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Mrain

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Mrain
May 21st, 2014
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  1. 1a)
  2. clear all
  3. clc
  4. t = -3*pi:0.01:3*pi;
  5. y = 2*cos(3*t) + 3*sin(2*t);
  6. plot(t, y)
  7. title('y=2cos(3t)+3sin(2t)')
  8. xlabel('t')
  9. ylabel('x1(t)')
  10. 1b)------------------------------------------------------------------------------------------------------
  11. clear all
  12. clc
  13. t = -pi:0.01:pi;
  14. subplot(2,1,1)
  15. y = abs(exp(1i*4*t) + exp(1i*11*t));
  16. plot(t, y)
  17. title('e^(4it)+e^(11it)')
  18. xlabel('t')
  19. ylabel('x2(t)')
  20. subplot(2,1,2)
  21. y1 =2*abs(cos((7/2)*t));
  22. plot(t , y1)
  23. title('2|cos(7/2t)|')
  24. xlabel('t')
  25. ylabel('x2(t)')
  26. //////////////////////////////////////
  27. x(t) = e^(j4t) + e^(j11t)
  28. x(t) = e^(j(15/2)t) * [e^(-j(7/2)t) + e^(j(7/2)t)]
  29.  
  30. e^(-j(7/2)t) = cos((7/2)t) - jsin((7/2)t)
  31. e^(j(7/2)t) = cos((7/2)t) + jsin((7/2)t)
  32.  
  33. x(t) = 2*e^(j(15/2)t) * [cos((7/2)t)]
  34. |x(t)| = 2|cos((7/2)t)|
  35. 2a)------------------------------------------------------------------------------------------------------
  36. clear all
  37. clc
  38. n = -20:20;
  39. x1 = 5*sin((1/8)*pi*n);
  40. stem(n, x1)
  41. title('5sin((1/8)pi*n)')
  42. xlabel('n')
  43. ylabel('x[n]')
  44. 2c)------------------------------------------------------------------------------------------------------
  45. m skripta clear all
  46. clc
  47. n = -20:20;
  48. for i=1:length(n)
  49. x(i) = dd1(n(i));
  50. end
  51. stem(n, x)
  52. title('u(n)')
  53. xlabel('n')
  54. ylabel('x2[n]')
  55.  
  56. funkcija function y=dd1(n)
  57. y=0;
  58. if n >= 0
  59. y=1;
  60. end
  61. 2b)------------------------------------------------------------------------------------------------------
  62. clear all
  63. clc
  64. n = -20:20;
  65. x3 = double (n == 3) - 4*double(n == 0) + 2*double(n == 1) + double(n == -2) - 6*double(n == -4) + 5*double(n == -5);
  66. stem(n, x3)
  67. title('δ[n+3] + 2δ[n+1] -4δ[n] + δ[n-2] -6δ[n-4] + 5δ[n-5]')
  68. xlabel('n')
  69. ylabel('x[n]')
  70. 3a)------------------------------------------------------------------------------------------------------
  71. clear all
  72. clc
  73. syms t
  74. ezplot('2*cos(3*t) + 3*sin(2*t)', [-3*pi, 3*pi])
  75. title ('x = 2cos(3t) + 3sin(2t)')
  76. ylabel('x(t)')
  77. 3b)------------------------------------------------------------------------------------------------------
  78. clear all
  79. clc
  80. syms t
  81. x = t*cos(t);
  82. y = t*sin(t);
  83. ezplot(x, y, [0*pi, 20*pi])
  84. title('x = t*cos(t) y = t*sin(t)')
  85. 4a)------------------------------------------------------------------------------------------------------
  86. m skripta clear all
  87. clc
  88. t = -3:0.01:4;
  89. plot(t, x1(t), 'LineWidth', 3)
  90. funkcija function y = x1(t);
  91. for i=1:length(t)
  92. y(i) = 0;
  93. if(0 <= t(i)) & (t(i)<1)
  94. y(i) = t(i);
  95. end
  96. if(1 <= t(i)) & (t(i)<2)
  97. y(i) = -t(i) + 2;
  98. end
  99. end
  100. 4b)------------------------------------------------------------------------------------------------------
  101. funkcija function y = x2(t)
  102. for i=1:length(t)
  103. y(i) = 0;
  104. if(-2 <= t(i)) & (t(i) < -1)
  105. y(i) = t(i) +2;
  106. end
  107. if(-1 <= t(i)) & (t(i) < 0)
  108. y(i) = -t(i);
  109. end
  110. if(0 <= t(i)) & (t(i) < 1)
  111. y(i) = t(i);
  112. end
  113. if(t(i) >= 1)
  114. y(i) = 1;
  115. end
  116. end
  117. m skripta clear all
  118. clc
  119. t = -3:0.01:4;
  120. plot(t, x2(t), 'LineWidth', 3)
  121. 4c)------------------------------------------------------------------------------------------------------
  122. funkcija function y = x3(t)
  123. for i=1:length(t)
  124. y(i) = 0;
  125. if(0 <= t(i)) & (t(i) < 1.5)
  126. y(i) = 1;
  127. end
  128. if(1.5 <= t(i)) & (t(i) < 2)
  129. y(i) = -0.5;
  130. end
  131. end
  132. m skripta clear all
  133. clc
  134. t = -3:0.01:4;
  135. plot(t, x3(t), 'LineWidth', 3)
  136. 5a)------------------------------------------------------------------------------------------------------
  137. clear all
  138. clc
  139. t = -3:0.01:4;
  140. parni_dio = (1/2) * [x1(t) + x1(-t)];
  141. neparni_dio = (1/2) * [x1(t) - x1(-t)];
  142. subplot(3,1,1)
  143. plot(t, x1(t), 'LineWidth', 3)
  144. title('Original')
  145. subplot(3,1,2)
  146. plot(t, parni_dio, 'Linewidth', 3)
  147. title('Parni dio')
  148. subplot(3,1,3)
  149. plot(t, neparni_dio, 'LineWidth', 3)
  150. title('Neparni dio')
  151. 5b)------------------------------------------------------------------------------------------------------
  152. clear all
  153. clc
  154. t = -3:0.01:4;
  155. parni_dio = (1/2) * [x2(t) + x2(-t)];
  156. neparni_dio = (1/2) * [x2(t) - x2(-t)];
  157. subplot(3,1,1)
  158. plot(t, x2(t), 'LineWidth', 3)
  159. title('Original')
  160. subplot(3,1,2)
  161. plot(t, parni_dio, 'LineWidth', 3)
  162. title('Parni dio')
  163. subplot(3,1,3)
  164. plot(t, neparni_dio, 'LineWidth', 3)
  165. title('Neparni dio')
  166. 5c)------------------------------------------------------------------------------------------------------
  167. clear all
  168. clc
  169. t = -3:0.01:4;
  170. parni_dio = (1/2) * (x3(t) + x3(-t));
  171. neparni_dio = (1/2) * (x3(t) - x3(-t));
  172. subplot(3,1,1)
  173. plot(t, x3(t), 'LineWidth', 3)
  174. title('Original')
  175. subplot(3,1,2)
  176. plot(t, parni_dio , 'LineWidth', 3)
  177. title('Parni dio')
  178. subplot(3,1,3)
  179. plot(t, neparni_dio, 'LineWidth', 3)
  180. title('Neparni dio')
  181. 6)-------------------------------------------------------------------------------------------------------
  182. clear all
  183. clc
  184. t = -4:0.01:10;
  185. obrtanje = x3(-t);
  186. skaliranje = x3((1/3)*t);
  187. pomak = x3(t - 3);
  188. subplot(4,1,1)
  189. plot(t, x3(t), 'LineWIdth', 3)
  190. title('Originalni signal')
  191. subplot(4,1,2)
  192. plot(t, pomak, 'LineWIdth', 3)
  193. title('Pomaknuti signal')
  194. subplot(4,1,3)
  195. plot(t, obrtanje, 'LineWIdth', 3)
  196. title('Obrnuti signal')
  197. subplot(4,1,4)
  198. plot(t, skaliranje, 'LineWIdth', 3)
  199. title('Skalirani signal')
  200. 7)-------------------------------------------------------------------------------------------------------
  201. clear all
  202. clc
  203. t = -4:0.01:10;
  204. transformirani = x2(-3*t + 2.5);
  205. subplot(2,1,1)
  206. plot(t, x2(t), 'LineWidth', 3)
  207. title('Originalni')
  208. subplot(2,1,2)
  209. plot(t, transformirani, 'LineWidth', 3)
  210. title('Transformirani')
  211. 8)-------------------------------------------------------------------------------------------------------
  212. clear all
  213. clc
  214. n = -27:25;
  215. x3 = double (n == 3) - 4*double(n == 0) + 2*double(n == 1) + double(n == -2) - 6*double(n == -4) + 5*double(n == -5);
  216. graf1 = -x3;
  217. graf2 = 2*x3;
  218. graf3 = (1/3)*x3;
  219. subplot(4,1,1)
  220. stem(n, x3)
  221. title('x3 = d[n+3] + 2d[n+1] -4d[n] + d[n-2] -6d[n-4] + 5d[n-5]')
  222. xlabel(' ')
  223. ylabel('x[n]')
  224. axis([-20 20 -6 5])
  225. subplot(4,1,2)
  226. stem(n-5, graf1)
  227. title('x3(-n - 5)')
  228. xlabel(' ')
  229. ylabel('x[n]')
  230. axis([-20 20 -5 6])
  231. subplot(4,1,3)
  232. stem(n+8, graf2)
  233. title('x3[2n + 8]')
  234. xlabel(' ')
  235. ylabel('x[n]')
  236. axis([-20 20 -12 10])
  237. subplot(4,1,4)
  238. stem(n-2, graf3)
  239. title('x3[1/3n - 2]')
  240. xlabel(' ')
  241. ylabel('x[n]')
  242. axis([-20 20 -2 1.7])
  243. 9)-------------------------------------------------------------------------------------------------------
  244. clear all
  245. clc
  246. n = 0:30;
  247. x = cos((2*pi*1*n)/7);
  248. x1 = cos((2*pi*(5/2)*n)/7);
  249. x2 = cos((2*pi*6*n)/7);
  250. x3 = cos((2*pi*8*n)/7);
  251. subplot(4,1,1)
  252. stem(n,x)
  253. title('cos(n2pi/7)')
  254. subplot(4,1,2)
  255. stem(n,x1)
  256. title('cos(5npi/7)')
  257. subplot(4,1,3)
  258. stem(n,x2)
  259. title('cos(12npi/7)')
  260. subplot(4,1,4)
  261. stem(n,x3)
  262. title('cos(16npi/7)')
  263. 10)------------------------------------------------------------------------------------------------------
  264. clear all
  265. clc
  266. t = -5:0.01:5;
  267. x = cos(((3*pi*t)/1)-(pi/4)).^2;
  268. x1 = cos(((3*pi*t)/3)-(pi/4)).^2;
  269. x2 = cos(((3*pi*t)/6)-(pi/4)).^2;
  270. subplot(3,1,1)
  271. plot(t,x)
  272. title('(cos(t*3pi/1 - pi/4))^2')
  273. subplot(3,1,2)
  274. plot(t,x1)
  275. title('(cos(t*3pi/3 - pi/4))^2')
  276. subplot(3,1,3)
  277. plot(t,x2)
  278. title('(cos(t*3pi/6 - pi/4))^2')
  279. 11)-------------------------------------------------------------------------------------------------------
  280. clear all
  281. clc
  282. n = 0:40;
  283. x = 2*sin((3*pi)/4*n + 1/3);
  284. x1= 1.5*cos(n/7 + pi/5);
  285. x2 = cos(pi/4*n).*cos(pi/8*n);
  286. x3 = 3*cos(pi/8*n) + 2*sin(pi/2*n) - 4*sin(pi/4*n);
  287. subplot(4,1,1)
  288. stem(n,x)
  289. title('2sin(3pi/4n + 1/3)')
  290. subplot(4,1,2)
  291. stem(n,x1)
  292. title('1.5cos(n/7 + pi/5)')
  293. subplot(4,1,3)
  294. stem(n,x2)
  295. title('cos(pi/4n)cos(pi/8n)')
  296. subplot(4,1,4)
  297. stem(n,x3)
  298. title('3cos(pi/8n) + 2sin(pi/2n) - 4sin(pi/4n)')
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