{"id":58,"date":"2018-12-24T11:11:51","date_gmt":"2018-12-24T11:11:51","guid":{"rendered":"http:\/\/gantovnik.com\/bio-tips\/?p=58"},"modified":"2024-11-13T02:27:42","modified_gmt":"2024-11-13T10:27:42","slug":"fourier-expansion-of-a-rectangular-wave","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/fourier-expansion-of-a-rectangular-wave\/","title":{"rendered":"#7: Fourier expansion of a rectangular wave"},"content":{"rendered":"

\"\"<\/a><\/p>\n

import os\nimport matplotlib.pyplot as plt\nimport numpy as np\nos.chdir('\/home\/vg\/Downloads\/projects\/ex7')\nos.getcwd()\n\nplt.figure(figsize=(10,8)) \nN = 2**8\nt = np.linspace(0,1,N)\ny = np.zeros(N)\n\nfor n in range(1,32,2):\ny = y + 4\/(np.pi*n)*np.sin(2*np.pi*n*t*2)\nplt.plot(t,y)\n\nplt.axis([0,1,-1.4,1.4])\nplt.grid()\nplt.xlabel('Time, sec')\nplt.ylabel('Value')\nplt.title('Fourier expansion of a rectangular wave')\nplt.savefig(\"example7.png\", dpi=100)\nplt.show()\nplt.close()<\/pre>\n","protected":false},"excerpt":{"rendered":"
import os import matplotlib.pyplot as plt import numpy as np os.chdir(‘\/home\/vg\/Downloads\/projects\/ex7’) os.getcwd() plt.figure(figsize=(10,8)) N = 2**8 t = np.linspace(0,1,N) y = np.zeros(N) for n in range(1,32,2): y = y + 4\/(np.pi*n)*np.sin(2*np.pi*n*t*2) plt.plot(t,y) plt.axis([0,1,-1.4,1.4]) plt.grid() plt.xlabel(‘Time, sec’) plt.ylabel(‘Value’) plt.title(‘Fourier expansion of a rectangular wave’) plt.savefig(“example7.png”, dpi=100) plt.show() plt.close()<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[56,69,2],"tags":[137],"class_list":["post-58","post","type-post","status-publish","format-standard","hentry","category-math","category-matplotlib","category-python","tag-fourier-series"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-W","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":3022,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/442-the-partial-sums-of-the-fourier-series-for-the-square-wave-function-using-python\/","url_meta":{"origin":58,"position":0},"title":"#442 The partial sums of the Fourier series for the square-wave function using python","author":"gantovnik","date":"2024-07-25","format":false,"excerpt":"import numpy as np import matplotlib.pyplot as plt from matplotlib.widgets import Slider nmax = 5 pi = np.pi x = np.linspace(-2*pi, 2*pi, 1001) def f(xarray): y = np.zeros_like(xarray) for ind, x in enumerate(xarray): xmod = x%(2*pi) if xmod