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# Untitled

Cinster May 22nd, 2019 70 Never
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1. %Zachary Orsoli 40004528
2. %ELEC 342 Lab2 Part1 Question2
3. clear all
4. clc
5.
6. % b)
7. n=[0:1];
8. x1=n;
9. x2=n;
10.
11. y1 =x1.^2;
12. y2 = x2.^2;
13. %if x3[n] = x1[n] + x2[n]
14. x3 = x1+x2;
15. y3 = x3.^2;
16. y4=y1+y2;
17. disp(' ') %create line spacing
18. disp('For the system y[n] = x^2[n] with input x[n]=[0,1] :')
19. if(y3 == y4)
20. disp('This function is linear since y3[n] = y4[n]')
21. else
22. disp('This function is not linear since y3[n] is not equal to y4[n]')
23. end
24. %Checking for Time Invariance
25. x1 = n;
26. x2 = x1+1;
27. y2 =(x2).^2;
28. y1_shifted = (x1+1).^2;
29. if(y1_shifted == y2)
30. disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
31. else
32. disp('This function is not Time-Invariant since y1[n+shift] is notequal to y2[n]')
33. end
34. %part b) (i) with range x[n]=[0:20]
35. n = [0:20];
36. x1 = n;
37. x2 = n;
38. %if y[n] = x^2[n]
39. y1 =x1.^2;
40. y2 = x2.^2;
41. %if x3[n] = x1[n] + x2[n]
42. x3 = x1+x2;
43. y3 = x3.^2;
44. y4=y1+y2;
45. disp(' ') %create line spacing
46. disp('For the system y[n] = x^2[n] with input x[n]=[0:20] :')
47. if(y3 == y4)
48. disp('This function is linear since y3[n] = y4[n]')
49. else
50. disp('This function is not linear since y3[n] is not equal to y4[n]')
51. end
52. %Checking for Time Invariance
53. x1 = n;
54. x2 = x1+1;
55. y2 =(x2).^2;
56.
57.
58. y1_shifted = (x1+1).^2;
59. if(y1_shifted == y2)
60. disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
61. else
62. disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
63. end
64.
65.
66.
67. %part b)(i) with range x[n]=[0:1]
68. n = [0:1];
69. x1 = n;
70. x2 = n;
71. %if y[n] = 2*x[n] + 5*delta[n]
72. y1 = 2*x1;
73. y1(1) = y1(1) + 5; % +5*delta[n]
74. y2 = 2*x2;
75. y2(1) =y2(1)+ 5; % +5*delta[n]
76. %if x3[n] = x1[n] + x2[n]
77. x3 = x1+x2;
78. y3 = 2*x3;
79. y3(1) =y3(1)+ 5; % +5*delta[n]
80. y4=y1+y2;
81. subplot(2,2,1)
82. stem(n,x1)
83. hold
84. stem(n,y1)
85. title('x1[n] and y1[n]')
86. xlabel('n')
87. ylabel('x1 and y1')
88. subplot(2,2,2)
89. stem(n,x2)
90. hold
91. stem(n,y2)
92. title('x2[n] and y2[n]')
93. xlabel('n')
94. ylabel('x2 and y2')
95. subplot(2,2,3)
96. stem(n,x3)
97.
98. hold
99. stem(n,y3)
100. title('x3[n] and y3[n]')
101. xlabel('n')
102. ylabel('x3 and y3')
103. subplot(2,2,4)
104. stem(n,y1)
105. title('x4[n] and y4[n]')
106. xlabel('n')
107. ylabel('y4')
108.
109. disp(' ') %create line spacing
110. disp('For the system y[n] = 2*x[n] + 5*delta[n] with input x[n]=[0,1] :')
111. if(y3 == y4)
112. disp('This function is linear since y3[n] = y4[n]')
113. else
114. disp('This function is not linear since y3[n] is not equal to y4[n]')
115. end
116. %Checking for Time Invariance
117. x1 = n;
118. x2 = x1+1;
119. y2 =(x2).^2;
120. y1_shifted = (x1+1).^2;
121. if(y1_shifted == y2)
122. disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
123. else
124. disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
125. end
126. %part b) (i) with range x[n]=[0:20]
127. n = [0:20];
128. x1 = n;
129. x2 = n;
130. %if y[n] = 2*x[n]
131. y1 =x1.^2;
132. y2 = x2.^2;
133. %if x3[n] = x1[n] + x2[n]
134. x3 = x1+x2;
135. y3 = x3.^2;
136. y4=y1+y2;
137. disp(' ') %create line spacing
138. disp('For the system y[n] = 2*x[n] + 5*delta[n] with input x[n]=[0:20] :')
139. if(y3 == y4)
140. disp('This function is linear since y3[n] = y4[n]')
141. else
142. disp('This function is not linear since y3[n] is not equal to y4[n]')
143. end
144.
145. %Checking for Time Invariance
146. x1 = n;
147. x2 = x1+1;
148. y2 =(x2).^2;
149. y1_shifted = (x1+1).^2;
150. if(y1_shifted == y2)
151. disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
152. else
153. disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
154. end
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