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Hw01_Sol_Su09

Hw01_Sol_Su09 - ECE220 Homework#1 Solutions Solution to...

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ECE220 Homework #1 Solutions Solution to Problem 2.1 Considering the function u ( t ): 1. u ( t ) can have only two values: 0 and 1 2. u (1) = 1 3. u (1000) = 1 4. u ( - 1) = 0 5. u ( - 1000) = 0 6. u (0) = 1 7. u ( t ) can never be 1000 8. u ( t ) can never be -1 Solution to Problem 2.2 (even problems) 2. g (1000) = 0, f (1000) = - 1, h (1000) = 0 4. g ( - 1000) = 1, f ( - 1000) = 0, h ( - 1000) = -1 6. m (1) = 0, n (1) = 1 8. m ( - 1) = 1, n ( - 1) = - 1 10. m (0) = 2, n (0) = 0 12. p (1000) = 1, q (1000) = 0 14. p ( - 1000) = 0, q ( - 1000) = 0 Solution to Problem 2.10 The following MATLAB code will generate all these plots: 1

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clear close all % Define the time interval first t = -4:0.001:6; limit = 0.5; % Calculate the signal u(t) % using logical operators in a vectorized fashion s1 = (t-2) >= 0 ; s2 = (t>=0) - ((t-2) >=0); s3 = t.*(((t+1)>=0) - ((t-1) >=0)); s4 = ((t+2)>=0) + 2*(t >=0) - ((t-1) >=0) - 3*((t-3) >=0) + ((t-4) >=0); s5 = (2*t-4).*(((2*t-4+1)>=0) - ((2*t-4-1) >=0)); s6 = ((-t/2+2)>=0) + 2*(-t/2 >=0) - ((-t/2-1) >=0) - 3*((-t/2-3) >=0) + ((-t/2-4) >=0); % Plot the function subplot(3,2,1); plot(t,s1,’b’,’Linewidth’,2); title(’s_1(t)’); xlabel(’t -->’); ylabel(’magnitude’); grid on; axis([min(t)-limit max(t)+limit min(s1)-limit max(s1)+limit]); subplot(3,2,2); plot(t,s2,’b’,’Linewidth’,2); title(’s_2(t)’); xlabel(’t -->’); ylabel(’magnitude’);
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Hw01_Sol_Su09 - ECE220 Homework#1 Solutions Solution to...

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