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   Signal Processing
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class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20135 href=/products/igorpro/datastorage/datafolders> Data Folders </a></ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20017 data-region=sidebar href=/products/igorpro/creatinggraphs> Creating Graphics </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20018 data-region=sidebar href=/products/igorpro/creatinggraphs/2dgraphs> 2D graphs </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20024 data-region=sidebar href=/products/igorpro/creatinggraphs/2dgraphs/linegraphs> XY plots </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20027 href=/products/igorpro/creatinggraphs/2dgraphs/linegraphs/newgraph> New graph details </a><li><a data-drupal-link-system-path=node/20026 href=/products/igorpro/creatinggraphs/2dgraphs/linegraphs/graphmodes> Trace settings </a><li><a data-drupal-link-system-path=node/20025 href=/products/igorpro/creatinggraphs/2dgraphs/linegraphs/axis> Axis settings </a></ul><li><a data-drupal-link-system-path=node/20021 href=/products/igorpro/creatinggraphs/2dgraphs/catplot> Category Plots </a><li><a data-drupal-link-system-path=node/20022 href=/products/igorpro/creatinggraphs/2dgraphs/contourgraphs> Contour Plots </a><li><a data-drupal-link-system-path=node/20020 href=/products/igorpro/creatinggraphs/2dgraphs/axes> Flexible axes </a><li><a data-drupal-link-system-path=node/20019 href=/products/igorpro/creatinggraphs/2dgraphs/animations> Animations </a><li><a data-drupal-link-system-path=node/20028 href=/products/igorpro/creatinggraphs/2dgraphs/preferences> Preferences and templates </a></ul><li><a data-drupal-link-system-path=node/20042 href=/products/igorpro/creatinggraphs/pagelayouts> Page Layouts </a><li><a data-drupal-link-system-path=node/20044 href=/products/igorpro/creatinggraphs/tables> Tables </a><li><a data-drupal-link-system-path=node/20040 href=/products/igorpro/creatinggraphs/drawingtools> Drawing tools </a><li><a data-drupal-link-system-path=node/20038 href=/products/igorpro/creatinggraphs/annotations> Annotations </a><li><a data-drupal-link-system-path=node/20039 href=/products/igorpro/creatinggraphs/colortab> Color Tables </a><li><a data-drupal-link-system-path=node/20043 href=/products/igorpro/creatinggraphs/subwindows> Subwindows </a><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20029 data-region=sidebar href=/products/igorpro/creatinggraphs/3dandvolume> 3D and Volume </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20036 href=/products/igorpro/creatinggraphs/3dandvolume/surface> Surface Plots </a><li><a data-drupal-link-system-path=node/20033 href=/products/igorpro/creatinggraphs/3dandvolume/path> Path and Ribbon Plots </a><li><a data-drupal-link-system-path=node/20034 href=/products/igorpro/creatinggraphs/3dandvolume/scatter> 3D Scatter </a><li><a data-drupal-link-system-path=node/20032 href=/products/igorpro/creatinggraphs/3dandvolume/objects> 3D Object Plots </a><li><a data-drupal-link-system-path=node/20031 href=/products/igorpro/creatinggraphs/3dandvolume/isosurface> Isosurfaces </a><li><a data-drupal-link-system-path=node/20037 href=/products/igorpro/creatinggraphs/3dandvolume/voxelgrams> Voxelgrams </a><li><a data-drupal-link-system-path=node/20035 href=/products/igorpro/creatinggraphs/3dandvolume/slicer> Volume Slices </a><li><a data-drupal-link-system-path=node/20030 href=/products/igorpro/creatinggraphs/3dandvolume/animations> 3D Animations </a></ul><li><a data-drupal-link-system-path=node/20041 href=/products/igorpro/creatinggraphs/exportinggraphics> Exporting Graphics </a></ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20137 data-region=sidebar href=/products/igorpro/imageprocessing> Image Processing </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20141 href=/products/igorpro/imageprocessing/imageacquisition> Image Acquisition </a><li><a data-drupal-link-system-path=node/20155 href=/products/igorpro/imageprocessing/roi> ROI </a><li><a data-drupal-link-system-path=node/20138 href=/products/igorpro/imageprocessing/colortransforms> Color Spaces </a><li><a data-drupal-link-system-path=node/20156 href=/products/igorpro/imageprocessing/thresholding> Thresholding </a><li><a data-drupal-link-system-path=node/20139 href=/products/igorpro/imageprocessing/convolutionfilters> Localized Filters </a><li><a data-drupal-link-system-path=node/20140 href=/products/igorpro/imageprocessing/edgedetectors> Edge Detectors </a><li><a data-drupal-link-system-path=node/20154 href=/products/igorpro/imageprocessing/morphologicaloperations> Morphology </a><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20142 data-region=sidebar href=/products/igorpro/imageprocessing/imageanalysis> Image Analysis </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20145 href=/products/igorpro/imageprocessing/imageanalysis/imagestats> Image Statistics </a><li><a data-drupal-link-system-path=node/20144 href=/products/igorpro/imageprocessing/imageanalysis/imagelineprofile> Line Profile </a><li><a data-drupal-link-system-path=node/20146 href=/products/igorpro/imageprocessing/imageanalysis/particleanalysis> Particle Analysis </a><li><a data-drupal-link-system-path=node/20143 href=/products/igorpro/imageprocessing/imageanalysis/ImageSnake> Image Snake </a></ul></ul><li class="expanded active-trail has-children active-item"><a block=block-mainnavigation data-drupal-link-system-path=node/20059 data-region=sidebar href=/products/igorpro/dataanalysis> Data Analysis </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20061 data-region=sidebar href=/products/igorpro/dataanalysis/curvefitting> Curve Fitting </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20062 href=/products/igorpro/dataanalysis/curvefitting/builtintypes> Built-in types </a><li><a data-drupal-link-system-path=node/20067 href=/products/igorpro/dataanalysis/curvefitting/userdefined> User-defined </a><li><a data-drupal-link-system-path=node/20063 href=/products/igorpro/dataanalysis/curvefitting/constraints> Constraints </a><li><a data-drupal-link-system-path=node/20064 href=/products/igorpro/dataanalysis/curvefitting/errorsinvariables> Errors in Variables </a><li><a data-drupal-link-system-path=node/20065 href=/products/igorpro/dataanalysis/curvefitting/globalfitting> Global Fitting </a><li><a data-drupal-link-system-path=node/20066 href=/products/igorpro/dataanalysis/curvefitting/multidimensional> Multidimensional </a></ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20068 data-region=sidebar href=/products/igorpro/dataanalysis/peakanalysis> Peak Analysis </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20071 href=/products/igorpro/dataanalysis/peakanalysis/peakfinding> Peak finding </a><li><a data-drupal-link-system-path=node/20069 href=/products/igorpro/dataanalysis/peakanalysis/baselineremoval> Baseline removal </a><li><a data-drupal-link-system-path=node/20070 href=/products/igorpro/dataanalysis/peakanalysis/multipeakfitting> Multi-peak fitting </a></ul><li class="expanded active-trail has-children active-item"><a block=block-mainnavigation class=is-active data-drupal-link-system-path=node/20072 data-region=sidebar href=/products/igorpro/dataanalysis/signalprocessing> Signal Processing </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20075 href=/products/igorpro/dataanalysis/signalprocessing/fouriertransforms> Fourier transforms </a><li><a data-drupal-link-system-path=node/20080 href=/products/igorpro/dataanalysis/signalprocessing/spectralwindowing> Spectral windowing </a><li><a data-drupal-link-system-path=node/20078 href=/products/igorpro/dataanalysis/signalprocessing/powerspectra> Power spectra </a><li><a data-drupal-link-system-path=node/20076 href=/products/igorpro/dataanalysis/signalprocessing/hilberttransform> Hilbert transforms </a><li><a data-drupal-link-system-path=node/20081 href=/products/igorpro/dataanalysis/signalprocessing/timefrequency> Time frequency analysis </a><li><a data-drupal-link-system-path=node/20074 href=/products/igorpro/dataanalysis/signalprocessing/digitalfilters> Digital filters </a><li><a data-drupal-link-system-path=node/20079 href=/products/igorpro/dataanalysis/signalprocessing/smoothing> Smoothing </a><li><a data-drupal-link-system-path=node/20073 href=/products/igorpro/dataanalysis/signalprocessing/convolution> Convolution and Correlation </a><li><a data-drupal-link-system-path=node/20077 href=/products/igorpro/dataanalysis/signalprocessing/leveldetection> Level detection </a></ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20082 data-region=sidebar href=/products/igorpro/dataanalysis/statistics> Statistics </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20089 data-region=sidebar href=/products/igorpro/dataanalysis/statistics/tests> Statistical Tests </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20091 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp1> Angular Distribution Tests </a><li><a data-drupal-link-system-path=node/20090 href=/products/igorpro/dataanalysis/statistics/tests/Statistics_pxp2> ANOVA1 Tests </a><li><a data-drupal-link-system-path=node/20112 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp3> ANOVA2(NR) Tests </a><li><a data-drupal-link-system-path=node/20119 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp4> ANOVA2(RM) Tests </a><li><a data-drupal-link-system-path=node/20120 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp5> Chi-Squared Tests </a><li><a data-drupal-link-system-path=node/20121 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp6> Angular-Correlation Tests </a><li><a data-drupal-link-system-path=node/20122 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp7> Circular Means Tests </a><li><a data-drupal-link-system-path=node/20123 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp8> Circular Moment Tests </a><li><a data-drupal-link-system-path=node/20124 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp9> Circular Two Sample Tests </a><li><a data-drupal-link-system-path=node/20092 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp10> Cochran Test </a><li><a data-drupal-link-system-path=node/20093 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp11> Dunnett Test </a><li><a data-drupal-link-system-path=node/20094 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp12> Friedman Test </a><li><a data-drupal-link-system-path=node/20095 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp13> F Test </a><li><a data-drupal-link-system-path=node/20096 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp14> Hodges-Ajne Test </a><li><a data-drupal-link-system-path=node/20097 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp15> Jarque-Bera Simulation </a><li><a data-drupal-link-system-path=node/20098 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp16> Kendall's Tau </a><li><a data-drupal-link-system-path=node/20099 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp17> Kolmogorov-Smirnov Test </a><li><a data-drupal-link-system-path=node/20100 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp18> Kruskal-Wallis Test </a><li><a data-drupal-link-system-path=node/20101 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp19> Linear Correlation </a><li><a data-drupal-link-system-path=node/20102 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp20> Linear Regression </a><li><a data-drupal-link-system-path=node/20103 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp21> Multi-Correlations </a><li><a data-drupal-link-system-path=node/20104 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp22> NP Multi-Comparison </a><li><a data-drupal-link-system-path=node/20105 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp23> Nominal Serial Randomness </a><li><a data-drupal-link-system-path=node/20106 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp24> Spearman Rank Correlation </a><li><a data-drupal-link-system-path=node/20107 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp25> Bootstrap and Jacknife </a><li><a data-drupal-link-system-path=node/20108 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp26> Scheffe's Test </a><li><a data-drupal-link-system-path=node/20109 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp27> Serial Randomeness </a><li><a data-drupal-link-system-path=node/20110 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp28> T-Test Examples </a><li><a data-drupal-link-system-path=node/20111 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp29> Tukey Text Examples </a><li><a data-drupal-link-system-path=node/20113 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp30> Variances Test Examples </a><li><a data-drupal-link-system-path=node/20114 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp31> Watson's U&ampsup2; Test </a><li><a data-drupal-link-system-path=node/20115 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp32> Watson-Williams Test </a><li><a data-drupal-link-system-path=node/20116 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp33> Wheeler-Watson Test </a><li><a data-drupal-link-system-path=node/20117 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp34> Wilcoxon Tests </a><li><a data-drupal-link-system-path=node/20118 href=/products/igorpro/dataanalysis/statistics/tests/statistics_pxp35> Weighted Rank Correlation </a></ul><li><a data-drupal-link-system-path=node/20086 href=/products/igorpro/dataanalysis/statistics/noise> Noise Functions </a><li><a data-drupal-link-system-path=node/20087 href=/products/igorpro/dataanalysis/statistics/pdfs> Probability Distribution Functions </a><li><a data-drupal-link-system-path=node/20083 href=/products/igorpro/dataanalysis/statistics/cdfs> Cumulative Distribution Functions </a><li><a data-drupal-link-system-path=node/20085 href=/products/igorpro/dataanalysis/statistics/invcdfs> Inverse CDFs </a><li><a data-drupal-link-system-path=node/20084 href=/products/igorpro/dataanalysis/statistics/genpurpose> General Purpose </a><li><a data-drupal-link-system-path=node/20088 href=/products/igorpro/dataanalysis/statistics/procs> Procedures and Packages </a></ul><li><a data-drupal-link-system-path=node/20060 href=/products/igorpro/dataanalysis/compgeometry> Computational Geometry </a></ul><li class="expanded has-children"><a block=block-mainnavigation 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Log in to share your own code snippet."data-drupal-link-system-path=code-snippets href=/code-snippets> Code Snippets </a><li><a title="User-contributed packages of related Igor procedure files and XOPs (Igor extensions). Login to share your contribution."data-drupal-link-system-path=projects href=/projects> Projects </a></ul><li class="expanded has-children"><a block=block-mainnavigation data-drupal-link-system-path=node/20001 data-region=sidebar href=/support> Support Center </a> <span class=toggle-container> <span class=toggle-inner-wrapper> <span class=toggle-item> </span> <span class=toggle-item> </span> <span class=toggle-item> </span> </span> </span> <ul class=sub-menu-ul><li><a data-drupal-link-system-path=node/20445 href=/contact-us> Contact Us </a><li><a data-drupal-link-system-path=faq href=/faq> FAQ </a><li><a data-drupal-link-system-path=node/20157 href=/products/igorpro/manual> Manual </a><li><a title="Guided Tour of Igor and 3D Plotting Tutorials"data-drupal-link-system-path=node/20185 href=/products/igorpro/videotutorials> Video Tutorials </a><li><a title="Current and Previous Software Versions"data-drupal-link-system-path=node/20215 href=/support/versions> Current and Legacy Versions </a><li><a data-drupal-link-system-path=node/20228 href=/users/users> User Resources & Contributions </a></ul></ul></nav></div></div><div class=page-content-wrapper><header aria-label="Site header"id=header role=banner><a href=/> <img class=mobile-logo src=/profiles/wavemetrics/themes/wavemetrics/logo.png> </a><nav aria-labelledby=block-useraccountmenu-menu id=block-useraccountmenu role=navigation><h2 class=visually-hidden id=block-useraccountmenu-menu>User account menu</h2><ul block=block-useraccountmenu class=menu-ul id=main-menu><li class=menu-item-li><a data-drupal-link-system-path=user/login href=/user/login> Forum Log In </a></ul></nav><a class=hamburger href=#> <div class=patty></div> <div class=patty></div> <div class=patty></div> </a><a class=site-search-icon href=/search/wavemetrics?keys=> </a></header><div class=content-wrapper><div class=clearit></div><div class=hidden data-drupal-messages-fallback></div><section class=basic-page-hero></section><section class="paragraph full-html"><span class=field-paragraph-full-html> <p>Signal Processing is the art and science of modifying acquired time-series data for the purposes of analysis or enhancement. Examples include spectral analysis (using the Fast Fourier or other transforms) and enhancing acquired data using digital filtering. <br> <img alt=fftexample.png data-entity-type data-entity-uuid src=/sites/www.wavemetrics.com/files/fftexample.png></p> <p>Igor is ideally suited for signal processing because of its strong <a href=/products/igorpro/datastorage> support for lengthy time-series (or "waveform") data </a> , and because its many <a href=/products/igorpro/dataanalysis/signalprocessing#commands> built-in signal processing commands </a> can easily be used through simple dialogs.</p> <p>In addition, Igor´s <a href=/products/igorpro/programming> programming language </a> makes it straightforward to implement any kind of custom signal processing algorithm, greatly aided by the power of Igor´s Fourier (and other) Transforms.</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/fouriertransforms> Fourier Transforms </a></h3> <p>Igor uses the Fast Fourier Transform (FFT) algorithm to compute a Discrete Fourier Transform (DFT). The FFT can be used to simply characterize the magnitude and phase of a signal, or it can be used in combination with other operations to perform more involved computations such as <a href=/products/igorpro/dataanalysis/signalprocessing#convolution> convolution or correlation </a> .</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/spectralwindowing> Spectral Windowing </a></h3> <p>The FFT computation presumes that the input data repeats over and over. This is important when the initial and final values of your data are not the same: the discontinuity causes aberrations in the spectrum computed by the FFT. "Windowing" smooths the ends of the data to eliminate these aberrations.</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/powerspectra> Power Spectra </a></h3> <p>"Power Spectra" answer the question "which frequencies contain the signal´s power?" The answer is in the form of a distribution of power values as a function of frequency, where "power" is considered to be the average of the signal². In the frequency domain, this is the square of FFT´s magnitude.</p> <p>Power spectra can be computed for the entire signal at once (a "periodogram") or periodograms of segments of the time signal can be averaged together to form the "power spectral density".</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/hilberttransform> Hilbert Transform </a></h3> <p>The Hilbert Transform computes a time-domain signal that is 90 degrees "out of phase" with the input signal. One-dimensional applications include computing the envelope of a modulated signal and the measurement of the decay rate of an exponentially decaying sinusoid often encountered in underdamped linear and non-linear systems.</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/timefrequency> Time Frequency Analysis </a></h3> <p>When you compute the Fourier spectrum (or Power Spectra) of a signal you dispose of all the phase information contained in the Fourier transform. You can find out which frequencies a signal contains but you do not know when these frequencies appear in the signal. For example, consider the signal: <br> <img alt=twotonesignaleqn.png data-entity-type data-entity-uuid src=/sites/www.wavemetrics.com/files/twotonesignaleqn.png> <br> The spectral representation of <em> f </em> ( <em> t </em> ) remains essentially unchanged if we interchange the two frequencies f <sub> 1 </sub> and f <sub> 2 </sub> : <br> <img alt=twotonesfft.png data-entity-type data-entity-uuid src=/sites/www.wavemetrics.com/files/twotonesfft.png></p> <p>Clearly the Fourier spectrum is not the best analysis tool for signals whose spectra fluctuate in time.</p> <p>One solution to this problem is the so-called "Short-time Fourier Transform" (or <a href=/products/igorpro/dataanalysis/signalprocessing/timefrequency#Sonogram> "Sonogram" </a> ) in which you can compute the Fourier spectra using a sliding temporal window. By adjusting the width of the window you can determine the time resolution of the resulting spectra.</p> <p>Other alternative tools are the <a href=/products/igorpro/dataanalysis/signalprocessing/timefrequency#Wigner> Wigner transform </a> , the <a href=/products/igorpro/dataanalysis/signalprocessing/timefrequency#CWT> Continuous Wavelet Transform (CWT) </a> , and the <a href=/products/igorpro/dataanalysis/signalprocessing/timefrequency#DWT> Discrete Wavelet Transform (DWT) </a> .</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/convolution> Convolution and Correlation </a></h3> <p>You can use convolution to compute the response of a linear system to an input signal. The linear system is defined by its impulse response. The convolution of the input signal and the impulse response is the output signal response. <a href=/products/igorpro/dataanalysis/signalprocessing#digitalfiltering> Digital filtering </a> is accomplished by defining a linear system´s impulse response that when convolved with the signal accomplishes the desired result (low-pass or high-pass filter).</p> <p>The correlation algorithm is very similar mathematically to convolution, but is used for different purposes. It is most frequently used to identify the time delay at which two signals "line up", or are "most similar".</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/smoothing> Smoothing </a></h3> <p>Smoothing removes short-term variations, or "noise" to reveal the important underlying form of the data.</p> <p>The simplest form of smoothing is the " <a href=/products/igorpro/dataanalysis/signalprocessing/smoothing#MovingAverage> moving average </a> " which simply replaces each data value with the average of neighboring values. (Other terms for this kind of smoothing are "sliding average", "box smoothing", or "boxcar smoothing".)</p> <p>Igor´s Smooth operation performs box smoothing, "binomial" (Gaussian) smoothing, and Savitzky-Golay (polynomial) smoothing. The different smoothing algorithms compute weighted averages that multiply neighboring values by differing weights or "coefficients" to compute the smoothed value.</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/digitalfilters> Digital Filters </a></h3> <p>Digital filters are a natural tool when data is already digitized. Reasons for applying digital filtering to data include:</p> <dl><dd>Elimination of unwanted signal components ("noise")<dd>Enhancing of desired signal components<dd>Detecting the presence of certain signals<dd>Simulation of linear systems (compute the output signal given the input signal and the system´s "transfer function")</dl> <p>Digital filters generally come in two flavors: Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters.</p> <p>Igor implements digital filtering primarily through time-domain convolution using the FilterFIR, FilterIIR, and <a href=/products/igorpro/dataanalysis/signalprocessing/smoothing> Smooth </a> commands.</p> <p>Igor 6 and later have an Analysis→Filter menu item which opens a Filter Design and Application dialog: <br> <img alt=FilterDesignAndApplicationDialog.png data-entity-type data-entity-uuid src=/sites/www.wavemetrics.com/files/FilterDesignAndApplicationDialog.png></p> <p>Another method for designing FIR and IIR filters is the <a href=/products/igorpro/ifdl> Igor Filter Design Laboratory </a> .</p> <h3><a href=/products/igorpro/dataanalysis/signalprocessing/leveldetection> Level Detection </a></h3> <p>Level detection is the process of locating the X coordinate at which your data passes through or reaches a given Y value. This is sometimes called "inverse interpolation". Stated another way, level detection answers the question: "given a Y level, what is the corresponding X value?"</p> <p>Igor provides two kinds of answers to that question. One answer assumes your Y data is a list of unique Y values that increases or decreases monotonically.</p> <p>The other answer assumes that your Y data varies irregularly, as it would with acquired data. In this case, there may be multiple X values that cross the Y level. Important examples of this are <a href=/products/igorpro/dataanalysis/signalprocessing/leveldetection#edgestats> edge </a> and <a href=/products/igorpro/dataanalysis/signalprocessing/leveldetection#pulsestats> pulse statistics </a> .</p> <p>A related, but different question is "given a function y = f(x), find x where y is zero (or some other value)". This question is answered by the <a href=/products/igorpro/analysisoffunctions/rootfinding> FindRoots </a> operation.</p> <p>To detect peaks; see <a href=/products/igorpro/dataanalysis/peakanalysis> Peak Analysis </a> .</p> <h3><a> Igor´s Signal Processing Commands </a></h3> <table><tbody><tr><td>area<td>areaXY<td>BinarySearch<tr><td>BinarySearchInterp<td>Convolve<td>Correlate<tr><td>CWT<td>Differentiate<td>DSPDetrend<tr><td>DSPPeriodogram<td>DWT<td>EdgeStats<tr><td>faverage<td>faverageXY<td>FFT<tr><td>FindLevel<td>FindLevels<td>Hanning<tr><td>HilbertTransform<td>IFFT<td>ImageWindow<tr><td>Integrate<td>Interp2D<td>Interp3d<tr><td>interp<td>PCA<td>PulseStats<tr><td>Rotate<td>Smooth<td>SmoothCustom<tr><td>Unwrap<td>WignerTransform<td> </table> </span></section><div class=clearit></div><section class=support-cta-wrapper><a class="support-column support-column-first"href=/forum> <img class=icon src=/sites/www.wavemetrics.com/files/styles/medium/public/fc-images-3-link/Artboard%206.png> <p>Forum</p> </a><a class=support-column href=/support> <img class=icon src=/sites/www.wavemetrics.com/files/styles/medium/public/fc-images-3-link/support.png> <p>Support</p> </a><a class="support-column support-column-last"href=/photo-gallery> <img class=icon src=/sites/www.wavemetrics.com/files/styles/medium/public/fc-images-3-link/Artboard%204_0.png> <p>Gallery</p> </a><div class=clearit></div></section><section class=product-cta-wrapper><a class="product-cta-column product-cta-column-first"href=/products/igorpro> <h3>Igor Pro 9</h3> <p>Learn More</p> </a><a class=product-cta-column href=/products/xoptoolkit> <h3>Igor XOP Toolkit</h3> <p>Learn More</p> </a><a class="product-cta-column product-cta-column-last"href=/products/nidaqtools> <h3>Igor NIDAQ Tools MX</h3> <p>Learn More</p> </a><div class=clearit></div></section></div><div class=clearit></div><footer class=site-footer><div class=clearfix role=complementary><section class=schema-organization itemscope itemtype=http://schema.org/LocalBusiness><div class=content-wrapper><h2 itemprop=name><span class=field-block-field-company-name> WaveMetrics </span></h2><p itemprop=description><span class=field-block-field-company-descri> Scientific graphic and data analysis software for scientists and engineers </span><div class="two-column two-column-first"><h3>Business Information</h3><h4>Hours:</h4><ul><li>Mon-Fri<li><meta content="Mo-Fr 09:00-17:00"itemprop=openingHours> 9:00 am - 5:00 pm</ul><h4>Phone Number:</h4><ul><li>Portland: <span itemprop=telephone> <a href=tel:> <span class=field-block-field-phone-number> (503) 620-3001 </span> </a> </span></ul><h4>Address:</h4><ul><li itemprop=address itemscope itemtype=http://schema.org/PostalAddress><span itemprop=streetAddress> WaveMetrics, Inc. 10200 SW Nimbus, G-7 </span> <span itemprop=addressLocality> Portland , OR </span> <span itemprop=postalCode> 97223 </span></ul></div><div class="two-column two-column-last"><h3>Support Information</h3><h4>Customer Support:</h4><ul><li>sales@wavemetrics.com</ul><h4>Technical Support:</h4><ul><li>support@wavemetrics.com</ul><h4>Mailing Address:</h4><ul><li>WaveMetrics, Inc. 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