5.34. Two signals æ[n] and h[n] are given by - 3, 4, 1, 6 arn]{2, t...
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].
Signals and Systems
Problem 1: Given: x[n] = [0 0 2 -2] y[n] = [1 0 -2 0] (8 points) It is desired to use the DFT/FFT to obtain the cross correlation rxy[l]. Show the steps that need to be accomplished - DO NOT compute the final result. Show data patterns and any numbers required.
8) Convolution Integral (7 points). Given the following signals x(t) and h(t), compute and plot the convolution y(t) = x(t) *h(t). x(t) = u(t+2) - u(t – 4) h(t) = 5u(t)e-2t
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
Please show using MATLAB Answer
7. Obtain the convolution of the pairs of signals in Figure 7 h(t) a(t) 0 2 h(t) r(t) 0 0 Figure 7: Signal pairs Therefore, y(t) = 0 otherwise
7. Obtain the convolution of the pairs of signals in Figure 7 h(t) a(t) 0 2 h(t) r(t) 0 0 Figure 7: Signal pairs
Therefore, y(t) = 0 otherwise
my id is 1633168
Given the two signals x,(n) = [a , b, c) 1 x,(n) = [ your ID number] RO 0 If y(n) = x;(n) * x2(n) [ convolution sum] and if you know that y(0)=3, y(1)= -5, y(2)=8, find y(5). Enter your answer
(b) Perform convolution to obtain the discreet if input x[n] = [1 3 2 1] and impulse response, h[n] signal output of y[n], [1 -4 2]. [3 marks] (c) An analogue signal is sampled every 50ms for a duration of 1000 seconds. i) Calculate how much data (samples) are collected. [2 marks] If a Discrete Fourier Transform (DFT) is performed what is the maximum frequency information that can be obtained? [2 marks] Calculate the minimum frequency (the frequency resolution) 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(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...