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-2.1755705|\n|1970-01-01T08:00:03.000+08:00| -1.9021131|\n|1970-01-01T08:00:04.000+08:00| 1.0|\n|1970-01-01T08:00:05.000+08:00| 1.9021131|\n|1970-01-01T08:00:06.000+08:00| 0.1755705|\n|1970-01-01T08:00:07.000+08:00| -1.1755705|\n|1970-01-01T08:00:08.000+08:00| -0.902113|\n|1970-01-01T08:00:09.000+08:00| 0.0|\n|1970-01-01T08:00:10.000+08:00| 0.902113|\n|1970-01-01T08:00:11.000+08:00| 1.1755705|\n|1970-01-01T08:00:12.000+08:00| -0.1755705|\n|1970-01-01T08:00:13.000+08:00| -1.9021131|\n|1970-01-01T08:00:14.000+08:00| -1.0|\n|1970-01-01T08:00:15.000+08:00| 1.9021131|\n|1970-01-01T08:00:16.000+08:00| 2.1755705|\n|1970-01-01T08:00:17.000+08:00| -1.1755705|\n|1970-01-01T08:00:18.000+08:00| -2.902113|\n|1970-01-01T08:00:19.000+08:00| 0.0|\n+-----------------------------+---------------+\n")])]),s._v(" 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fft(root.test.d1.s1)|\n+-----------------------------+----------------------+\n|1970-01-01T08:00:00.000+08:00| 0.0|\n|1970-01-01T08:00:00.001+08:00| 1.2727111142703152E-8|\n|1970-01-01T08:00:00.002+08:00| 2.385520799101839E-7|\n|1970-01-01T08:00:00.003+08:00| 8.723291723972645E-8|\n|1970-01-01T08:00:00.004+08:00| 19.999999960195904|\n|1970-01-01T08:00:00.005+08:00| 9.999999850988388|\n|1970-01-01T08:00:00.006+08:00| 3.2260694930700566E-7|\n|1970-01-01T08:00:00.007+08:00| 8.723291605373329E-8|\n|1970-01-01T08:00:00.008+08:00| 1.108657103979944E-7|\n|1970-01-01T08:00:00.009+08:00| 1.2727110997246171E-8|\n|1970-01-01T08:00:00.010+08:00|1.9852334701272664E-23|\n|1970-01-01T08:00:00.011+08:00| 1.2727111194499847E-8|\n|1970-01-01T08:00:00.012+08:00| 1.108657103979944E-7|\n|1970-01-01T08:00:00.013+08:00| 8.723291785769131E-8|\n|1970-01-01T08:00:00.014+08:00| 3.226069493070057E-7|\n|1970-01-01T08:00:00.015+08:00| 9.999999850988388|\n|1970-01-01T08:00:00.016+08:00| 19.999999960195904|\n|1970-01-01T08:00:00.017+08:00| 8.723291747109068E-8|\n|1970-01-01T08:00:00.018+08:00| 2.3855207991018386E-7|\n|1970-01-01T08:00:00.019+08:00| 1.2727112069910878E-8|\n+-----------------------------+----------------------+\n")])]),s._v(" 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The input is $y=sin(2\\pi t/4)+2sin(2\\pi t/5)$ with a length of 20. Thus, there are peaks in $k=4$ and $k=5$ of the output.")]),s._v(" "),t("h4",{attrs:{id:"uniform-fft-with-compression"}},[t("a",{staticClass:"header-anchor",attrs:{href:"#uniform-fft-with-compression"}},[s._v("#")]),s._v(" Uniform FFT with Compression")]),s._v(" "),t("p",[s._v("Input series is the same as above, the SQL for query is shown below:")]),s._v(" "),t("div",{staticClass:"language-sql line-numbers-mode"},[t("pre",{pre:!0,attrs:{class:"language-sql"}},[t("code",[t("span",{pre:!0,attrs:{class:"token keyword"}},[s._v("select")]),s._v(" fft"),t("span",{pre:!0,attrs:{class:"token punctuation"}},[s._v("(")]),s._v("s1"),t("span",{pre:!0,attrs:{class:"token punctuation"}},[s._v(",")]),s._v(" "),t("span",{pre:!0,attrs:{class:"token string"}},[s._v("'result'")]),t("span",{pre:!0,attrs:{class:"token operator"}},[s._v("=")]),t("span",{pre:!0,attrs:{class:"token string"}},[s._v("'real'")]),t("span",{pre:!0,attrs:{class:"token punctuation"}},[s._v(",")]),s._v(" 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1.2104201863039066E-8|\n|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|\n|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 5.127422242345858E-8|\n|1970-01-01T08:00:00.004+08:00| 19.021130288047125| -6.180339875198807|\n|1970-01-01T08:00:00.005+08:00| 9.999999850988388| 3.501852745067114E-16|\n|1970-01-01T08:00:00.019+08:00| -3.932894898639461E-9|-1.2104202549376264E-8|\n+-----------------------------+----------------------+----------------------+\n')])]),s._v(" "),t("div",{staticClass:"line-numbers-wrapper"},[t("span",{staticClass:"line-number"},[s._v("1")]),t("br"),t("span",{staticClass:"line-number"},[s._v("2")]),t("br"),t("span",{staticClass:"line-number"},[s._v("3")]),t("br"),t("span",{staticClass:"line-number"},[s._v("4")]),t("br"),t("span",{staticClass:"line-number"},[s._v("5")]),t("br"),t("span",{staticClass:"line-number"},[s._v("6")]),t("br"),t("span",{staticClass:"line-number"},[s._v("7")]),t("br"),t("span",{staticClass:"line-number"},[s._v("8")]),t("br"),t("span",{staticClass:"line-number"},[s._v("9")]),t("br"),t("span",{staticClass:"line-number"},[s._v("10")]),t("br"),t("span",{staticClass:"line-number"},[s._v("11")]),t("br"),t("span",{staticClass:"line-number"},[s._v("12")]),t("br"),t("span",{staticClass:"line-number"},[s._v("13")]),t("br")])]),t("p",[s._v("Note: Based on the conjugation of the Fourier transform result, only the first half of the compression result is reserved.\nAccording to the given parameter, data points are 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-1.1755705|\n|1970-01-01T08:00:08.000+08:00| -0.902113|\n|1970-01-01T08:00:09.000+08:00| 0.0|\n|1970-01-01T08:00:10.000+08:00| 0.902113|\n|1970-01-01T08:00:11.000+08:00| 1.1755705|\n|1970-01-01T08:00:12.000+08:00| -0.1755705|\n|1970-01-01T08:00:13.000+08:00| -1.9021131|\n|1970-01-01T08:00:14.000+08:00| -1.0|\n|1970-01-01T08:00:15.000+08:00| 1.9021131|\n|1970-01-01T08:00:16.000+08:00| 2.1755705|\n|1970-01-01T08:00:17.000+08:00| -1.1755705|\n|1970-01-01T08:00:18.000+08:00| -2.902113|\n|1970-01-01T08:00:19.000+08:00| 0.0|\n+-----------------------------+---------------+\n")])]),s._v(" 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-3.097210911744423E-17|\n|1970-01-01T08:00:10.000+08:00| -1.0000000018134794|\n|1970-01-01T08:00:11.000+08:00| -6.260191627862097E-10|\n|1970-01-01T08:00:12.000+08:00| 1.0000000183304454|\n|1970-01-01T08:00:13.000+08:00| -3.328126501424346E-8|\n|1970-01-01T08:00:14.000+08:00| -0.9999999925494196|\n|1970-01-01T08:00:15.000+08:00| 4.111526915498874E-8|\n|1970-01-01T08:00:16.000+08:00| 0.9999999593178128|\n|1970-01-01T08:00:17.000+08:00| -1.7462829341296528E-8|\n|1970-01-01T08:00:18.000+08:00| -0.9999999534830369|\n|1970-01-01T08:00:19.000+08:00| -1.035237222742873E-16|\n+-----------------------------+-----------------------------------------+\n')])]),s._v(" 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The input is $y=sin(2\\pi t/4)+2sin(2\\pi t/5)$ with a length of 20. Thus, the output is $y=sin(2\\pi t/4)$ after high-pass filtering.")]),s._v(" "),t("h2",{attrs:{id:"ifft"}},[t("a",{staticClass:"header-anchor",attrs:{href:"#ifft"}},[s._v("#")]),s._v(" IFFT")]),s._v(" "),t("h3",{attrs:{id:"usage-6"}},[t("a",{staticClass:"header-anchor",attrs:{href:"#usage-6"}},[s._v("#")]),s._v(" Usage")]),s._v(" "),t("p",[s._v("This function treats the two input series as the real and imaginary part of a complex series, performs an inverse fast Fourier transform (IFFT), and outputs the real part of the result.\nFor the input format, please refer to the output format of "),t("code",[s._v("FFT")]),s._v(" function.\nMoreover, the compressed output of "),t("code",[s._v("FFT")]),s._v(" function is also supported.")]),s._v(" "),t("p",[t("strong",[s._v("Name:")]),s._v(" IFFT")]),s._v(" "),t("p",[t("strong",[s._v("Input:")]),s._v(" Only support two input series. 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The values are the results of IFFT.")]),s._v(" "),t("p",[t("strong",[s._v("Note:")]),s._v(" If a row contains null points or "),t("code",[s._v("NaN")]),s._v(", it will be ignored.")]),s._v(" "),t("h3",{attrs:{id:"examples-6"}},[t("a",{staticClass:"header-anchor",attrs:{href:"#examples-6"}},[s._v("#")]),s._v(" Examples")]),s._v(" "),t("p",[s._v("Input series:")]),s._v(" "),t("div",{staticClass:"language- line-numbers-mode"},[t("pre",{pre:!0,attrs:{class:"language-text"}},[t("code",[s._v("+-----------------------------+----------------------+----------------------+\n| Time| root.test.d1.re| root.test.d1.im|\n+-----------------------------+----------------------+----------------------+\n|1970-01-01T08:00:00.000+08:00| 0.0| 0.0|\n|1970-01-01T08:00:00.001+08:00| -3.932894010461041E-9| 1.2104201863039066E-8|\n|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|\n|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 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-1.1755704886020932|\n|2021-01-01T00:08:00.000+08:00| -0.9021130371347148|\n|2021-01-01T00:09:00.000+08:00| 3.552713678800501E-16|\n|2021-01-01T00:10:00.000+08:00| 0.9021130371347154|\n|2021-01-01T00:11:00.000+08:00| 1.1755704886020932|\n|2021-01-01T00:12:00.000+08:00| -0.17557053610884144|\n|2021-01-01T00:13:00.000+08:00| -1.902113046743454|\n|2021-01-01T00:14:00.000+08:00| -0.9999999925494196|\n|2021-01-01T00:15:00.000+08:00| 1.9021130389094498|\n|2021-01-01T00:16:00.000+08:00| 2.1755705137571004|\n|2021-01-01T00:17:00.000+08:00| -1.1755704705132448|\n|2021-01-01T00:18:00.000+08:00| -2.902112992431231|\n|2021-01-01T00:19:00.000+08:00| -3.552713678800501E-16|\n+-----------------------------+-------------------------------------------------------+\n')])]),s._v(" 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-1.1755705|\n|1970-01-01T08:00:08.000+08:00| -0.902113|\n|1970-01-01T08:00:09.000+08:00| 0.0|\n|1970-01-01T08:00:10.000+08:00| 0.902113|\n|1970-01-01T08:00:11.000+08:00| 1.1755705|\n|1970-01-01T08:00:12.000+08:00| -0.1755705|\n|1970-01-01T08:00:13.000+08:00| -1.9021131|\n|1970-01-01T08:00:14.000+08:00| -1.0|\n|1970-01-01T08:00:15.000+08:00| 1.9021131|\n|1970-01-01T08:00:16.000+08:00| 2.1755705|\n|1970-01-01T08:00:17.000+08:00| -1.1755705|\n|1970-01-01T08:00:18.000+08:00| -2.902113|\n|1970-01-01T08:00:19.000+08:00| 0.0|\n+-----------------------------+---------------+\n")])]),s._v(" 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3.552713678800501E-16|\n|1970-01-01T08:00:10.000+08:00| 1.9021130222335536|\n|1970-01-01T08:00:11.000+08:00| 1.1755704886020932|\n|1970-01-01T08:00:12.000+08:00| -1.1755705212076801|\n|1970-01-01T08:00:13.000+08:00| -1.902113046743454|\n|1970-01-01T08:00:14.000+08:00| -7.45058112983088E-9|\n|1970-01-01T08:00:15.000+08:00| 1.9021130389094498|\n|1970-01-01T08:00:16.000+08:00| 1.1755705286582616|\n|1970-01-01T08:00:17.000+08:00| -1.1755704705132448|\n|1970-01-01T08:00:18.000+08:00| -1.9021130073323924|\n|1970-01-01T08:00:19.000+08:00| -2.664535259100376E-16|\n+-----------------------------+----------------------------------------+\n')])]),s._v(" 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The input is $y=sin(2\\pi t/4)+2sin(2\\pi t/5)$ with a length of 20. Thus, the output is $y=2sin(2\\pi t/5)$ after low-pass filtering.")])])}),[],!1,null,null,null);t.default=e.exports}}]); |