1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N...
DSP 4. (12 points) (a) (4 points) Let x[n] = {1,2, 1, 2} and h[n] = {1,-1,1, -1} be two length-4 sequences defined for 0 <n<3. Determine the circular convolution of length-4 y[n] = x[n] 4 hin). (b) (6 points) Find the 4-point discrete Fourier transform (DFT) X[k], H[k], and Y[k]. (c) (2 points) Find the 4-point inverse DFT (IDFT) of Z[k] = {X[k]H[k].
Find N-point DFT of x[n]= n=0,1,…,N-1 X[n] = Using the periodicity of the complex exponentials, we can write x[n] follows: X[n] = The DFT coefficients are 9N/2 k=0 X[k]= N/4 k=2 and k=-2 0 else
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...
1. Let {X[k]}K=o be the N = 8-point DFT of the real-valued sequence x[n] = [1, 2, 3, 4]. (a) Let Y[k] = X[k]ejak + X[<k – 4 >8] be the N = 8-point DFT of a sequence y[n]. Compute y[n]. Note: Do NOT compute X[k]. (b) Let Y[k] = X*[k] be the DFT of the sequence y[n], where * denotes the conjugate. Compute the sequence y[n]. Note: Do NOT compute X[k].
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...
(5) Consider the following discrete time signal zln-S[n] + δ[n-1] + a[n-2] + δ n-3] a) Compute the DTFT of n b) Compute the DFT4 (DFT with N 4) coefficients for zn], i.e., Xk for k 0,1,2,3. c) Compute the DFTs (DFT with N-8) coefficients for r[n], i.e., Xk for k 0,1,...,7.
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...
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. For each of the following choices of r(n) and N, you will perform the five tasks stated below (a) x(n (b) r(n)-2-a(n), Л-16, (d) x(n) is same as in part (c) with N = 8 otherwise Task 4: Compute DTFT of y. You may not be able to obtain a closed form expression for the DTFT of y. However since y has finite duration of length N, you can just code the analysis equation in Matlab. Let y(k 1)...
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = { x[r]y[n – r) r=<N> be their period convolution. Let z[n] = sin(7") and y[n] = { . 0 <n<3 4 <n <7 Asns? be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.