{"id":1086,"date":"2021-11-03T07:16:58","date_gmt":"2021-11-03T07:16:58","guid":{"rendered":"https:\/\/projects.jayanwerdesigns.com\/goldammer\/?page_id=1086"},"modified":"2022-01-19T22:01:37","modified_gmt":"2022-01-19T22:01:37","slug":"digitale-filter","status":"publish","type":"page","link":"https:\/\/goldammer.de\/eng\/digitale-filter\/","title":{"rendered":"Digital Filter"},"content":{"rendered":"<div id='av_section_1'  class='avia-section main_color avia-section-default avia-no-border-styling  avia-bg-style-scroll  avia-builder-el-0  avia-builder-el-no-sibling  tab-sec  container_wrap fullsize' style=' '  ><div class='container' ><main  role=\"main\" itemprop=\"mainContentOfPage\"  class='template-page content  av-content-full alpha units'><div class='post-entry post-entry-type-page post-entry-1086'><div class='entry-content-wrapper clearfix'>\n<div class=\"flex_column av_one_full  flex_column_div av-zero-column-padding first  avia-builder-el-1  avia-builder-el-no-sibling  \" style='border-radius:0px; '><p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h1  blockquote modern-quote  avia-builder-el-2  el_before_av_hr  avia-builder-el-first  '><h1 class='av-special-heading-tag '  itemprop=\"headline\"  >Frequency selective digital filters<\/h1><div class ='av-subheading av-subheading_below  ' style='font-size:15px;'><p>Importance and application of digital filters on sampled signals<\/p>\n<\/div><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<div  style=' margin-top:0px; margin-bottom:10px;'  class='hr hr-custom hr-left hr-icon-no   avia-builder-el-3  el_after_av_heading  el_before_av_textblock '><span class='hr-inner  inner-border-av-border-fat' style=' width:70px; border-color:#ff0000;' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3 style=\"font-weight: 400;\"><u>table of contents<\/u><\/h3>\n<p><a href=\"#\">1 Digitale Filter<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#Me\u00dfkarten\">1.1 The real-time concept of the Goldammer measurement cards<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#das-abtasttheorem-oder\">1.2 The sampling theorem or rules for sampling time signals<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#wirkungsweise-digitaler\">1.3 How digital filters work<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#filtertypen\">1.4 Filter types<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#das-toleranz\">1.5 The tolerance scheme<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#rekursive-filter\">1.6 Recursive filters (IIR filters)<\/a><\/p>\n<ul>\n<li><a href=\"#\">1.6.1 Butterworth<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#butterworth\">1.6.2 Butterworth<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#chebycheff1\">1.6.3 Chebycheff 1<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#chebycheff2\">1.6.4 Chebycheff 2<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#cauer\">1.6.5 Cauer<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#bessel\">1.6.6 Bessel<\/a><\/li>\n<\/ul>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#nichtrekursive-filter\">1.7 Non-recursive filters (FIR filters)<\/a><\/p>\n<ul>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#Design process\">1.7.1 Entwurfsverfahren<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#Window method\">1.7.2 Fenster-Methode<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#frequenzabtastung\">1.7.3 Frequenzabtastung<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#remez-methode\">1.7.4 Remez-Methode<\/a><\/li>\n<li><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#ensterfunktion\">1.7.5 Window function<\/a><\/li>\n<\/ul>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#vergleich\">1.8 Comparison of IIR and FIR filters<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#einstellungen\">1.9 Settings for digital filters in DIAdem<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#einstellungen2\">1.10 Settings for digital filters under Dasylab<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#eistungsdaten\">1.11 Performance data<\/a><\/p>\n<p><a href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/#fir\">1.11.1 FIR-Filter<\/a><\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-5  el_after_av_textblock  el_before_av_heading '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<div  id=\"digitale-filter\"  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h1  blockquote modern-quote  avia-builder-el-6  el_after_av_hr  el_before_av_hr  '><h1 class='av-special-heading-tag '  itemprop=\"headline\"  >1 Digitale Filter<\/h1><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<div  style=' margin-top:0px; margin-bottom:10px;'  class='hr hr-custom hr-left hr-icon-no   avia-builder-el-7  el_after_av_heading  el_before_av_textblock '><span class='hr-inner  inner-border-av-border-fat' style=' width:70px; border-color:#ff0000;' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"messkarten\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h1><a name=\"_Toc514749119\"><\/a>1\u00a0digital filter<\/h1>\n<h2><a name=\"_Toc514749120\"><\/a>1.1\u00a0The real-time concept of the Goldammer measurement cards<\/h2>\n<p style=\"font-weight: 400;\">The intelligent measurement cards of the MC4-PCI series from Goldammer relieve the PC when it comes to recording and outputting signals.\u00a0This includes real-time processing of acquired signals.\u00a0This real-time processing is integrated in our drivers and is therefore very easy to activate and configure.\u00a0Each channel is treated individually.<\/p>\n<p style=\"font-weight: 400;\">Acquired signals can be digitally filtered in real time on the map.\u00a0Filtering may be necessary, for example to isolate the measurement signal from interfering signals.\u00a0For this purpose, the sampled values \u200b\u200bare fed to a filter algorithm immediately after the conversion.\u00a0The required coefficients are determined using a program library that is integrated in our drivers for the most common measurement acquisition systems such as DIAdem, Dasylab and Labview and therefore does not require any additional programs.\u00a0The user only needs to specify the conditions for the filter design.\u00a0All further work is automatically taken over and carried out by our drivers.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-9  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"das-abtasttheorem-oder\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749121\"><\/a>1.2\u00a0The sampling theorem or rules for sampling time signals<\/h2>\n<p style=\"font-weight: 400;\">There are some requirements for the sampling and processing of sampled signals with digital systems.\u00a0These are:<\/p>\n<ol style=\"font-weight: 400;\">\n<li>The signal must be band-limited, ie all frequency components must be zero above a limit frequency.<\/li>\n<li>The sampling frequency must be at least twice as high as the limit frequency of the signal<\/li>\n<\/ol>\n<p style=\"font-weight: 400;\">These rules are called &#8220;SHANNON&#8217;s sampling theorem&#8221;.\u00a0If it is not adhered to, ie the sampling rate is not at least twice as large as the limit frequency of a signal, frequency components occur in the spectrum that are actually not contained in the signal.\u00a0This effect is called &#8220;aliasing&#8221; and results from the reflection of frequencies above the cutoff frequency into the area below the cutoff frequency.\u00a0The cutoff frequency is called the \u201cNyquist frequency\u201d.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-11  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"wirkungsweise-digitaler\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749122\"><\/a>1.3\u00a0How digital filters work<\/h2>\n<p style=\"font-weight: 400;\">Sampled signals are generally a mixture of a useful signal (which contains information) and interfering signals.\u00a0The interference signals can be signals with a different frequency or noise that is superimposed on the useful signal.<\/p>\n<p style=\"font-weight: 400;\">In most cases, the interfering signals are of significantly smaller amplitude than the useful signal and therefore do not need to be taken into account.\u00a0If this is not the case, the useful signal can be covered by the interference component and the information in the useful signal cannot be evaluated.<\/p>\n<p style=\"font-weight: 400;\">If the interfering components can be removed from the sampled signal using a suitable method, the information from the useful signal is available again.\u00a0Selective filters are often used here.\u00a0These filters make use of the fact that the interference components generally have a different frequency than the useful signal.\u00a0They select the frequencies of the useful signal from the sampled signal and suppress all other frequency components.<\/p>\n<p style=\"font-weight: 400;\">The filtering of a signal sometimes requires a lot of computing time.\u00a0In order to relieve the PC of filtering the sampled signal, the sampled signal can be filtered immediately on cards from Goldammer and the filtered signal can be transferred to the PC.<\/p>\n<p style=\"font-weight: 400;\">The last sub-chapter shows performance measurements.\u00a0They show the possible number of coefficients of FIR filters depending on the number of channels and the total sampling rate.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-13  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"filtertypen\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749123\"><\/a>1.4\u00a0Filter types<\/h2>\n<p style=\"font-weight: 400;\">There are four standard types of selective filters:<\/p>\n<p style=\"font-weight: 400;\">Low-\u00a0<u>pass<\/u>\u00a0high frequencies are suppressed, low frequencies are retained<\/p>\n<p style=\"font-weight: 400;\"><u><br \/>\n<\/u>High-\u00a0<u>pass<\/u>\u00a0low frequencies are suppressed, high frequencies are retained<\/p>\n<p style=\"font-weight: 400;\"><u>Bandpass<br \/>\n<\/u>frequencies within a range are retained, outside they are suppressed<\/p>\n<p style=\"font-weight: 400;\"><u>Band stop<br \/>\n<\/u>frequencies within a range are suppressed, outside they are retained<\/p>\n<p style=\"font-weight: 400;\">There are also multiband filters that have several pass and stop ranges and other types of filters that are not discussed further here.<\/p>\n<p style=\"font-weight: 400;\">Which filter type is to be used and how the pass and stop bands are distributed over the frequency response is determined by coefficients and is therefore independent of the calculation algorithm.\u00a0However, the coefficients have to be determined in different ways for each filter algorithm and cannot be directly transferred to other algorithms.\u00a0Filter algorithms are also known as filter structures<\/p>\n<p style=\"font-weight: 400;\">The most common structures for digital filters are recursive (IIR) and non-recursive (FIR) filters.\u00a0Both are supported by Goldammer measuring cards.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-15  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"das-toleranz\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749124\"><\/a>1.5\u00a0The tolerance scheme<\/h2>\n<p style=\"font-weight: 400;\">The tolerance scheme is the basis of the filter design.\u00a0All information required for the filter design is entered in this scheme.<\/p>\n<p style=\"font-weight: 400;\">The necessary parameters are:<\/p>\n<p style=\"font-weight: 400;\">Cut-off frequencies\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0You define the width of the transition area from the pass band to the stop band<br \/>\n.\u00a0The number varies depending on the filter type.<br \/>\nA pair of cut-off frequencies is required for each filter edge.<br \/>\nIt follows from this: low and high passes need 2 cut-off frequencies, band-passes and bandstop filters need 4 cut-off frequencies.<\/p>\n<p style=\"font-weight: 400;\">Blocking attenuation\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Frequencies in the blocking range should be attenuated by at least this value.<\/p>\n<p style=\"font-weight: 400;\">Pass-\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0through attenuation Frequencies in the\u00a0pass-\u00a0band may be attenuated by this value<br \/>\nat most.<\/p>\n<p style=\"font-weight: 400;\">Sometimes allowable ripples are given.\u00a0The permissible ripples can be converted into attenuation and vice versa.<\/p>\n<p style=\"font-weight: 400;\">The width of the transition area and the specified attenuation determine the filter order.\u00a0The narrower the transition area and the higher the blocking attenuation, the greater the filter order required and thus the computational effort of the filter.<\/p>\n<p style=\"font-weight: 400;\">The tolerance scheme can be represented in several ways.\u00a0In most cases the attenuation is given.<\/p>\n<p style=\"font-weight: 400;\">Figure\u00a0<strong>1.2<\/strong>\u00a0shows such a tolerance scheme in which the attenuations are specified.\u00a0In<\/p>\n<p style=\"font-weight: 400;\">Figure\u00a0<strong>1.1<\/strong>\u00a0shows the permissible ripples.\u00a0In order to meet the tolerance scheme, the frequency response of the filter must not cross the hatched areas.\u00a0In that case the tolerance scheme would be violated.\u00a0In order to reduce the filter order, it can be decided on a case-by-case basis whether a slight violation of the tolerance scheme is permissible.<\/p>\n<p style=\"font-weight: 400;\">Tolerance scheme of a low pass with:<\/p>\n<p style=\"font-weight: 400;\">Sampling frequency:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01000 Hz<br \/>\nlower limit frequency:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0100 Hz<br \/>\nupper limit frequency:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0200 Hz<br \/>\npermissible ripple in the pass band:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0d\u00a0<sub>d<br \/>\n<\/sub>permissible ripple in the blocking range:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0d\u00a0<sub>s<\/sub><\/p>\n<table>\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1121 alignleft\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image004.gif\" alt=\"\" width=\"297\" height=\"172\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td><strong>Picture\u00a01\u00a0.\u00a01<\/strong><strong>\u00a0:<\/strong>\u00a0Tolerance scheme with details of the frequencies and permissible ripples<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Instead of the ripples, the attenuation is given in the following tolerance scheme. The following also applies here: the hatched areas must not be traversed by the frequency response of the filter.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1122 alignleft\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image006.gif\" alt=\"\" width=\"297\" height=\"172\" \/><\/p>\n<p>Picture 1 . 2 : Tolerance scheme with details of the frequencies and attenuations<\/p>\n<\/div><\/section><br \/>\n<section class=\"av_textblock_section \"  id=\"rekursive-filter\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749125\"><\/a>1.6\u00a0Recursive filters\u00a0\u00a0\u00a0(IIR filters)<\/h2>\n<p style=\"font-weight: 400;\">Recursive filters are filters in which the output signal of the filter is fed back to the filter input.\u00a0The name comes from English and means &#8220;infinite\u00a0\u00a0<u>i<\/u>\u00a0mpuls\u00a0\u00a0<u>r<\/u>\u00a0esponse&#8221; (infinite impulse response).\u00a0The required filter order can be reduced by the feedback.\u00a0However, the generally non-linear phase has a disadvantageous effect.<\/p>\n<p style=\"font-weight: 400;\">The design of IIR filters can be traced back to the design of analog filters.\u00a0In this way, among other things, the order can be determined which is required to meet the tolerance scheme.\u00a0Likewise, the design of a high-pass filter can be traced back to the design of a low-pass filter by means of a transformation.\u00a0So only a low pass needs to be determined.\u00a0Other filter types (low-pass, high-pass, band-pass, band-stop) can be calculated from this low-pass prototype using so-called frequency transformations.\u00a0It is not necessary to limit the coefficients.\u00a0This is a great advantage over FIR filters.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-18  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"butterworth\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749127\"><\/a>1.6.1\u00a0Butterworth<\/h3>\n<p style=\"font-weight: 400;\">Straight-line frequency response in the passband and stopband, therefore no full use of the tolerance scheme.\u00a0The degree of filtering is therefore relatively high.\u00a0The group delays hardly change over the frequency response.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-20  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"chebycheff1\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749128\"><\/a>1.6.2\u00a0Chebycheff 1<\/h3>\n<p style=\"font-weight: 400;\">Straight-line frequency response only in the stop band and ripple in the pass band, thus only full utilization of the tolerance scheme in the pass band.\u00a0Due to\u00a0\u00a0\u00a0better utilization of\u00a0\u00a0\u00a0the tolerance scheme, the degree of filtering is smaller than with Butterworth filters.\u00a0The group delays change slightly over the frequency response.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-22  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"chebycheff2\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749129\"><\/a>1.6.3\u00a0Chebycheff 2<\/h3>\n<p style=\"font-weight: 400;\">Straight-line frequency response only in the pass band and ripple in the stop band, thus only full utilization of the tolerance scheme of the stop band.\u00a0Otherwise as with Chebycheff 1.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-24  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"cauer\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749130\"><\/a>1.6.4\u00a0Cauer<\/h3>\n<p style=\"font-weight: 400;\">Ripple in the passage as well as in the blocked area, thus full utilization of the tolerance scheme.\u00a0The degree of filtering is smaller than with Chebycheff 1\/2 filters.\u00a0The group delays change strongly over the frequency response.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-26  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"bessel\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749131\"><\/a>1.6.5\u00a0Bessel<\/h3>\n<p style=\"font-weight: 400;\">Very poor utilization of the tolerance scheme, therefore a higher degree of filtering than with all other filter types.\u00a0The group delays are almost constant over the entire frequency response.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-28  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"nichtrekursive-filter\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749132\"><\/a>1.7\u00a0Non-recursive filters\u00a0\u00a0\u00a0(FIR filters)<\/h2>\n<p style=\"font-weight: 400;\">Non-recursive filters are filters in which the output signal of the filter is not fed back to the filter input.\u00a0The name comes from English and means &#8221;\u00a0<u>f<\/u>\u00a0inite\u00a0\u00a0<u>i<\/u>\u00a0mpuls\u00a0\u00a0<u>r<\/u>\u00a0esponse&#8221; (finite impulse response).\u00a0These types of filters are always stable.\u00a0With them it is possible to realize a linear phase and thus a constant group delay without additional effort.\u00a0This advantage over the IIR filters is bought at the price of a higher filter order.<\/p>\n<p style=\"font-weight: 400;\">The design of FIR filters cannot be traced back to the design of analog filters.\u00a0Likewise, the order that is required to meet the tolerance scheme cannot be determined.\u00a0This leads to a try-and-fail approach in which the design process is performed recursively.\u00a0With each pass, the order is increased and it is checked whether the tolerance scheme is met.\u00a0If it is fulfilled, the recursion is canceled.\u00a0There are also no known transformations that can be used to convert a low-pass filter into a different type of filter, such as a high-pass filter.\u00a0Every design problem has to be solved anew.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-30  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"entwurfsverfahren\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749133\"><\/a>1.7.1\u00a0Design process<\/h3>\n<p style=\"font-weight: 400;\">The driver for the cards\u00a0<strong>from Goldammer<\/strong>\u00a0support several design methods for calculating coefficients for FIR filters.\u00a0Any design process can<\/p>\n<p style=\"font-weight: 400;\">Calculate low-pass, high-pass, band-pass and band-stop filters.<\/p>\n<p style=\"font-weight: 400;\">Since the order of an FIR filter cannot be calculated absolutely, an additional function is implemented that uses the tolerance scheme to determine the order with which the tolerance scheme is fulfilled.\u00a0However, this can take some time, as the design process is repeated recursively until the correct order has been found.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-32  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"fenster-methode\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749134\"><\/a>1.7.2\u00a0Window method<\/h3>\n<p style=\"font-weight: 400;\">With the window method, an impulse response is calculated.\u00a0For this purpose, functions are used with which the coefficients can be calculated directly.\u00a0However, only a linear phase can be achieved in this way.<\/p>\n<p style=\"font-weight: 400;\">The length of the calculated impulse response is limited.\u00a0If the impulse response is cut off, one speaks of a limitation with a rectangular window.\u00a0This leads to overshoots on the filter flanks.\u00a0These overshoots decrease as the distance to the flank increases.\u00a0Increasing the order does not reduce the overshoot amplitudes.\u00a0By using a different window function that does not cut off the impulse response, but rather attenuates the coefficients at the edges more and more towards zero.\u00a0In this way, the overshoots are greatly reduced.\u00a0This is paid for by a less steep slope.\u00a0The function\u00a0courses of\u00a0some window functions are shown\u00a0in (\u00a01.7.5\u00a0).<\/p>\n<p style=\"font-weight: 400;\">The following figures show the frequency responses of filters with different orders. It can be seen that the overshoots do not disappear when the order is increased, but that they are only concentrated in a smaller area around the flank. The Hanning window reduces the overshoot clear, but the flank is less steep.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1128 aligncenter\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image008-1.gif\" alt=\"\" width=\"378\" height=\"285\" \/><\/p>\n<p>Picture 1 . 3 : Frequency response of a 20th order filter designed with the window method. The waviness can be clearly seen by using the rectangular window. The Hanning window reduces the ripple, but reduces the slope.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1129\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image010-1.gif\" alt=\"\" width=\"378\" height=\"281\" \/><\/p>\n<p>Picture 1 . 4 : Frequency response of a 60th order filter designed according to the window method. The flank became steeper, but the waviness did not decrease.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-34  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"frequenzabtastung\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749135\"><\/a>1.7.3\u00a0Frequenzabtastung<\/h3>\n<p style=\"font-weight: 400;\">The frequency sampling generates an impulse response from a frequency and a phase response with the help of the inverse FFT.\u00a0The advantage here is that any frequency and phase responses can be implemented.\u00a0The computational effort is mainly determined by the FFT.\u00a0The filter order plays a subordinate role.<\/p>\n<p style=\"font-weight: 400;\">The coefficients calculated here are only an approximation of the real impulse response.\u00a0The accuracy can be increased by increasing the FFT points.\u00a0This increases the computing time required, however.<\/p>\n<p style=\"font-weight: 400;\">The problem of overshoots at the filter flanks also occurs here.\u00a0By using window functions, these overshoots can be reduced at the expense of a less steep slope.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-36  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"remez-methode\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749136\"><\/a>1.7.4\u00a0Remez-Methode<\/h3>\n<p style=\"font-weight: 400;\">The Remez method generates filter coefficients known as &#8220;equi-ripple-filters&#8221;.\u00a0Another term is &#8220;optimal FIR filter&#8221;.\u00a0The filters designed according to this method are optimal in that they optimally fill the tolerance scheme in the passage and blocking area.\u00a0This creates a uniform ripple in both the pass band and the blocked area (similar to the Chebyshev3 IIR filter).\u00a0Furthermore, these filters often require a lower order to meet the tolerance scheme than the design methods mentioned above.<\/p>\n<p style=\"font-weight: 400;\">A disadvantage is the high computational effort.\u00a0In return, this design method offers great flexibility.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1130\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image012-1.gif\" alt=\"\" width=\"378\" height=\"282\" \/><\/p>\n<p>Picture 1 . 5 : Frequency response of a 20th order filter designed using the Remez method.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1131\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image014.gif\" alt=\"\" width=\"378\" height=\"277\" \/><\/p>\n<p>Picture 1 . 6 : Frequency response of a 60th order filter designed with the Remez method.<\/p>\n<p>A window function is not necessary with the Remez method. The waviness becomes smaller with increasing order.<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-38  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"fensterfunktion\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><a name=\"_Toc514749137\"><\/a>1.7.5\u00a0Window function<\/h3>\n<p style=\"font-weight: 400;\">This design method only creates a window function and transfers it to the calling routine.<br \/>\nThe number of coefficients of the window function is the transferred order plus one.<\/p>\n<p style=\"font-weight: 400;\">Over 200 window functions are known.\u00a0The most frequently used window functions are offered by our driver.<\/p>\n<p>Various window functions are shown in the picture below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1133\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image016.gif\" alt=\"\" width=\"359\" height=\"254\" \/><\/p>\n<p>Picture 1 . 7 : Functional history of some window functions<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-40  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"vergleich\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749138\"><\/a>1.8\u00a0Comparison of IIR and FIR filters<\/h2>\n<p style=\"font-weight: 400;\">A direct comparison between IIR and FIR filters is not possible.\u00a0Depending on the task and the boundary conditions, the user must decide which type of filter should be used.<\/p>\n<p style=\"font-weight: 400;\">To do this, the advantages and disadvantages of the two types of filter must be weighed against each other.<\/p>\n<p style=\"font-weight: 400;\">The following table is intended to help:<\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"2\" width=\"326\"><strong>FIR Filter<\/strong><\/td>\n<td colspan=\"2\" width=\"326\"><strong>IIR filter<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"163\"><strong>advantages<\/strong><\/td>\n<td width=\"163\"><strong>disadvantage<\/strong><\/td>\n<td width=\"163\"><strong>advantages<\/strong><\/td>\n<td width=\"163\"><strong>disadvantage<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"163\">always stable<\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\">not always stable, therefore check stability<\/td>\n<\/tr>\n<tr>\n<td width=\"163\">constant (linear) group delay<\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\">variable (non-linear) group delay<\/td>\n<\/tr>\n<tr>\n<td width=\"163\">The output signal is not falsified<\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\"><\/td>\n<td width=\"163\">The output signal is falsified<\/td>\n<\/tr>\n<tr>\n<td width=\"163\"><\/td>\n<td width=\"163\">finite impulse response, thus overshoots at jump points<\/td>\n<td width=\"163\">Infinite impulse response, therefore no overshoots at jump points<\/td>\n<td width=\"163\"><\/td>\n<\/tr>\n<tr>\n<td width=\"163\"><\/td>\n<td width=\"163\">higher order necessary to fulfill the tolerance scheme than with IIR<\/td>\n<td width=\"163\">lower order necessary to fulfill the tolerance scheme than FIR<\/td>\n<td width=\"163\"><\/td>\n<\/tr>\n<tr>\n<td width=\"163\"><\/td>\n<td width=\"163\">large group delays and high computational effort<\/td>\n<td width=\"163\">smaller group delays and lower computational effort<\/td>\n<td width=\"163\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><\/h3>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-42  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"einstellungen\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749139\"><\/a>1.9\u00a0Settings for digital filters in DIAdem<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1134\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image017.gif\" alt=\"\" width=\"552\" height=\"560\" \/><\/p>\n<p>Picture 1 . 8 : Input mask for filters under DIAdem<\/p>\n<p style=\"font-weight: 400;\">To activate and configure filters, click on &#8220;Device ..&#8221;.\u00a0The various setting options are listed at the top of the dialog that opens.<\/p>\n<ol style=\"font-weight: 400;\">\n<li>The inputs are configured on this page.<\/li>\n<li>Here are the settings for the filter of a channel, which can be selected under (3).\u00a0The settings on this page can be set individually for each channel.<\/li>\n<li>Here you can select a channel that you want to configure.\u00a0If the selected channel is configured, the next channel can be selected here.<\/li>\n<li>At this point you can specify for the channel selected under (3) whether the sampled values \u200b\u200bof this channel should be subjected to a filter.<\/li>\n<li>Selection of filter structures (recursive IIR or non-recursive FIR filters).\u00a0The filter structure selected here influences the meaning and entries of other input fields.<\/li>\n<li>Definition of the filter type.\u00a0Possible settings: low pass, high pass, band pass, band stop<\/li>\n<li>Limit frequencies of the 1st filter edge, left the lower, right the upper limit frequency of the edge.<br \/>\nThe specification of this edge is required for low pass and high pass.\u00a0With these types, the 2nd flank is ignored.<\/li>\n<li>Limit frequencies of the 2nd filter edge, left the lower, right the upper limit frequency of the edge.<br \/>\nThis edge is also required for bandpass and bandstop.<\/li>\n<li>Frequencies can be specified as absolute (in Hz) or standardized.\u00a0Normalized frequencies have the advantage that the sampling frequency does not have to be taken into account.\u00a0Absolute frequencies can be converted into normalized frequencies if the sampling rate is known and given.\u00a0With the &#8220;absolute frequencies&#8221; setting, the sampling frequency is taken from the clock block during initialization.<\/li>\n<li>The attenuation in the pass-through and blocked areas are specified here.<br \/>\nOn the left the transmission attenuation, on the right the blocking attenuation.\u00a0The blocking attenuation should always be greater than the transmission attenuation.<\/li>\n<li>Attenuation can also be specified as an indication of permissible ripples.\u00a0A conversion is carried out internally.\u00a0Here it is specified whether the input is to be interpreted as damping or as waviness.<\/li>\n<li>The design process is specified here.\u00a0At this point, a distinction must be made between which filter structure was selected under (5).\u00a0Advantages, disadvantages and peculiarities of the design method are explained above.<br \/>\nFIR filter\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0window method, frequency scanning, Remez method, window function<br \/>\nIIR filter\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Butterworth, Tschebyscheff 1, Tschebyscheff 2, Cauer<\/li>\n<li>This field is used to select the window function with which the coefficients are to be evaluated in order to minimize the ripples in the filter edges.<br \/>\nThis selection is only available for FIR filters.<\/li>\n<li>A click on this field opens a window in which the frequency response and the group delay of the filter are displayed.\u00a0In this way, the user can get a visual overview of the behavior of the filter he has defined.<\/li>\n<li>Once the parameters have been set for all channels, the configuration window can be closed.<\/li>\n<\/ol>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-44  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"einstellungen2\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749140\"><\/a>1.10\u00a0Settings for digital filters under Dasylab<\/h2>\n<p style=\"font-weight: 400;\">Digital filters are only supported under Dasylab with the Extension Toolkit.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1136\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image018.gif\" alt=\"\" width=\"572\" height=\"256\" \/><\/p>\n<p>Picture 1 . 9 : Input mask for filters under Dasylab<\/p>\n<p style=\"font-weight: 400;\">You open this dialog box by clicking on the &#8220;Filter Settings&#8221; field in the configuration dialog for the selected block.<\/p>\n<ol style=\"font-weight: 400;\">\n<li>At this point you can specify for the selected channel whether the sampled values \u200b\u200bof this channel should be subjected to a filter.<\/li>\n<li>Selection of filter structures (recursive IIR or non-recursive FIR filters).\u00a0The filter structure selected here influences the meaning and entries of other input fields.<\/li>\n<li>Definition of the filter type.\u00a0Possible settings: low pass, high pass, band pass, band stop<\/li>\n<li>Frequencies can be specified as absolute (in Hz) or standardized.\u00a0Normalized frequencies have the advantage that the sampling frequency does not have to be taken into account.\u00a0Absolute frequencies can be converted into normalized frequencies if the sampling rate is known and given.\u00a0The limit frequencies of the 1st and 2nd filter edge are also entered here.<br \/>\nThe lower limit frequency of the edge is defined on the left and the upper limit frequency on the right.<br \/>\nLow passes and high passes only require the 1st filter edge, the 2nd edge is ignored. &#8216;<br \/>\nBandpasses and bandstop filters also require the specification of the 2nd filter edge.<\/li>\n<li>Attenuation can also be specified as an indication of permissible ripples.\u00a0A conversion is carried out internally.\u00a0Here it is specified whether the input is to be interpreted as damping or as waviness.\u00a0The attenuation in the pass-through and blocked areas are also specified here.\u00a0The blocking attenuation should always be greater than the transmission attenuation.<\/li>\n<li>The design process is specified here.\u00a0At this point, a distinction must be made between which filter structure was selected under (5).\u00a0Advantages, disadvantages and peculiarities of the design method are explained above.<br \/>\nFIR filter\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0window method, frequency scanning, Remez method, window function<br \/>\nIIR filter\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Butterworth, Tschebyscheff 1, Tschebyscheff 2, Cauer<\/li>\n<li>This field is used to select the window function with which the coefficients are to be evaluated in order to minimize the ripples in the filter edges.<br \/>\nThis selection is only available for FIR filters.<\/li>\n<li>A click on this field opens a window in which the frequency response and the group delay of the filter are displayed.\u00a0In this way, the user can get a visual overview of the behavior of the filter he has defined.<\/li>\n<li>Once all parameters have been set, the configuration window can be closed.<\/li>\n<\/ol>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-46  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"leistungsdaten\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h2><a name=\"_Toc514749141\"><\/a>1.11\u00a0Performance\u00a0data<\/h2>\n<p style=\"font-weight: 400;\">The performance measurements were carried out with the following measuring system:<\/p>\n<p style=\"font-weight: 400;\">PC:<\/p>\n<p style=\"font-weight: 400;\">Processor:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0AMD K6-200<\/p>\n<p style=\"font-weight: 400;\">Speicher:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0128MB PC-100 (DIMM)<\/p>\n<p style=\"font-weight: 400;\">Mainboard:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Asus P5A B<\/p>\n<p style=\"font-weight: 400;\">Chipset:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0ALI<\/p>\n<p style=\"font-weight: 400;\">Graphics card:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Diamond Viper AGP (RIVA 128)<\/p>\n<p style=\"font-weight: 400;\">Me\u00df-Software:<\/p>\n<p style=\"font-weight: 400;\">DIAdem 7.02<\/p>\n<p style=\"font-weight: 400;\">Measurement in the hardware cycle<\/p>\n<p style=\"font-weight: 400;\">Display by graph<\/p>\n<p style=\"font-weight: 400;\">DLL-Version:\u00a0\u00a0\u00a0\u00a0\u00a05.2.0.0<\/p>\n<p style=\"font-weight: 400;\">DSP driver:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05.2.1.1<\/p>\n<p style=\"font-weight: 400;\">Measurement card:<\/p>\n<p style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0MC4Light \/ HS from Goldammer<\/p>\n<\/div><\/section><br \/>\n<div  style='height:30px' class='hr hr-invisible   avia-builder-el-48  el_after_av_textblock  el_before_av_textblock '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<section class=\"av_textblock_section \"  id=\"fir\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock  '   itemprop=\"text\" ><h3><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1137\" src=\"https:\/\/goldammer.de\/eng\/wp-content\/uploads\/2021\/11\/image020.gif\" alt=\"\" width=\"642\" height=\"450\" \/>1.11.1 FIR-Filter<\/h3>\n<p style=\"font-weight: 400;\">Some conclusions can be drawn from this data:<\/p>\n<p style=\"font-weight: 400;\">1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0With a constant total sampling rate, the number of coefficients per channel remains almost constant.<\/p>\n<p style=\"font-weight: 400;\">2)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Changing the total sampling rate by a factor of\u00a0\u00a0\u00a0a\u00a0\u00a0\u00a0increases the number of coefficients per channel by a factor of\u00a0\u00a0\u00a01 \/ a.<\/p>\n<p style=\"font-weight: 400;\">3)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0The total number of coefficients increases almost linearly with the number of channels.<\/p>\n<p style=\"font-weight: 400;\">4)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0The change in the number of coefficients per channel is real\u00a0\u00a0\u00a01 \/ (a \u200b\u200b- 1.5% .. 5%).\u00a0Reducing the sampling rate increases the number of possible coefficients per channel by a factor that allows approx. 1.5% .. 5% more coefficients.<\/p>\n<\/div><\/section><\/p><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[58],"tags":[],"class_list":["post-1086","page","type-page","status-publish","hentry","category-onlinefunktionen-multichoice"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Digital Filter - Goldammer GmbH<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/goldammer.de\/eng\/digitale-filter\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Digital Filter - Goldammer GmbH\" \/>\n<meta property=\"og:url\" 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