vs k. Label axes of these plots and include title for each of these plots
I Need Help with 4,6,8,10,15,18 Problems 123 If f(n) is a periodic sequence with period N, it is also periodic with period 2N. Tet 8(k) denote the DFS coefficients of X(n) considered as a periodic sequence with period N and X,(k) denote the DFS coefficients of x(n) considered as a periodic sequence with period 2N. X,(k) is, of course, periodic with period N and X2(k) is periodic with period 2N. Determine 8(k) in terms of X (k). 5. Consider two...
8.32. Considera finite-duration sequence x[n] of length P such that xlnj=Ofor n <0andn> P. We want to compute samples of the Fourier transform at the N equally spaced frequencies 2nk Determine and justify procedures for computing the N samples of the Fourier transform using only one N-point DFT for the following two cases: (a) N > /P (b) N < P
The DFT sequence of x[n] of length x[n] is given as follows: X[0] = 2 X[1] = 2 + jα X[2] = 5-j4 X[3] = β+j3 X[k1] = 2 X[k3] = 2-j3 X[k2] = 5+j4 X[7] = γ+j3 Find α, β, γ, k1, k2 & k3