Quiz_1_+EENG2620

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2620

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Electrical Engineering

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Jan 9, 2024

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QUIZ 1 EENG2620 due 2/10/2022 @ 11:59 PM. Submit under quiz 2 1. Example of DT convolution of a system h(n) with an input x(n) x = [1 2 0 0 -3]; h = [3 2]; Step 1: invert one the two, for instance h=[2 3] Step 2: shift h along x and do the sum-of-products x = [1 2 0 0 -3]; h = [2 3]; y1=3x1=3 keep shifting to the right x = [1 2 0 0 -3]; h = [2 3]; y2=1x2+3x2=8 keep shifting to the right x = [1 2 0 0 -3]; h = [2 3]; y3=2x2+3x0=4 keep shifting to the right x = [1 2 0 0 -3]; h = [2 3]; y4=2x0+3x0=0 keep shifting to the right x = [1 2 0 0 -3]; h = [2 3]; y5=0x2+3x-3=-9 keep shifting to the right x = [1 2 0 0 -3]; h = [2 3]; y6=-3x2=-6 …now you see why it is called convolution Use the MATLAB code below to verify the answer above: x = [1 2 0 0 -3]; h = [3 2]; y = conv(x,h)
Problem 1: Try the convolution of these two signal/system, x = [-1 0 2 5 0 -3 4 7]; h = [-1 -2]; then verify your answer using MATLAB. No need to show the hand results. Copy and paste the results from MATLAB here: 2. Example of CT convolution of a system h(t) with an input x(t) Go to https://lpsa.swarthmore.edu/Convolution/CI.html 1. Set the parameters of the convolution as shown below. Move the slider to perform convolution. Observe the output y(t).
2. Swap the choices between h(t) and f(t) (by the way f(t)=x(t)). then repeat step 1. Do you get the same result for y(t)? Why or why not? Note: with convolution, the signal that gets inverted, gets shifted. PROBLEM 2 If you pick both f(t) and h(t) as 1 Sec. Pulse, 2 High as shown below, what convolution output do you get for y(t)? a. By handwork, by taking the convolution integral but you do not need to show this part. b. By using the animation used earlier. c. By MATLAB code below clc; t = linspace(0, 2); % range for t. h=2*(heaviside(t)-heaviside(t-1)); x=2*(heaviside(t)-heaviside(t-1)); y= conv(h, x); % Plot u subplot(311);
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plot(h); grid on ; % Plot g subplot(312); plot(x); grid on ; % Plot out subplot(313); plot(y); Include below a screen shot from part b and part c above.