5.8 Determine the N-point DFTs of the following length-N sequences defined for 0snN-1: -Crn/N), (c) xeln]...
Compute the N-point DFT of the following finite-length sequences
considered to be of length N (N is even):
1, n odd 0, n even (a) x[n] = COS Tn
12.3 Determine the time-limited sequence, with length 0 <k < N – 1, cor- responding to the following DFTs X[r], which are defined for the DFT index 0 <r <N – 1: (iv) X[r]= where ko is a constant; elsewhere (0.5N r = ko, N – ko To elsewhere (vi) X[r]= 0 ) for Osr<N – 1.
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
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]) d) x.[n]=0.5a cos(nn/2)u[n] e) 2n-2 u[-n+41 Xcn
\ Can anyone explain a and b
how they got this answer. what formula they use
P-8.2 For each ofthe following 10-point DF「s, determine a formula the l0-point IDFT Use MATLAB to check your work numerically. 1に0 (a) Xa[k] = 0 k = 1, 2, . . . ,9 (b) Xolk-1 for k = 0, 1,2, ,9 (c)Xc[k] =10 k = 0,1,2, 4, 5, 6, 8, 9 (d) Xalk]cos(2mk/5) for k 0,1,2,...,9 k=3, 7 I (a) Substituting into the inverse...
PROBLEM 1: Let xfn], O < n 3 N-1 be a length-N sequence with an N-point DFT X[k], 0 k N-1. Determine the N-point DFT's of the following length-N sequences in terms of X[k]: (a) w[n] = az[M-m1〉N] + β (n-m2)N], where m 1 and m 2 are positive integers less than N. (b) g[n] ={z[n] for n even for odd
1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an= n-cos(n) 4n2-7 Tn (d) { } 2. Prove that the following sequences diverge. (Def 7.10 pg 596) READ Sequences that Diverge to oo or-oo (b) ann infinity. Hint: Provide an M -N proof that an approaches
1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an=...
Find the limits of the following sequences, if they exist. n+ (-1)" COS n An = an = n
3.96 Determine the z-transforms of the following sequences and their respective ROCs: (a) x1[n] = -a"u[-n-1], (b) x2[n] = "Min + 1], and (c) x3[n] = "u-n).
8.2 Determine the limits of the following sequences, and then prove your claims. (a) (n = (b) b = 1 (c) C = Amis = 1 sinn