{"id":34887,"date":"2019-10-31T22:01:05","date_gmt":"2019-10-31T19:01:05","guid":{"rendered":"https:\/\/prohoster.info\/blog\/voprosy-prioriteta-najkvist-shennon-ili-kotelnikov\/"},"modified":"2026-05-20T17:51:22","modified_gmt":"2026-05-20T15:51:22","slug":"voprosy-prioriteta-najkvist-shennon-ili-kotelnikov","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sv\/blog\/news\/voprosy-prioriteta-najkvist-shennon-ili-kotelnikov","title":{"rendered":"Prioriteringsfr\u00e5gor: Nyquist, Shannon eller Kotelnikov?","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Om prioriteringen av arbete inom informations\u00f6verf\u00f6ring.<\/p>\n

Pionj\u00e4ren i denna moderna fr\u00e5ga \u00e4r V.A. Kotelnikov. Under sin doktorandutbildning vid MIE publicerades det 1932 arbeten, varav ett hette \"Om \u00f6verf\u00f6ringskapaciteten hos \"eetter\" och tr\u00e5d i telekommunikation\" och anm\u00e4ldes f\u00f6r f\u00f6redrag vid den f\u00f6rsta allunionella kongressen om teknisk ombyggnad av kommunikationssystem och utveckling av l\u00e5gsp\u00e4nningsindustrin. Kongressen \u00e4gde inte rum. Det publicerades 1933 som material till f\u00f6redraget (godk\u00e4nt f\u00f6r tryck i
\nnovember 1932). <\/a><\/noindex>\u0427\u0442\u043e \u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0444\u0438\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u043c \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u0430. \u0417\u0430\u043a\u0430\u043d\u0447\u0438\u0432\u0430\u044f \u0430\u0441\u043f\u0438\u0440\u0430\u043d\u0442\u0443\u0440\u0443, \u0412\u043b\u0430\u0434\u0438\u043c\u0438\u0440 \u0434\u043e\u043b\u043e\u0436\u0438\u043b \u0441\u0432\u043e\u0438 \u0440\u0430\u0431\u043e\u0442\u044b \u043d\u0430 \u0423\u0447\u0435\u043d\u043e\u043c \u0441\u043e\u0432\u0435\u0442\u0435. \u0414\u043e\u043a\u043b\u0430\u0434 \u043e\u0434\u043e\u0431\u0440\u0438\u043b\u0438, \u0440\u0430\u0431\u043e\u0442\u0443 » \u041e \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u043d\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u0438…» \u043d\u0435 \u043f\u043e\u043d\u044f\u043b\u0438- «\u2026 \u0432\u0440\u043e\u0434\u0435 \u0432\u0435\u0440\u043d\u043e, \u043d\u043e \u043d\u0430\u0443\u0447\u043d\u0430\u044f \u0444\u0430\u043d\u0442\u0430\u0441\u0442\u0438\u043a\u0430.» <\/p>\n

F\u00f6r det f\u00f6rsta angav detta arbete de framtida utvecklingsriktningarna f\u00f6r kommunikation och avskilde de meningsl\u00f6sa riktningarna. F\u00f6r det andra, i den informationsm\u00e4ssiga aspekten av kommunikationsproblemen, matematiskt motiverades digital \u00f6verf\u00f6ring av information, den ber\u00f6mda teoremet
\nKotelnikovs teorem. Egentligen inneh\u00f6ll detta arbete 7 teorem.<\/p>\n

Den som Shannon och hans likar kallar \"samplingsteoremet\", som han publicerade 15 \u00e5r senare 1948. D\u00e4refter, under 1970-talet, med elektronikens utveckling, intr\u00e4ffade ett naturligt uppsving av intresset f\u00f6r digital information\u00f6verf\u00f6ring. 1977 uppstod fr\u00e5gan vid prioriteringsuppr\u00e4ttande och namnet WKS-teoremet f\u00f6reslogs, Whittaker-Kotelnikov-Shannon.<\/p>\n

\u00c5r 1999 tilldelade Edouard Reins stiftelse, vid sammanst\u00e4llningen av framst\u00e5ende vetenskapliga prestationer under 1900-talet, priset till den sovjetiske forskaren Vladimir Alexandrovich Kotelnikov i kategorin \"f\u00f6r fundamentala studier\" f\u00f6r \"f\u00f6r f\u00f6rsta g\u00e5ngen matematiskt exakt formulerad och publicerad samplingsteorem.\"<\/p>\n

En annan intressant punkt. <\/p>\n

Namnet H. Nyquist, (eng. Harry Nyquist), dyker upp, som troligen var en av de f\u00f6rsta som f\u00f6rstod och uttryckte tanken att signalprovtagning b\u00f6r skiljas av tidsintervall som \u00e4r lika
\n\u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u043f\u043e\u043b\u043e\u0441\u0435 \u0435\u0433\u043e \u0441\u043f\u0435\u043a\u0442\u0440\u0430\u043b\u044c\u043d\u043e\u0439 \u0448\u0438\u0440\u0438\u043d\u044b. \u042d\u0442\u043e \u0447\u0430\u0441\u0442\u043e \u0434\u0430\u0451\u0442 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u0437\u0430\u043f\u0430\u0434\u043d\u044b\u043c \u0443\u0447\u0451\u043d\u044b\u043c, \u0443\u043f\u043e\u0442\u0440\u0435\u0431\u043b\u044f\u0442\u044c \u0442\u0435\u0440\u043c\u0438\u043d \u00ab\u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0432\u044b\u0431\u043e\u0440\u043e\u043a \u041d\u0430\u0439\u043a\u0432\u0438\u0441\u0442\u0430\u00bb. \u041d\u043e \u0435\u0433\u043e \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u043b\u0438\u0441\u044c \u043a \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0435 \u043d\u0435\u0438\u0441\u043a\u0430\u0436\u0451\u043d\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0442\u0435\u043b\u0435\u0433\u0440\u0430\u0444\u043d\u043e\u0433\u043e \u0441\u0438\u0433\u043d\u0430\u043b\u0430, \u0445\u043e\u0442\u044f \u0438 \u0431\u044b\u043b\u0438 \u0431\u043b\u0438\u0437\u043a\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0435 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u043d\u0435\u0438\u0441\u043a\u0430\u0436\u0451\u043d\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u043e\u0432\u043e\u0433\u043e \u0441\u0438\u0433\u043d\u0430\u043b\u0430. \u041f\u0440\u043e\u0444\u0435\u0441\u0441\u043e\u0440 \u041b\u044e\u043a\u0435 \u0414. \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u043e \u043f\u0440\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0432\u044b\u0431\u043e\u0440\u043e\u043a \u0443\u043a\u0430\u0437\u044b\u0432\u044b\u0430\u0435\u0442 \u043d\u0430 \u044d\u0442\u043e:» \u043f\u0435\u0440\u0432\u044b\u043c \u0443\u0447\u0451\u043d\u044b\u043c, \u0442\u043e\u0447\u043d\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0432\u0448\u0438\u043c \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u043e \u0432\u044b\u0431\u043e\u0440\u043a\u0430\u0445 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0438\u0432\u0448\u0438\u043c \u0435\u0451 \u043a \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0435 \u0442\u0435\u043e\u0440\u0438\u0438 \u0438 \u0442\u0435\u0445\u043d\u0438\u043a\u0438 \u0441\u0432\u044f\u0437\u0438, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e, \u0412.\u0410.\u041a\u043e\u0442\u0435\u043b\u044c\u043d\u0438\u043a\u043e\u0432».<\/p>\n

Ett litet avsnitt och \u00e4ven om prioriteringar.<\/p>\n

\u00c5r 1939 skapade Vladimir Alexandrovich kommunikationsutrustning p\u00e5 en sidoband, och han byggde den sj\u00e4lv, sj\u00e4lvklart inte ensam, eftersom industrin avb\u00f6jde: \"Ingen har n\u00e5gonsin gjort n\u00e5got s\u00e5dant.\" Den installerades men godk\u00e4ndes inte p\u00e5 linjen Moskva-Khabarovsk. Den godk\u00e4ndes inte: \"L\u00e4tt att avlyssna.\" Efter att ha l\u00e4st en artikel av H. Dudley skapade Kotelnikov en tal krypteringsapparat och
\nredogjorde f\u00f6r dess id\u00e9 i rapporten \"Grundl\u00e4ggande principer f\u00f6r automatisk kryptering\" den 19 juni 1941. I detta dokument formulerades f\u00f6r f\u00f6rsta g\u00e5ngen krav p\u00e5 matematiskt oskiljaktiga
\nsystem med bevis p\u00e5 om\u00f6jligheten av dekryptering. I den offentliga publikationen fanns det inget (eller kanske finns det redan?).
\nK. Shannon presenterade den 1 september 1945 tillv\u00e4gag\u00e5ngss\u00e4tt f\u00f6r att bygga motst\u00e5ndskraftiga krypteringssystem, den offentliga publiceringen av rapporten s\u00e5gs 1949.<\/p>\n

Kortsiktig bearbetning av \"Framsteg inom fysikens vetenskaper\", konferenser och symposier, juli 2006, volym 176, nr 7<\/p>\n

Detaljerat material med matematiska ber\u00e4kningar kan laddas ner via l\u00e4nken<\/p>\n

Avslutningsvis kan jag s\u00e4ga att v\u00e4ldigt ofta i vetenskaplig och praktisk litteratur undanh\u00e5ller utl\u00e4ndska f\u00f6rfattare, tillskriver sig sj\u00e4lva eller i v\u00e4rsta fall nedv\u00e4rderar ryska-sovjetiska-ryska prestationer och prioriteringar.<\/a><\/noindex>.<\/p>\n

Den n\u00e4sta publikationen kommer att vara en redog\u00f6relse f\u00f6r material om fr\u00e5gan \"Vem \u00e4r uppfinnaren av radion, Popov eller Marconi?\" om jag f\u00e5r samma brand i f\u00f6rr\u00e5det som idag. <\/p>\n

Richard Hamming: Kapitel 13. Informationsteori
\n
K\u00e4lla: habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

\u041e \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u0435 \u0440\u0430\u0431\u043e\u0442 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438. \u041f\u0435\u0440\u0432\u043e\u043f\u0440\u043e\u0445\u043e\u0434\u0446\u0435\u043c \u0432 \u044d\u0442\u043e\u043c \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u043c \u0432\u043e\u043f\u0440\u043e\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0412.\u0410.\u041a\u043e\u0442\u0435\u043b\u044c\u043d\u0438\u043a\u043e\u0432. \u0412\u043e \u0432\u0440\u0435\u043c\u044f \u0430\u0441\u043f\u0438\u0440\u0430\u043d\u0442\u0443\u0440\u044b \u0432 \u041c\u042d\u0418 \u0431\u044b\u043b\u0438 \u043e\u043f\u0443\u0431\u043b\u0438\u043a\u043e\u0432\u0430\u043d\u044b \u0432 1932\u0433. \u0440\u0430\u0431\u043e\u0442\u044b, \u043e\u0434\u043d\u0430 \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0430\u0437\u044b\u0432\u0430\u043b\u0430\u0441\u044c \u00ab\u041e \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u043d\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u0438 \u201e\u044d\u0444\u0438\u0440\u0430\u201c \u0438 \u043f\u0440\u043e\u0432\u043e\u043b\u043e\u043a\u0438 \u0432 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u0441\u0432\u044f\u0437\u0438\u00bb \u0438 \u0437\u0430\u044f\u0432\u043b\u0435\u043d\u0430 \u043a \u0434\u043e\u043a\u043b\u0430\u0434\u0443 I \u0412\u0441\u0435\u0441\u043e\u044e\u0437\u043d\u043e\u0433\u043e \u0441\u044a\u0435\u0437\u0434\u0430 \u043f\u043e \u0432\u043e\u043f\u0440\u043e\u0441\u0430\u043c \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0440\u0435\u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u0434\u0435\u043b\u0430 \u0441\u0432\u044f\u0437\u0438 \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u0441\u043b\u0430\u0431\u043e\u0442\u043e\u0447\u043d\u043e\u0439 \u043f\u0440\u043e\u043c\u044b\u0448\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438. \u0421\u044a\u0435\u0437\u0434 \u043d\u0435 […]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-34887","post","type-post","status-publish","format-standard","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\n","aioseo_head_json":{"title":"Fr\u00e5gor om prioritet: Nyquist, Shannon eller Kotelnikov? | ProHoster","description":"\ud83e\udd47Fr\u00e5gor om prioritet: Nyquist, Shannon eller Kotelnikov? | ProHoster","canonical_url":"https:\/\/prohoster.info\/sv\/blog\/news\/voprosy-prioriteta-najkvist-shennon-ili-kotelnikov","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":null,"og:locale":"sv_SE","og:site_name":"ProHoster | \u041a\u0443\u043f\u0438\u0442\u044c \u043d\u0430\u0434\u0435\u0436\u043d\u044b\u0439 \u0445\u043e\u0441\u0442\u0438\u043d\u0433 \u0434\u043b\u044f \u0441\u0430\u0439\u0442\u043e\u0432 \u0441 \u0437\u0430\u0449\u0438\u0442\u043e\u0439 \u043e\u0442 DDoS, VPS VDS \u0441\u0435\u0440\u0432\u0435\u0440\u044b","og:type":"article","og:title":"\ud83e\udd47\u0412\u043e\u043f\u0440\u043e\u0441\u044b \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u0430: \u041d\u0430\u0439\u043a\u0432\u0438\u0441\u0442, \u0428\u0435\u043d\u043d\u043e\u043d \u0438\u043b\u0438 \u041a\u043e\u0442\u0435\u043b\u044c\u043d\u0438\u043a\u043e\u0432? | ProHoster","og:description":"\u041e \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u0435 \u0440\u0430\u0431\u043e\u0442 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438. \u041f\u0435\u0440\u0432\u043e\u043f\u0440\u043e\u0445\u043e\u0434\u0446\u0435\u043c \u0432 \u044d\u0442\u043e\u043c \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u043c \u0432\u043e\u043f\u0440\u043e\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0412.\u0410.\u041a\u043e\u0442\u0435\u043b\u044c\u043d\u0438\u043a\u043e\u0432. \u0412\u043e \u0432\u0440\u0435\u043c\u044f \u0430\u0441\u043f\u0438\u0440\u0430\u043d\u0442\u0443\u0440\u044b \u0432 \u041c\u042d\u0418 \u0431\u044b\u043b\u0438 \u043e\u043f\u0443\u0431\u043b\u0438\u043a\u043e\u0432\u0430\u043d\u044b \u0432 1932\u0433.","og:url":"https:\/\/prohoster.info\/sv\/blog\/news\/voprosy-prioriteta-najkvist-shennon-ili-kotelnikov","og:image":"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg","og:image:secure_url":"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg","og:image:width":350,"og:image:height":350,"article:published_time":"2019-10-31T19:01:05+00:00","article:modified_time":"2026-05-20T15:51:22+00:00","article:publisher":"https:\/\/www.facebook.com\/prohoster","article:author":"https:\/\/www.facebook.com\/prohoster"},"aioseo_meta_data":{"post_id":"34887","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":null,"schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"seo_analyzer_scan_date":"2026-01-21 20:58:19","breadcrumb_settings":null,"limit_modified_date":false,"reviewed_by":null,"ai":null,"created":"2021-03-01 02:13:27","updated":"2026-01-21 20:58:19","focus_keyword":null,"additional_keywords":null,"truseo_locale":null},"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/posts\/34887","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/comments?post=34887"}],"version-history":[{"count":1,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/posts\/34887\/revisions"}],"predecessor-version":[{"id":173269,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/posts\/34887\/revisions\/173269"}],"wp:attachment":[{"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/media?parent=34887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/categories?post=34887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prohoster.info\/sv\/wp-json\/wp\/v2\/tags?post=34887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}