12 |
13 | 6 | This project follows the working and events of Signals and System laboratory of NIT-DGP. Classmates are welcome to get the help as and when required 7 |
8 | 9 | 10 |
11 |
![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\"){kind=icon}
"
27 | ]
28 | },
29 | {
30 | "cell_type": "code",
31 | "source": [
32 | "!pip install sympy"
33 | ],
34 | "metadata": {
35 | "id": "ogtks4HZHC-s",
36 | "outputId": "865bc134-c6bd-4cb8-cca8-5391d7a444cb",
37 | "colab": {
38 | "base_uri": "https://localhost:8080/"
39 | }
40 | },
41 | "execution_count": 6,
42 | "outputs": [
43 | {
44 | "output_type": "stream",
45 | "name": "stdout",
46 | "text": [
47 | "Requirement already satisfied: sympy in /usr/local/lib/python3.10/dist-packages (1.12)\n",
48 | "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy) (1.3.0)\n"
49 | ]
50 | }
51 | ]
52 | },
53 | {
54 | "cell_type": "code",
55 | "execution_count": 18,
56 | "metadata": {
57 | "id": "ZnnTAe1UE-kQ"
58 | },
59 | "outputs": [],
60 | "source": [
61 | "import matplotlib.pyplot as plt\n",
62 | "import numpy as np\n",
63 | "from sympy import sin,cos,symbols,summation,Heaviside,oo\n",
64 | "from sympy.abc import n"
65 | ]
66 | },
67 | {
68 | "cell_type": "code",
69 | "source": [
70 | "n,a,z = symbols(\"n ,a,z\")\n",
71 | "\n",
72 | "f1 = sin(n)\n",
73 | "f2 = a**n\n",
74 | "f3 = Heaviside(n-3)\n",
75 | "f4 = (2**(-2*n))*Heaviside(n)\n",
76 | "f5 = 2**(n+1)+2**(2-n)\n"
77 | ],
78 | "metadata": {
79 | "id": "YHQcnuiEF3_J"
80 | },
81 | "execution_count": 10,
82 | "outputs": []
83 | },
84 | {
85 | "cell_type": "code",
86 | "source": [],
87 | "metadata": {
88 | "id": "IZT5xPDHHoal"
89 | },
90 | "execution_count": null,
91 | "outputs": []
92 | },
93 | {
94 | "cell_type": "code",
95 | "source": [
96 | "\n",
97 | "f1_z = summation(f1*z**(-n),(n,-oo,oo))\n",
98 | "f1_z"
99 | ],
100 | "metadata": {
101 | "colab": {
102 | "base_uri": "https://localhost:8080/",
103 | "height": 67
104 | },
105 | "id": "0bSGGyRsGDZl",
106 | "outputId": "fb1ad118-1eec-4e83-d3ce-4a2af61dad39"
107 | },
108 | "execution_count": 19,
109 | "outputs": [
110 | {
111 | "output_type": "execute_result",
112 | "data": {
113 | "text/plain": [
114 | "Sum(sin(n)/z**n, (n, -oo, oo))"
115 | ],
116 | "text/latex": "$\\displaystyle \\sum_{n=-\\infty}^{\\infty} z^{- n} \\sin{\\left(n \\right)}$"
117 | },
118 | "metadata": {},
119 | "execution_count": 19
120 | }
121 | ]
122 | },
123 | {
124 | "cell_type": "code",
125 | "source": [
126 | "f2_z = summation(f2*z*(-n), (n, -oo, 0))+summation(f2*z*(-n), (n,0,oo))\n",
127 | "f2_z\n",
128 | "f2_z"
129 | ],
130 | "metadata": {
131 | "id": "xH4dg_p2Hwcu",
132 | "outputId": "6940be89-d408-4d57-c93f-cf8324d23225",
133 | "colab": {
134 | "base_uri": "https://localhost:8080/",
135 | "height": 78
136 | }
137 | },
138 | "execution_count": 23,
139 | "outputs": [
140 | {
141 | "output_type": "execute_result",
142 | "data": {
143 | "text/plain": [
144 | "-z*Piecewise((-1/(a*(1 - 1/a)**2), 1/Abs(a) < 1), (Sum(a**n*n, (n, -oo, 0)), True)) - z*Piecewise((a/(1 - a)**2, Abs(a) < 1), (Sum(a**n*n, (n, 0, oo)), True))"
145 | ],
146 | "text/latex": "$\\displaystyle - z \\left(\\begin{cases} - \\frac{1}{a \\left(1 - \\frac{1}{a}\\right)^{2}} & \\text{for}\\: \\frac{1}{\\left|{a}\\right|} < 1 \\\\\\sum_{n=-\\infty}^{0} a^{n} n & \\text{otherwise} \\end{cases}\\right) - z \\left(\\begin{cases} \\frac{a}{\\left(1 - a\\right)^{2}} & \\text{for}\\: \\left|{a}\\right| < 1 \\\\\\sum_{n=0}^{\\infty} a^{n} n & \\text{otherwise} \\end{cases}\\right)$"
147 | },
148 | "metadata": {},
149 | "execution_count": 23
150 | }
151 | ]
152 | },
153 | {
154 | "cell_type": "code",
155 | "source": [
156 | "\n",
157 | "f3_z = summation(f3*z**(-n), (n, -oo, oo))\n",
158 | "f3_z"
159 | ],
160 | "metadata": {
161 | "colab": {
162 | "base_uri": "https://localhost:8080/",
163 | "height": 67
164 | },
165 | "id": "-UCsKVw2GHdr",
166 | "outputId": "f0892c50-9a62-44e9-96eb-1b3b1a2f3258"
167 | },
168 | "execution_count": 13,
169 | "outputs": [
170 | {
171 | "output_type": "execute_result",
172 | "data": {
173 | "text/plain": [
174 | "Sum(Heaviside(n - 3)/z**n, (n, -oo, oo))"
175 | ],
176 | "text/latex": "$\\displaystyle \\sum_{n=-\\infty}^{\\infty} z^{- n} \\theta\\left(n - 3\\right)$"
177 | },
178 | "metadata": {},
179 | "execution_count": 13
180 | }
181 | ]
182 | },
183 | {
184 | "cell_type": "code",
185 | "source": [
186 | "\n",
187 | "f4_z = summation(f4*z**(-n), (n, -oo, oo))\n",
188 | "f4_z"
189 | ],
190 | "metadata": {
191 | "colab": {
192 | "base_uri": "https://localhost:8080/",
193 | "height": 67
194 | },
195 | "id": "xHzHEL41GOTF",
196 | "outputId": "ecdbb540-4fa8-46c5-fa26-9cb87771a410"
197 | },
198 | "execution_count": 14,
199 | "outputs": [
200 | {
201 | "output_type": "execute_result",
202 | "data": {
203 | "text/plain": [
204 | "Sum(Heaviside(n)/(2**(2*n)*z**n), (n, -oo, oo))"
205 | ],
206 | "text/latex": "$\\displaystyle \\sum_{n=-\\infty}^{\\infty} 2^{- 2 n} z^{- n} \\theta\\left(n\\right)$"
207 | },
208 | "metadata": {},
209 | "execution_count": 14
210 | }
211 | ]
212 | },
213 | {
214 | "cell_type": "code",
215 | "source": [
216 | "\n",
217 | "f5_z =summation(f5*z**(-n), (n, -oo, oo))\n",
218 | "f5_z"
219 | ],
220 | "metadata": {
221 | "colab": {
222 | "base_uri": "https://localhost:8080/",
223 | "height": 67
224 | },
225 | "id": "hS0vaFOIGYt3",
226 | "outputId": "8d23ec98-6d64-4134-f53d-51fb2b3a9a28"
227 | },
228 | "execution_count": 15,
229 | "outputs": [
230 | {
231 | "output_type": "execute_result",
232 | "data": {
233 | "text/plain": [
234 | "Sum((2**(2 - n) + 2**(n + 1))/z**n, (n, -oo, oo))"
235 | ],
236 | "text/latex": "$\\displaystyle \\sum_{n=-\\infty}^{\\infty} z^{- n} \\left(2^{2 - n} + 2^{n + 1}\\right)$"
237 | },
238 | "metadata": {},
239 | "execution_count": 15
240 | }
241 | ]
242 | }
243 | ]
244 | }
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