[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/328248#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/328248","headline":"\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 &#8211; Wikipedia","name":"\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 &#8211; Wikipedia","description":"before-content-x4 \u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\uff08\u306b\u3058\u3087\u3046\u3078\u3044\u304d\u3093\u3078\u3044\u307b\u3046\u3053\u3093\u3001\u82f1: root mean square, RMS\uff09\u3068\u306f\u3001\u30c7\u30fc\u30bf\u3084\u78ba\u7387\u5909\u6570\u3092\u4e8c\u4e57\u3057\u305f\u5024\u306e\u7b97\u8853\u5e73\u5747\u306e\u5e73\u65b9\u6839\u3067\u3042\u308b\u3002\u7d50\u679c\u3068\u3057\u3066\u5358\u4f4d\u304c\u5143\u306e\u7d71\u8a08\u5024\u30fb\u78ba\u7387\u5909\u6570\u3068\u540c\u3058\u3068\u3044\u3046\u70b9\u304c\u7279\u5fb4\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u7d76\u5bfe\u5024\u306e\u5e73\u5747\u3088\u308a\u3082\u8a08\u7b97\u304c\u7a4d\u548c\u6f14\u7b97\u3067\u3042\u308b\u305f\u3081\u9ad8\u901f\u5316\u304c\u5bb9\u6613\u3067\u3042\u308b\u3053\u3068\u304c\u6319\u3052\u3089\u308c\u308b\u3002 after-content-x4 \u5909\u91cf x \u306e\u30c7\u30fc\u30bf xi (i = 1, 2, \u2026, n) \u306b\u5bfe\u3057\u3066\u3001x \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 RMS(x)","datePublished":"2022-04-19","dateModified":"2022-04-19","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1b0adfb48482e76c707790de2f2f64bf025e39d6","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1b0adfb48482e76c707790de2f2f64bf025e39d6","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/328248","about":["Wiki"],"wordCount":5374,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\uff08\u306b\u3058\u3087\u3046\u3078\u3044\u304d\u3093\u3078\u3044\u307b\u3046\u3053\u3093\u3001\u82f1: root mean square, RMS\uff09\u3068\u306f\u3001\u30c7\u30fc\u30bf\u3084\u78ba\u7387\u5909\u6570\u3092\u4e8c\u4e57\u3057\u305f\u5024\u306e\u7b97\u8853\u5e73\u5747\u306e\u5e73\u65b9\u6839\u3067\u3042\u308b\u3002\u7d50\u679c\u3068\u3057\u3066\u5358\u4f4d\u304c\u5143\u306e\u7d71\u8a08\u5024\u30fb\u78ba\u7387\u5909\u6570\u3068\u540c\u3058\u3068\u3044\u3046\u70b9\u304c\u7279\u5fb4\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u7d76\u5bfe\u5024\u306e\u5e73\u5747\u3088\u308a\u3082\u8a08\u7b97\u304c\u7a4d\u548c\u6f14\u7b97\u3067\u3042\u308b\u305f\u3081\u9ad8\u901f\u5316\u304c\u5bb9\u6613\u3067\u3042\u308b\u3053\u3068\u304c\u6319\u3052\u3089\u308c\u308b\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5909\u91cf x \u306e\u30c7\u30fc\u30bf xi (i = 1, 2, \u2026, n) \u306b\u5bfe\u3057\u3066\u3001x \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 RMS(x) \u306f\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\uff1aRMS\u2061[x]=1n\u2211i=1nxi2{displaystyle operatorname {RMS} [x]={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}{x_{i}}^{2}}}}\u3064\u307e\u308a\u3001xi2 \u306e\u7b97\u8853\u5e73\u5747\u306e\u5e73\u65b9\u6839\u304c x \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 RMS[x] \u3068\u306a\u308b\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4f8b\u3048\u3070\u3001\u30c7\u30fc\u30bf 1, 1, 2, 3, 5 \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002RMS\u2061[x]=15(12+12+22+32+52)=8\u22482.8284271{displaystyle {begin{aligned}operatorname {RMS} [x]&#038;={sqrt {{frac {1}{5}}left(1^{2}+1^{2}+2^{2}+3^{2}+5^{2}right)}}\\&#038;={sqrt {8}}approx 2.8284271end{aligned}}} \/\/\u7d71\u8a08\u5024\u306e\u4e8c\u4e57\u3092\u53d6\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u91cf\u306e\u5927\u304d\u3055\u306e\u5e73\u5747\u5024\u3092\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u304b\u3089\u6982\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u307e\u305f\u3001\u5149\u306e\u5f37\u5ea6\u306f\u96fb\u78c1\u5834\u306e\u4e8c\u4e57\u3068\u3057\u3066\u3057\u3070\u3057\u3070\u5b9a\u7fa9\u3055\u308c\u308b\u305f\u3081\u3001\u305d\u306e\u5e73\u5747\u5f37\u5ea6\u306f\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306e\u5f62\u3092\u53d6\u308b\u3002\u6642\u9593\u7684\u306b\u5909\u5316\u3059\u308b\u4fe1\u53f7\u306e\u5927\u304d\u3055\u3092\u8a55\u4fa1\u3059\u308b\u76ee\u7684\u3067\u3001\u7269\u7406\u5b66\u3084\u96fb\u6c17\u5de5\u5b66\u306a\u3069\u306e\u5206\u91ce\u3067\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u304c\u7528\u3044\u3089\u308c\u308b\u3002\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306f\u3001\u4e00\u822c\u5316\u5e73\u5747\u306b\u304a\u3044\u3066\u6307\u6570\u30d1\u30e9\u30e1\u30fc\u30bf\u3092 2 \u3068\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3068\u3082\u8a00\u3048\u308b\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5927\u304d\u3055 n \u306e\u30c7\u30fc\u30bf x1, x2, \u2026, xn \u306b\u5bfe\u3057\u3066\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306fRMS\u2061[x]=1n\u2211i=1nxi2=x12+x22+\u22ef+xn2n{displaystyle operatorname {RMS} [x]={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}{x_{i}}^{2}}}={sqrt {frac {{x_{1}}^{2}+{x_{2}}^{2}+cdots +{x_{n}}^{2}}{n}}}}\u3068\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u5145\u5206\u5c0f\u3055\u306a \u0394x\u2032 \u306b\u5bfe\u3057\u3066 x \u2208 [x&#8217;, x + \u0394x\u2032] \u3068\u306a\u308b\u78ba\u7387\u3092 f(x)\u0394x\u2032 \u3068\u3057\u305f\u3068\u304d\u3001x \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 RMS[x] \u306fRMS\u2061[x]=\u222b\u2212\u221e\u221ex\u20322f(x\u2032)dx\u2032{displaystyle operatorname {RMS} [x]={sqrt {int _{-infty }^{infty }x&#8217;^{2}f(x&#8217;)dx&#8217;}}}\u3068\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3053\u3053\u3067\u95a2\u6570 f(x&#8217;) \u306f\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u547c\u3070\u308c\u308b\u3002\u9023\u7d9a\u95a2\u6570 x(t) \u306e\u533a\u9593 t \u2208 [t1, t2]  (t1 < t2) \u306b\u3064\u3044\u3066\u306f\u5a92\u4ecb\u5909\u6570\u306e\u7a4d\u5206\u3092\u7528\u3044\u3066\u3001RMS\u2061[x(t)]=1t2\u2212t1\u222bt1t2(x(t))2dt{displaystyle operatorname {RMS} [x(t)]={sqrt {{frac {1}{t_{2}-t_{1}}}int _{t_{1}}^{t_{2}}(x(t))^{2},dt}}}\u3068\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u5468\u671f\u95a2\u6570\u306b\u3064\u3044\u3066\u306f\u901a\u5e38\u3001\u7a4d\u5206\u533a\u9593\u3092\u5468\u671f\u306e\u6574\u6570\u500d\u306b\u4e00\u81f4\u3055\u305b\u3066\u6c42\u3081\u308b\u3002\u305f\u3068\u3048\u3070 x(t) = sin(\u03c9t) \u306b\u3064\u3044\u3066\u306f\u3001\u5468\u671f\u3092 \u03c4 = 2\u03c0\/\u03c9 \u3067\u8868\u3057\u3001RMS\u2061[sin\u2061\u03c9t]=1\u03c4\u222b0\u03c4sin2\u2061\u03c9tdt=1\u03c4\u222b0\u03c41\u2212cos\u20612\u03c9t2dt=12{displaystyle operatorname {RMS} [sin omega t]={sqrt {{frac {1}{tau }}int _{0}^{tau }sin ^{2}omega t,dt}}={sqrt {{frac {1}{tau }}int _{0}^{tau }{frac {1-cos 2omega t}{2}},dt}}={frac {1}{sqrt {2}}}}\u306e\u3088\u3046\u306b\u3059\u308b\u3002\u540c\u69d8\u306b\u4e09\u89d2\u95a2\u6570\u306e\u548c\u306b\u3064\u3044\u3066\u3001\u9069\u5f53\u306a\u5468\u671f\u3092 \u03c4 \u3068\u3057\u3066\u3001RMS\u2061[\u2211ncnsin\u2061\u03c9nt]=1\u03c4\u222b0\u03c4(\u2211ncnsin\u2061\u03c9nt)2dt=1\u03c4\u2211m,n\u222b0\u03c4cmcnsin\u2061(\u03c9mt)sin\u2061(\u03c9nt)dt=1\u03c4\u2211m,n\u222b0\u03c4cmcncos\u2061(\u03c9mt\u2212\u03c9nt)\u2212cos\u2061(\u03c9mt+\u03c9nt)2dt=12\u2211n(cn)2{displaystyle {begin{aligned}operatorname {RMS} left[sum _{n}c_{n}sin omega _{n}tright]&#038;={sqrt {{frac {1}{tau }}int _{0}^{tau }left(sum _{n}c_{n}sin omega _{n}tright)^{2},dt}}\\&#038;={sqrt {{frac {1}{tau }}sum _{m,n}int _{0}^{tau }c_{m}c_{n}sin(omega _{m}t)sin(omega _{n}t),dt}}\\&#038;={sqrt {{frac {1}{tau }}sum _{m,n}int _{0}^{tau }c_{m}c_{n}{frac {cos(omega _{m}t-omega _{n}t)-cos(omega _{m}t+omega _{n}t)}{2}},dt}}\\&#038;={sqrt {{frac {1}{2}}sum _{n}(c_{n})^{2}}}end{aligned}}}\u3068\u306a\u308b\u3002\u975e\u5bfe\u89d2\u6210\u5206\u306f\u7a4d\u5206\u3059\u308b\u3068 0 \u306b\u306a\u308b\uff08\u76f4\u4ea4\uff09\u306e\u3067\u3001\u5bfe\u89d2\u6210\u5206\u306e\u7a4d\u5206\u3060\u3051\u304c\u6b8b\u308b\u3002\u5e73\u5747\u5024\u304a\u3088\u3073\u6a19\u6e96\u504f\u5dee\u3068\u306e\u95a2\u4fc2[\u7de8\u96c6]\u5909\u91cf x \u306b\u5bfe\u3057\u3066\u671f\u5f85\u5024 \u27e8x\u27e9 \u304c\u5b9a\u307e\u308b\u306a\u3089\u3001\u305d\u306e\u91cf\u306e\u671f\u5f85\u5024\u304b\u3089\u306e\u504f\u5dee x \u2212 \u27e8x\u27e9 \u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839 RMS[x \u2212 \u27e8x\u27e9] \u3092\u4e0e\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u504f\u5dee\u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306f x \u306e\u6a19\u6e96\u504f\u5dee \u03c3x \u306b\u7b49\u3057\u3044\u3002\u03c3x=1n\u2211i=1n(xi\u2212\u27e8x\u27e9)2=RMS\u2061[x\u2212\u27e8x\u27e9]{displaystyle sigma _{x}={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}left(x_{i}-langle xrangle right)^{2}}}=operatorname {RMS} [x-langle xrangle ]}\u307e\u305f\u3001\u4e8c\u4e57\u504f\u5dee (x \u2212 \u27e8x\u27e9)2 \u3092\u5c55\u958b\u3059\u308c\u3070\u3001\u504f\u5dee\u306e\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u305b\u308b\u3002RMS\u2061[x\u2212\u27e8x\u27e9]=1n\u2211i=1n(xi\u2212\u27e8x\u27e9)2=1n\u2211i=1nxi2\u22122\u27e8x\u27e91n\u2211i=1nxi+\u27e8x\u27e92=(RMS\u2061[x])2\u2212\u27e8x\u27e92{displaystyle {begin{aligned}operatorname {RMS} [x-langle xrangle ]&#038;={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}left(x_{i}-langle xrangle right)^{2}}}\\&#038;={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}{x_{i}}^{2}-2langle xrangle {dfrac {1}{n}}sum limits _{i=1}^{n}x_{i}+langle xrangle ^{2}}}\\&#038;={sqrt {left(operatorname {RMS} [x]right)^{2}-langle xrangle ^{2}}}end{aligned}}}\u305f\u3060\u3057\u6700\u5f8c\u306b\u671f\u5f85\u5024 \u27e8x\u27e9 \u304c xi \u306e\u5e73\u5747\u5024 x \u306b\u7b49\u3057\u3044\u3053\u3068\u3092\u4f7f\u3063\u305f\u3002\u27e8x\u27e9=x\u00af=1n\u2211i=1nxi{displaystyle langle xrangle ={bar {x}}={frac {1}{n}}textstyle sum limits _{i=1}^{n}x_{i}}\u3053\u306e\u3068\u304d\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002(RMS\u2061[x])2=\u03c3x2+\u27e8x\u27e92{displaystyle left(operatorname {RMS} [x]right)^{2}={sigma _{x}}^{2}+langle xrangle ^{2}}\u671f\u5f85\u5024 \u27e8x\u27e9 \u304c xi \u306e\u7b97\u8853\u5e73\u5747 x \u306b\u7b49\u3057\u3044\u3053\u3068\u306f\u4e00\u822c\u306b\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u3002\u305f\u3068\u3048\u3070 xi \u3092 x \u306e\u5404\u56de\u306e\u6e2c\u5b9a\u5024\u3060\u3068\u3059\u308c\u3070\u3001\u305d\u306e\u6a19\u672c\u5e73\u5747 x \u306f\u671f\u5f85\u5024 \u27e8x\u27e9 \u304b\u3089\u3042\u308b\u7cbe\u5ea6\u3067\u5916\u308c\u305f\u5024\u306b\u306a\u308b\u3002\u5b9f\u9a13\u3067\u306f\u771f\u306e\u5024\u306f\u5206\u304b\u3089\u306a\u3044\u306e\u3067\u3001\u671f\u5f85\u5024 \u27e8x\u27e9 \u306e\u4ee3\u308f\u308a\u306b\u6e2c\u5b9a\u5024\u306e\u6a19\u672c\u5e73\u5747 x \u304c\u7528\u3044\u3089\u308c\u3001\u6a19\u6e96\u504f\u5dee\u306f\u6e2c\u5b9a\u5024\u306e\u5e73\u5747\u5024\u304b\u3089\u306e\u4e0d\u504f\u5206\u6563\u306e\u5e73\u65b9\u6839\u306b\u3088\u3063\u3066\u63a8\u5b9a\u3055\u308c\u308b\u3002\u4e0d\u504f\u3067\u306a\u3044\u5358\u7d14\u306a\u6a19\u672c\u6a19\u6e96\u504f\u5dee\u306f\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u304c\u3001\u4e0d\u504f\u6a19\u672c\u6a19\u6e96\u504f\u5dee ux \u306f\u305d\u308c\u3068\u306f\u7570\u306a\u308b\u3002RMS\u2061[x\u2212x\u00af]=1n\u2211i=1n(x\u2212x\u00af)2\u22601n\u22121\u2211i=1n(x\u2212x\u00af)2=ux{displaystyle operatorname {RMS} [x-{bar {x}}]={sqrt {{frac {1}{n}}textstyle sum limits _{i=1}^{n}(x-{bar {x}})^{2}}}neq {sqrt {{frac {1}{n-1}}textstyle sum limits _{i=1}^{n}(x-{bar {x}})^{2}}}=u_{x}}\u5358\u7d14\u306a\u6a19\u672c\u6a19\u6e96\u504f\u5dee\u3067\u306f\u5206\u6563\u306e\u91cd\u5fc3\u304c\u671f\u5f85\u5024\u3067\u306f\u306a\u304f\u6a19\u672c\u5e73\u5747\u306b\u306a\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u771f\u306e\u5024\u304b\u3089\u306e\u8aa4\u5dee\u3092\u8a55\u4fa1\u3057\u3066\u3044\u306a\u3044\u3002\u3053\u308c\u3089\u304c\u307b\u307c\u7b49\u4fa1\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u306e\u306f\u3001\u6e2c\u5b9a\u7cbe\u5ea6\u306b\u6bd4\u3079\u3066\u5145\u5206\u591a\u304f\u306e\u56de\u6570\u6e2c\u5b9a\u3092\u884c\u3063\u305f\u5834\u5408\u3060\u3051\u3067\u3042\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]     (adsbygoogle = window.adsbygoogle || 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