For x(n) = {1,2,3} and h(n) = (1,1), find the linear convolution y(n) =x(n)*h(n)
using DFT and inverse DFT. Use the following formula.
For x(n) = {1,2,3} and h(n) = (1,1), find the linear convolution y(n) =x(n)*h(n)
Forx(n) = {1,0,2} and h(n)=(1,1), find the linear convolution of the sequences using DFT method
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].
l(20 points) (1) Linear convolution: In a linca response h(n) impulse response h(n) f 2 -1). Use the direct linear convolution method to find the output y(n). r system, let input x(n) (n 2), 0s n s 1, and impulse
3. Given two sequences (rn)5 and (h[n)you are asked to compute their linear convo 514 lution y[n-r[n]*h[n]. You decide to use the DFT to speed up the computation (a) What is the length of the sequence yn)? (b) Find the smallest number of zeros that should be padded to each sequence so that the earconvolution can be computed using the (c) To further speed computation, you decide to use a radix-2 FFT to compute the DFT How should the sequences...
Determine the convolution y[n] = h[n]*x[n] of the following signals:
em 2: Given two sequences x[n] = 8 8[n - 8] and h[n] = (0.7)"u[n] Determine the z-transform of the convolution of the two sequences using the convolution property of the Z-transform Y(z) = X(z) H(2) Determine the convolution y[n] = x[n] * h[n] by using the inverse z-transform Problem 3: Find the inverse z-transform for the functions below. 4z-1 2-4 z-8 X(Z) = + 2-5 Z - 1 2-05 X(Z) = Z 2z2 + 2.7 z + 2
5.34. Two signals æ[n] and h[n] are given by - 3, 4, 1, 6 arn]{2, t n 0 h[n1, 1, , 0, 0} t n 0 Compute the circular convolution y[n] x[n]h[n] through direct application of the circular convolution sum a. b. Compute the 5-point transforms X k] and H[k] c. Compute Y[k] Xk] Hk, and the obtain y[n] as the inverse DFT of Y [k. Verify that the same result is obtained as in part (a)
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)...
2. (20 points) Let input x(n) (1 0 0) and impulse response h(n) (1 0). Each has length of N-3 and N 2, respectively. Append zeros to x(n) and h(n) to make the length of both equal to N+N-1 Find the output y(n) by using the DFT and the inverse DFT method.
x[n] = 9n u[n] h[n] = -7n u[n] Compute the convolution y[n]=x[n]∗h[n]. Choose the answer below which corresponds to {y[0],y[1],y[2],y[3]}