--- title: "What’s a Fourier transform?" description: "What’s a Fourier transform?" author: "Prakash nidhi Verma" published: 2018-06-27 updated: 2020-09-20 canonical: https://www.mindstick.com/interview/23448/what-s-a-fourier-transform category: "artificial intelligence" tags: ["python-3.4", "artificial intelligence"] reading_time: 1 minute --- # What’s a Fourier transform? A generic method to decompos functions into a superposition of symmetric functions is called Fourier transform .The Fourier transform finds the set of cycle speeds, amplitudes and phases to match any time signal. A Fourier transform converts a signal from time to frequency domain — it’s a very common way to extract from audio signals or other time series by using a sensor data. ![What’s a Fourier transform?](data:image/png;base64,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)\ ## Answers ### Answer by Prakash nidhi Verma A generic method to decompos functions into a superposition of symmetric functions is called Fourier transform .The Fourier transform finds the set of cycle speeds, amplitudes and phases to match any time signal. A Fourier transform converts a signal from time to frequency domain — it’s a very common way to extract from audio signals or other time series by using a sensor data. ![What’s a Fourier transform?](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAAC6CAMAAACHgTh+AAAB/lBMVEX///+oqKihoaEAAADp6enCwsLw8PC6urra2trS0tL/AAAAAP/MzMzg4ODk5OSlpaXv7///yMj/ZmZubm7/1NT/5+f/NjacnJy2trasrKz/3d2JiYn09PT/cnJkZGShAAD/qqr/Wlr/8PCWlpb/vLz/RUX6+v//9fX/srJISEj/nJzU1P/Bwf//goJ9fX3k5P//kZFISP9wcP9eXl5gYP9YWP+goP8/Pz/y8v8cHBze3v+MjP+BgYFSUlKzs/+np///d2dQUP91df//hXi/v/+UlP//jIT/TEw0NDT/zciyAIQkJCQ2Nv//KSnUAE4dHR2Bgf/XAAD/n5KmAJL/lIRFANtaAND/ZVMAAKH/RTgpKf/Ly//rAAAdHf+crKyurv+4lodra9D/YWG3i4vqPj6Pj74jI6gAALsICMrYfrEcHACynO4AAFQJL4XqAD16iLzrAELXAEWqa9M3KVq0oKCPnbgAAGbUn9C9kduHdPKDW+fJcrf/SzDmfn7JAHjBAAC+bW1Ga+ezVlaWgbCYAKP/wrGkc3N4Ec7Vl8nvkabfUISGNtE4OCCQoufTnJy+TEycKVadGBiQAIDgjoueg4OLhKN3Hx+mRUV7OcTu1OesPLP1tcFycrHLQjqdaHrgjbTXYWHWteKWALAtAADEAGG1AJLFTaKXACXMaK2EbGXYvBn1AAAUUklEQVR4nO2di2Pbxn3HjzwQJA98SKT4BmlKlKgHJUoUJVkPU4oUqVIj0ZbdpolFiWpst1mTxoszd1lXN3U3z0vjxllXr2m6acmyrdv+y90dABIHkhBfgEWZ38QiAIIH4IPf3f3uDfwRS1+KIn4QAX1VFQGWl30LF0qWPg9GfR6s+jxY9XmwasyjQP64JicdJt7Ny1cjHmICko+sSzT1dl66GvHwiJQH9MNXC0jj+EJ52AE/ST5t3kg+4r3kssRc5/HIyjywvF19DxdSnnN4ZPnw5KRL3readVcvT249HhwAPP7LK/uvOg+t+jxY9Xmw6vNg1efBqs+DVZ8Hqz4PVi3xEN2uhP/Gnj/hdXvauLGXJMN4WOFeIuXGsiUS0N8zRIzh4c7DPVd1l/NDv73FG3tJMoRHHmY1VQScF0K+/skXS63yGFe2B9KNznJM1q0wSUCuYcDVwMYbntN9jSgb6YHKsRZ5DO1KWwOLgrBRn0gKxurXH/lhov4XOznhaFvanJhp8la6oHEkbxyeCLlZebtFHjNIeoHzCwPTByf1gGShs9HPPYW6hrMhZGZPBSms3bkmb6UbQqP0IyMMzB4KMpAWefjQENmYpj8/WKs5A6ecelnJ5EodIMI0/nO0RDbHg6j2e6M0hYL0M0ceY0uQDrbK4w59gcIp+ZsRljUncDDROJEgmoQ27aGlI/K3RA0kOmYij7nRYgCQp6B7wjz9aI3HCEqSCF6SYeZ22O9F6Mdp00CDpBZ/MQC8UJvxCiX6cUAMZCgebPJWuqC5wTtR/LEoPcSAFGNa5DEcIC9w631pX2sg2QJYFo42T06ma3+7vChsbuKoEdGkIYtH0mfpTUzRN1Ucqf2pQYoPzsTxfb0pP8M8NRBdHpJLZaskkF6cvRAef0ZT0oFNxkCy0L0gLODs61SoAZIRFvF114X52TwDZFs2tWTxAf7eF/BNtfNobQlFhzCPgftFaXeZGogejxCtX49N7in9Q8ozc4TH6odzCL/GALpdEjIADNLvRnF+6s7lpBO3hSU2qA35QPpQWC3EKj8BaWH7dZpEowmEz/BFR03kAYZw5H+/iJJ4Zxh9fwsbSHSoMQ+nXWqPqrY3lGeGMFXw1TG4g0OKx4dvLeWGEE2mkwj9QTw9QWiGBv7ngxwYnCni5x6Jjw2BU+F/EUE4hB79cdMDj9EYPmsOodfXDwLIh32aoSLY/RSAYsBcHvjO//Ta0Bi5sQD6SliOo+fO89pfIOBoO67d6k3cuVu+9035j8fWp6j8EL14iv796MMza/Fe+ZfoD7+68y8n6N4LFL+7i75EvpOv0dkZ+v2L4+AZ8h18gr68h+4+R2dfoG9/vVv8z+JZ+Sl6+gI9ewedRdDT8tlZ+Ys3yg+PU4+/8VrNURmVU8j6s0++iKHn5eA35Xto4Rl6EWuCB1+Q94l9TCTBZzjaocEZHwAzvlvBZRBFPjQKH16nxhHdHZ4bB4H4W9e/xu7m7jA+N3N9dxfnbDPDw/jlD6Lihzx8iuII59yfBeOIGArAcSaA0tExMJrspgnoCl85CJZQAMzgVBEbL5pCn53bHuUChZQ/Ju8THsli+r9whJ9AOCD82K89w0lqIDCSSGSErwLqH68LG9LGhsD4bYH/EKZtMBoIkDzu9TjJT4I0/qD1uRkcbncfWkf4SsWJb2+TrSK5/kT8N0JaN39J4SyFB7GQsk94AJQhJMC4XPIqCauAlGgHtEkodmJz+Kv0muxgVLUulLJ+QHBsSQeksOJJNEjv0iThK00kqc8+rjzMwgnfiv/hDRIeyMccXMOZa+q9AWGx5nScmWARKBqtC5/DLMYxzxwdRUVgIo8oopGXPSh8rpd+aBUipbmJB5oH3BAO350nfkfzWhcW3t1SrKOi+yRvMY0H9bTv/6vmqG76oVWIetOC1h2f/bcPVjOt3cxqpvRTbTQC1DUzj0cS/9nZ0BxtyV+nPE6PtIcdjYv4OirEtEcO1oHZPATte2ydx8669vCNa+3cTy3FJVIpZDIP7dHW40tuW3N0ZbLeuU2Etqc5sEHuDkXbC61lER6zWh4ue0vpKeGhrfSI7Ld5Q+K+FiS5u/hEm8G1KsJjW5sL7Kda58Ee42sqNJqX9qfEU5kyk8e0pgInAh2txpdpDY9Eov1bkgqMVa1tmMyDra8AInS1nH6csm4op9OKcL728szuds5kHkes6zB5tcX6McKDzbET/o5uCjJdn5dfLg9S39MSjy8xj0XGPsIdtrrFCuq9AWHAPB67SZy9qHng2NIijytJTfbCwXBnN8VDt3oXl3WmzKoQwmWPDFPmCl0FrfIY1GQv2XyjU5tVjElS51dxEavTIJsUvk6GKUER82iRxyg2adW+qNv41JygOgFaODXPQcXXWVLzkNzDVnlMb6r2/R3ktYp4NdP1BVN5bKpdban40DIPVV2XJvK3KTXUVXN5LFbb9UFBKj20yqOk4tEN82CprubM5DGgNGKDqmvYKo/FKg9bV8yDwUoyXPN4zFbjvqhklDo8xBUatcOwUjDHPA4q2S0PuzT8g1e5uDlTeVSzW69S1tbhUbDRAVL5anqH89uDigfDulKd6NpKZTO3bCKPrWr9baXbgU75BYMgPGB2j9qHx+G5MsEdOR2SnDDsdnRJ0CoH5T7YcKOuBasrN+LmS8p2akU5rFP/IfPwyO2VbqfjSrIkOCU5CnmHs1uyQbu8dbrlQN0LV08O5DyZVnZgWLlouDEPOb7sV9tvrwyuKh6MCLs5CNWvOGWlQxPjS6UiOFut0tKJLzzEz1zwuKs9JW8OnipRrnupB70LJUnF2Tka7GbIDRVA4EB7ddBifovGF2SPztWlvFaRUm1QOgJz5vAYvVNSeEBVTX9rPMCC7MHsh/TPbFWc7LWnBTBjEo9bO3LNRURdpGyNR1r26GJXu3pvoJqCnJjIQ+7ExNTitsZjWer/w3c1MaVS6h1NtI8lKe5HVtSHW+Qhebi2rpsHNhDJQzzZ+I5ZPORObgWmkp/h4cjDkF46idak7GXfiIFBktlum8iDfrrZGk+Gxwp2OPQa29Aabe60QZ1z2paUrK2bzQOyja0Mj0QKZvXaYtEabZPfM2bcGDWQ9YPvm8ojtsIeZtOPVEr3URFtDk8ZNP9FhGYxglk8/pvw4LQ5g4qHmLJavF691kdEs5fuZy6SJDfRNB7fI/0UapqP1DzCWb89r+doUR6xNpvzzxetGDp547tGhc9I4lHTfMTElxs8cOump4SHUeZB3JowAKdm8rDU5AwMDxe8qtvVBx0YaR4AhG8AsGQaj1NVNVBFrflj20a4piphAymZxqNu1xWGx1UIoV6dOZoGNgPNQzKQN24ZeYWKCI86XVe09uFK6YRxPA32jZ1DaCUMfnDb0CsoKj4BoTo9mxgebodD9/1/W0oZ4ppWFUmAE3N4PBJ46Ko9zPCI+f1+veThSdrQ1AMQH4T/+Zixl5BV3PHX67rC8LDJ/xrpScjQ1IPI718yicdp3Z5NKh4chOekp0+MNg9yE2/vGn0Nqttvv1fvMGMfYV4Uq2UTN6TZswtW6kqfdLUSub7sPzaLR92YoLaPWKyQV/WiLjil9ijgVGLJ/5gx0eX/mcNj7K/qHla1N4g2F1b1kZX2OXm8mMtuu2KzG6+HQTOuYiv6617GWm2P4mOxVCpVnWs7zzE8RF4MibzxCtwsG38Z8WfHdS8iOhl/zBtSTT2ejzgoD0dY6SVmyvxB49c/MP4inr/+sP4XTHrqz9oSqraZyRUe+Dmx2l+f8vB00gG3CY1c/2mHnRabUOKD++TDU9NblK0v5IFDr76Q8LCFrnW3aU6rket/abATTNy+ecLDZQvr1n8U4B7c16k8t0r/jCrC4OQMe9AjD2Y7GCLQnPLXto4BnbwzRa6qesG15X2dylGZh0HJiMNuIZVzIw8O7R11im9CUPzoEd2wApvXoS7CMjyuneOfGssDl+bIjYwc/7zTXvHnyXpj+Qevkw2HE0caTm3vDI/JcyrOCYiw29XOaLlmlBVTJOjbH2Gv3aBLULmha4DycFk4G/CDmMrNZNvnVgq1o/xUooZhGA7gBG7yQl77CBu0kUuOYOuTeDicLl50A/UDse1zHM/pjVcwZ/7C195cBvaV889rVx7IgzUpvtSKTT/yEa9eed88HqSizCiRxGnr42Z42CPhiN59mMgjbJiBuEnz4tbHDSY6Y/Nb3u7P6gRlIg9wwygDyZMnPGyGh72Q0B/AYRYPMiSt05FXDUV8m7TQBA8PDAH9fM4kHn9zSD4M8kEspN9N+mAiXv9rtX1wKajvKZvDw/cxHTPgMcRJ9dA6v3TurQbD9DT+ujulNwLMLB5SR0hDDISmHoRHoP73F3D+ZN+Q1HPHCCdVng1uvad4BE6kDQOcVDk9WFvvLR50usia4eydyyF7NWul4R7iEV2Xew7vdzsFycu1XTs9xkOeZoDrcsWQW+n5JmTa4XGN1oW4Egml/sgcHjO+jDLIN9LdGKOYBxDAbus8srEw8V1iYY9SLWIOj6ivOgi8qwYSrng0AmjDPgqcMl5MOWLO+lGEhzIwNtxFA+GrvaME0Gie1UbjgbwpTm6fswBPZT5HU+ZavHuvvPCOfKUIzHbrmhHol4PyviP8MGipf1aj+RzDEb7gpjxiZq8vhu1jqTKHVfcMhKsWEDfWR4YbnKUzXsy2sm8FMT6UyCt2Zlr6UeWBo2uXglV1f9k4DTTioZe/eBxkkULgqNQBmMcjV72Jer2a2pBHVX9w2B6PGpnGI62aVaNmmrL2pO4dJWR6jId61hWxttNsG7Krq5cE0MM8gLfdCd9UEtX106s9yEM9+WUXDMSv7um1Pd9zPNbUPKwd17Uzk9CApZ2e43HITI4K9TpNNyN25paj6d7igUbAWk59xNFhVSrHmAeZEmqih3iA3RGwzPBQBqO2K9Y8MjmdWTQvIo+xETDA8gAdOWVOtlUpc4h5DDU496LyUE11RBTqYAS0U5P8bG31Hg+wwE7iLXaQpF7V/HRztvd54Jfcbmg27fDYnuRxqJ3Jd7LdGKNttZgllU09x2N2Xnv0RnuDCa5qh6jMEtI9x2O1Zq0u0NbcorU10tNk1rGe40FmItPoRz+umfn9PGXW3/6R9tg8adzpOR6BY83idqubwrsnwmbdH6TT9Vc0ywnv/oWgjXg/eQv0GA/fDFksj115Y0A4TNveW66ziggYmBcOhK0acwKZg6PUb8kP2cPF4jgAqC0eUr9MZ6U7s0k8vksWp/qarswSVe57gaSCCThQsygI2BLmZ3EiWbPKzKywRJdEmFXWaBgZIlP/B4K4ODDecJIzPR5SWhTa21cahUziMTiDbzjwpyRZcpPORjYY/5pkklGQeC8trLMtSZuyJ7uhiRjRhXkAY4TAjvCbGZIizRQJhbnP7syB8YbL/unwcEaU9bTMbW+gPMbAT/DdT+0mcbQZQbeOcVLqQygKU79AiHR1mkPkGSfQ/WdkZxcXz9LPimQVqBFEFscL+NCD9DXooydvoLdoKIFgEhcWPyWrrDXk0ai9gY4rrFlfzJy1vx6flR8Wy++gcrn4uIwel+M3P39wu/wcpb5ATyH6pxPkC82g391ED+Pon7+Hfh8aO/4d2rUG0ZNPUPIhuvkU/fIh+uRN9Cv4GIVeoOeW4+u/pqGU/y5YLqO/vzvmxcE3uHaj9qirK7ba9cXMs485H1g+HiVLGiXHBlFAeB+NkdeeRMc3+dOT4m2ycFM8WPxbYXU0GNzFEWssOAwywi8eBbE9DAYfvSGs/xDdQRPEkIrDJSGJcCjYRMDU/bS0sFgDnbe+mANctcSUJiGz0g8fnYTsya1hspjq8PA/5DZxwkobXIei16CYUzKZhRO2FHyqrGRWErYdcIimn2AIozvYkcOaQv9IVv1rzEM3f8EcUhyoLLdmFo8Aojw+pUsagsqKrMpNQe5ISjs3axYknpXy4wVhm2MKxEoIg+g+9sbic9H2eGhlEg9wDMYGlYVxAXm7zLdZiJ0KojrrMy/LX3CQHaehBEFXJxmdmmu4LPWF5IGGqGXIvR5K2kV84LndqNwaHNhAJCfkkDjrg2iq4ZxNF5LH3Bx1Thclz/JAu9AfDyf1hzQ6tDiIE0KMaZYuHgjQ3Gijn15IHqPoDvlYpS+1VLO+GxCzuv3s6+CQqa5LKfFu4zlnLySPCXnl850D4o5rzYPomk4LRE1koaJLoB+dyuE3/vFF5KEsMpYmieNs3TOy0F9//AMP6+LASUc1BY72Go8m5MnXHRDCnZ/Y6qpneQDghzX37fF2iKOXeQDbHkyo01V3HiY67QrQyzxwYuGH+34yyt1lD+/vw2znE2/2Ng8sTyoVgxCqJy7pRD3Po8vq82DV58Gqz4NVnwerPg9WfR6s+jxY6fEQab9Pe3V9sVebB5+n7Q3+al3Uq82Dk9tf/CuUCM/xMZ677HI14OHPO+X2KKc8Pspps7lsl19ifR5uhyjzmKyOF3s1pNs+l+ec8Ebnq9z2kprPb18N9Xmw6vNg1efBqs+DVZ8Hqz4PVn0erPo8WF0GHp4Q0/xCC6AW+ukIWd3WkNsbcoatdgAiVqsNF9Q5wJHCutvqD9esOXAZeISA6OZSwGnnHMDJ40Kqy8V7vaBAmrw9MQ7EbMBrkec6xv9jehFpITUvLq96ncBuwz/jPPTYZeBBXnYIWEOilbNZPJGwGLE7ssBCjcZu94CUDVgoD284jK3E67Q5vfIPrTa3w2NzAKvHmeIJkMvBw+2xAq+VQMHPh3m4HF4QIc9sBy4PtQ8v/lL+38rHRKv8Q6votAJMx8s5Y05SE3gZeICQCzhSojfsxk/IeZzAFnHgSBPmgCNm5SIh0R7iXCEym3Yo5HYDG/mPJhxky+sCETuwpTyOEGkQvxQ8JIXIjJR0y2pte0j3JeLRFfV5sOrzYGUBRk7+3nuKAH/E0peiiP//Aeu3U40ubRrOAAAAAElFTkSuQmCC)\ 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