{"id":93,"date":"2025-10-31T00:25:51","date_gmt":"2025-10-31T00:25:51","guid":{"rendered":"https:\/\/vibromera.eu\/glossary\/cross-spectrum\/"},"modified":"2026-05-23T22:41:17","modified_gmt":"2026-05-23T22:41:17","slug":"cross-spectrum","status":"publish","type":"glossary","link":"https:\/\/vibromera.eu\/tt\/glossary\/cross-spectrum\/","title":{"rendered":"What is Cross-Spectrum? Two-Channel Frequency Analysis"},"content":{"rendered":"<h1>Understanding Cross-Spectrum<\/h1>\n\t\t<section class=\"woocommerce hestia-shop products is-shortcode\" id=\"products\" data-sorder=\"hestia_shop\" >\n\t\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<div class=\"hestia-shop-content\">\n\t\t\t<div class=\"row\" data-aos=\"fade-up\" >\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" title=\"Portable balancer &#038; Vibration analyzer Balanset-1A\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A full kit portable balancer and vibration analyzer\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-272x182.webp 272w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/devices\/\" rel=\"tag\">Devices<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" title=\"Portable balancer &#038; Vibration analyzer Balanset-1A\">Portable balancer &#038; Vibration analyzer Balanset-1A<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>1,975.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=986\" data-quantity=\"1\" data-product_id=\"986\" data-product_sku=\"BS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=986\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_986\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"986\" data-product_sku=\"BS-1\" aria-label=\"Add to cart: \u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d\" rel=\"nofollow\" data-success_message=\"\u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_986\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" title=\"Vibration sensor\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A vibration sensor close-up\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" title=\"Vibration sensor\">Vibration sensor<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>90.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1820\" data-quantity=\"1\" data-product_id=\"1820\" data-product_sku=\"VS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1820\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1820\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1820\" data-product_sku=\"VS-1\" aria-label=\"Add to cart: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1820\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Optical Sensor (Laser Tachometer)\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Optical Sensor (Laser Tachometer)\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1536x1023.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU.webp 1600w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Optical Sensor (Laser Tachometer)\">Optical Sensor (Laser Tachometer)<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>124.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1832\" data-quantity=\"1\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1832\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1832\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" aria-label=\"Add to cart: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1832\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" title=\"Balanset-4\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Vibromera rotor balancing kit: carry case, multi-channel signal conditioner, handheld analyzer, magnetic base, vibration sensors, and coiled cables.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4.webp 640w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/devices\/\" rel=\"tag\">Devices<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" title=\"Balanset-4\">Balanset-4<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>6,803.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1833\" data-quantity=\"1\" data-product_id=\"1833\" data-product_sku=\"BS-4\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1833\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1833\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1833\" data-product_sku=\"BS-4\" aria-label=\"Add to cart: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1833\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div><!-- \/.row --><div class=\"row\">\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" title=\"Magnetic Stand Insize-60-kgf\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Magnet base.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" title=\"Magnetic Stand Insize-60-kgf\">Magnetic Stand Insize-60-kgf<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>46.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/93?add-to-cart=1852\" data-quantity=\"1\" data-product_id=\"1852\" data-product_sku=\"MS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" 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class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t\n<p><strong>Cross-spectrum<\/strong> \u2014 also called the cross-power spectrum or cross-spectral density \u2014 is the frequency-domain representation of the relationship between two simultaneously measured <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/vibration\/\">vibration<\/a> signals. It is computed by multiplying the <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/fft\/\">FFT<\/a> of one signal by the complex conjugate of the FFT of the other. Where an <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/auto-spectrum\/\">auto-spectrum<\/a> shows the frequency content of a single channel, the cross-spectrum reveals which frequencies are <em>common<\/em> to both signals and the <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/phase\/\">phase<\/a> relationship between them at every frequency.<\/p>\n<p>This makes the cross-spectrum the mathematical foundation of advanced multi-channel analysis: <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/transfer-function\/\">transfer function<\/a> estimation, <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/coherence\/\">coherence<\/a> analysis, and Operating Deflection Shape (<a href=\"https:\/\/vibromera.eu\/tt\/glossary\/ods-analysis\/\">ODS<\/a>) measurements all rest on it. In practical terms it lets an engineer see how vibration propagates through a structure and identify cause-and-effect relationships between measurement locations \u2014 something a single-channel <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/spectrum\/\">spectrum<\/a> simply cannot do.<\/p>\n<h2>1. Mathematical Definition<\/h2>\n<h3>Computation<\/h3>\n<p>The defining relationship is compact:<\/p>\n<blockquote>\n<p><strong>G<sub>xy<\/sub>(f) = X(f) \u00d7 Y*(f)<\/strong><\/p>\n<\/blockquote>\n<ul>\n<li>X(f) is the FFT of signal x(t).<\/li>\n<li>Y*(f) is the complex conjugate of the FFT of signal y(t).<\/li>\n<li>The result is complex-valued, carrying both magnitude and phase.<\/li>\n<\/ul>\n<h3>Components<\/h3>\n<ul>\n<li><strong>Magnitude \u2014 |G<sub>xy<\/sub>(f)|:<\/strong> shows the strength of the frequency content the two signals share.<\/li>\n<li><strong>Phase \u2014 \u2220G<sub>xy<\/sub>(f):<\/strong> shows the phase difference between the signals at each frequency.<\/li>\n<li><strong>Real part:<\/strong> the in-phase, or co-spectral, component.<\/li>\n<li><strong>Imaginary part:<\/strong> the quadrature, or 90\u00b0-out-of-phase, component.<\/li>\n<\/ul>\n<h2>2. Properties<\/h2>\n<p>Three properties set the cross-spectrum apart from the familiar auto-spectrum, and each one matters in interpretation.<\/p>\n<h3>It Is Complex-Valued<\/h3>\n<ul>\n<li>Unlike the auto-spectrum, which is real only, the cross-spectrum is complex.<\/li>\n<li>It therefore carries both magnitude and phase.<\/li>\n<li>That phase information is the whole point \u2014 it is what reveals how the two signals relate in time.<\/li>\n<\/ul>\n<h3>It Is Not Symmetric<\/h3>\n<ul>\n<li>In general G<sub>xy<\/sub>(f) \u2260 G<sub>yx<\/sub>(f).<\/li>\n<li>Order matters \u2014 which signal you treat as the reference changes the result.<\/li>\n<li>Formally, G<sub>yx<\/sub>(f) is the complex conjugate of G<sub>xy<\/sub>(f), so the phase simply flips sign.<\/li>\n<\/ul>\n<h3>It Requires Averaging<\/h3>\n<ul>\n<li>A single cross-spectrum is noisy and unreliable.<\/li>\n<li>Averaging many cross-spectra produces a stable estimate.<\/li>\n<li>Uncorrelated noise components average toward zero because their phase is random from block to block.<\/li>\n<li>Genuinely correlated components keep a consistent phase and reinforce \u2014 which is exactly why averaging cleans the estimate up.<\/li>\n<\/ul>\n<h2>3. Applications<\/h2>\n<h3>Transfer Function Calculation<\/h3>\n<p>This is the single most important application:<\/p>\n<blockquote>\n<p><strong>H(f) = G<sub>xy<\/sub>(f) \/ G<sub>xx<\/sub>(f)<\/strong><\/p>\n<\/blockquote>\n<ul>\n<li>Here x is the input and y is the output.<\/li>\n<li>The result shows how the system responds to excitation.<\/li>\n<li>Its magnitude shows amplification or attenuation at each frequency.<\/li>\n<li>Its phase shows time delay and <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/resonance\/\">resonance<\/a> behaviour.<\/li>\n<li>It is the core measurement of <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/modal-analysis\/\">modal analysis<\/a> and structural dynamics, closely related to the <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/frequency-response-function\/\">frequency response function<\/a>.<\/li>\n<\/ul>\n<h3>Coherence Calculation<\/h3>\n<ul>\n<li>Coherence is defined as <strong>|G<sub>xy<\/sub>|\u00b2 \/ (G<sub>xx<\/sub> \u00d7 G<sub>yy<\/sub>)<\/strong>.<\/li>\n<li>It measures the correlation between the two signals at each frequency.<\/li>\n<li>It ranges from 0 to 1: a value of 1 means perfect correlation, 0 means none at all.<\/li>\n<li>It validates measurement quality and flags where the result is being corrupted by noise \u2014 indispensable during a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/bump-test\/\">bump test<\/a> or modal survey.<\/li>\n<\/ul>\n<h3>Phase Relationship Determination<\/h3>\n<ul>\n<li>The phase from the cross-spectrum reveals time delay or resonance directly.<\/li>\n<li><strong>0\u00b0:<\/strong> the signals are in phase, moving together.<\/li>\n<li><strong>180\u00b0:<\/strong> the signals are out of phase, moving in opposition.<\/li>\n<li><strong>90\u00b0:<\/strong> quadrature, indicating resonance or a pure time delay.<\/li>\n<li>This is the diagnostic basis for <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/mode-shape\/\">mode shapes<\/a> and for tracing vibration transmission.<\/li>\n<\/ul>\n<h3>Common-Mode Rejection<\/h3>\n<ul>\n<li>The cross-spectrum isolates the frequency components common to both channels.<\/li>\n<li>Uncorrelated noise cancels through averaging.<\/li>\n<li>The true, shared signal components emerge from the background.<\/li>\n<li>The practical payoff is a better signal-to-noise ratio.<\/li>\n<\/ul>\n<h2>4. Practical Measurement Scenarios<\/h2>\n<p>The abstract idea becomes concrete the moment two sensors go onto a real machine. Three everyday set-ups show the value.<\/p>\n<h3>Bearing Comparison<\/h3>\n<ul>\n<li>Signal X: vibration at bearing 1. Signal Y: vibration at bearing 2.<\/li>\n<li>The cross-spectrum shows the frequencies that affect both bearings at once.<\/li>\n<li>That separates a shared, rotor-related issue from a problem local to one <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/bearing-defects\/\">bearing<\/a>.<\/li>\n<\/ul>\n<h3>Input\u2013Output Analysis<\/h3>\n<ul>\n<li>Signal X: force or vibration at the input \u2014 a coupling or the driver bearing.<\/li>\n<li>Signal Y: the response at the output \u2014 the driven-equipment bearing.<\/li>\n<li>The cross-spectrum reveals the transmission characteristics between them.<\/li>\n<li>The derived transfer function then quantifies exactly how vibration travels across a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/coupling-defects\/\">coupling<\/a>.<\/li>\n<\/ul>\n<h3>Structural Transmission<\/h3>\n<ul>\n<li>Signal X: bearing-housing vibration. Signal Y: foundation or frame vibration.<\/li>\n<li>The cross-spectrum shows which frequencies actually reach the structure.<\/li>\n<li>That guides decisions on isolation or stiffening, and connects directly to <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/foundation-stiffness\/\">foundation stiffness<\/a> and <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/structural-resonance\/\">structural resonance<\/a> problems.<\/li>\n<\/ul>\n<h2>5. Interpreting the Cross-Spectrum<\/h2>\n<h3>High Magnitude at a Frequency<\/h3>\n<ul>\n<li>Indicates strong correlation between the signals at that frequency.<\/li>\n<li>Points to a common source or strong coupling between the two locations.<\/li>\n<li>The component is genuinely present in both signals.<\/li>\n<\/ul>\n<h3>Low Magnitude at a Frequency<\/h3>\n<ul>\n<li>Indicates little correlation \u2014 weak coupling, or no shared source.<\/li>\n<li>The component may exist in one signal but not the other.<\/li>\n<li>Or it may simply be uncorrelated noise from different sources.<\/li>\n<\/ul>\n<h3>Phase Information<\/h3>\n<ul>\n<li><strong>0\u00b0:<\/strong> the signals move together \u2014 a rigid connection, or operation below resonance.<\/li>\n<li><strong>180\u00b0:<\/strong> the signals move oppositely \u2014 above resonance, or across a line of symmetry.<\/li>\n<li><strong>90\u00b0:<\/strong> quadrature \u2014 at resonance, or arising from a specific geometry.<\/li>\n<li><strong>Frequency-dependent phase:<\/strong> the way phase changes with frequency exposes the dynamic behaviour of the structure.<\/li>\n<\/ul>\n<h2>6. Advanced Applications<\/h2>\n<h3>Multiple Input \/ Output Analysis<\/h3>\n<ul>\n<li>Several reference signals are paired with several response signals.<\/li>\n<li>The result is a full matrix of cross-spectra.<\/li>\n<li>It identifies multiple, simultaneous transmission paths.<\/li>\n<li>This is how genuinely complex systems are characterised.<\/li>\n<\/ul>\n<h3>Operating Deflection Shapes<\/h3>\n<ul>\n<li>Cross-spectra are taken between many measurement points around a machine.<\/li>\n<li>Their phase relationships define the deflection pattern.<\/li>\n<li>The motion of the whole structure can then be visualised and animated.<\/li>\n<li>Resonant modes stand out clearly in the result.<\/li>\n<\/ul>\n<h2>7. Cross-Spectrum in Field Balancing<\/h2>\n<p>Although the cross-spectrum is most associated with modal and structural work, the same two-channel mathematics underpins everyday <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/field-balancing\/\">field balancing<\/a>. A portable two-channel instrument such as the <a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\">Balanset-1A<\/a> records vibration at two bearing planes simultaneously and references both to the once-per-revolution tachometer pulse, so it can resolve the amplitude-and-phase of the 1\u00d7 component at each plane and compute the cross-coupled <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/influence-coefficient\/\">influence coefficients<\/a> that link a weight in one plane to the response in the other. That two-channel, phase-referenced relationship is conceptually a cross-spectrum focused on running speed \u2014 and it is exactly what makes correct two-plane <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/dynamic-balancing\/\">dynamic balancing<\/a> possible on an assembled machine.<\/p>\n<p>In short, the cross-spectrum extends frequency analysis from one channel to many, exposing the relationships between signals that enable transfer-function calculation, coherence validation, and an understanding of how vibration travels through a machine and its supports. More demanding than the auto-spectrum, it is nonetheless essential for modal testing, structural dynamics, and any sophisticated diagnostic that relies on multi-point measurement.<\/p>\n<hr>\n<p><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/\">\u2190 Back to Main Index<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Learn about cross-spectrum, frequency analysis relating two vibration signals showing common frequency content and phase relationships, essential for transfer function and coherence analysis.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[114,109],"tags":[],"class_list":["post-93","glossary","type-glossary","status-publish","hentry","category-analysis","category-glossary"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/93","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary"}],"about":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/types\/glossary"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/93\/revisions"}],"predecessor-version":[{"id":101329,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/93\/revisions\/101329"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/media?parent=93"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/categories?post=93"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/tags?post=93"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}