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by: Rosie Zieme

LinearSystemsI EE321

Rosie Zieme
GPA 3.74


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Class Notes
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This 7 page Class Notes was uploaded by Rosie Zieme on Thursday October 29, 2015. The Class Notes belongs to EE321 at Wright State University taught by FredGarber in Fall. Since its upload, it has received 29 views. For similar materials see /class/231091/ee321-wright-state-university in Electrical Engineering at Wright State University.

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Date Created: 10/29/15
makeconvnb Make Your Own Convolution by H Joel Trussell Dept of Electrical and Computer Engineering North Carolina State University Raleigh NC 276957911 email hjtecehjtncsuedu This notebook let you create your own function and convolution kernel with which to demonstrate convolution I Initialization In1 makeE unctionx Block mr1yl ngthEXJ m Le n 1 Y Xll Fori2iltmi IfXil Yr1l gt 001 then y AppendEyxiF r1 n1 Return Y P makeconvnb I Make Your Function Enter your function on the graph below Click once in the graph area to set the frame around the axes To draw you function hold down the Command key and the left button on the mouse as you move the mouse The points will appear on the graph You can repeat the process until you have the graph you want Next press ltCommandgtc hold the Command key while pressing the c key to copy the point pairs that define your function A function fX will be defined using those pairs This calls for you to alter the command in the Mathematica file by deleting any preVious lists of points after inserting the list you have just copied Insert the list in the place indicated below ListPlot lO 5105 iGraphicsi makeconvnb insert list of point pairs after the sign for the variable x below x 2954321 0045341 2055959 0590436 123246 0015225 0858143 074202 0109508 1771645 0189947 1953344 0788855 2195609 13129 1468814 1836945 074202 2435853 0105907 3558805 0893268 385826 0832702 4157714 0529871 4532032 0408738 4681759 0105907 fs makeFunctionx eliminate points with duplicate abscissa values f InterpolationfsInterpolationOrder gtl defines the function fx fxmin MinTablefsi1iLengthfs fxmax MaxTablefsi1iLengthfs ListPlotTabletfttfxminfxmaxfxmax fxmin128 PlotJoined gtTrue PlotLabel gt quotFunction in Time Domainquot Function in Time Domain 7Graphic57 I Make Your Kernel Just as you de ned your function now define the kemel or impulse response that characterizes your system Notice that the scale has been changed This re ects the fact that most impulse responses are much shorter that the signals that are processed makeconvnb ListPlotH 2 12l l makeconvnb insert list of point pairs after the sign for the variable x below x 0014924 0021111 0029847 0081478 0029847 0129771 0029847 0190138 0029847 0250504 0029847 0298797 0029847 0359164 0029847 0407457 0029847 0467823 0029847 0516116 0029847 0588556 0059694 0660996 0059694 0709289 008954 0757582 0134311 0709289 0164158 0660996 0194005 0612702 0223851 0564409 0253698 0516116 0298468 0467823 0343239 041953 0402932 0371237 047755 031087 0537243 027465 0596937 0238431 0656631 0202211 0761095 0165991 0820788 0117698 0895405 0093551 0970022 0057331 1059563 0033185 1119256 0009038 117895 0003035 1238644 0003035 hs makeFunctionx eliminate points with duplicate abscissa values h InterpolationhsInterpolationOrder gtl defines the function fx hxmin MinTablehsi1iLengthhs h max MaxTablehsi1iLengthhs ListPlotTabletht thxmin0001hxmax 0001hxmax hxmin 0002128 PlotJoined gtTrue PlotLabel gt quotImpulse Response in Time Domainquot Impulse Response 11 Time Domain sGraphicss I Compute Your Convolution The following commands set up the product for the convolutional integral and perform the integration For the Interpolation function to yield the proper values in the range of the integral the function must be defined over the entire range of the integral We de ne it zero in the regions where you have not defined it makeconvnb If hxmin lt 0 fsx else fsx fs If hxmax gt 0 fsx Joinfxminhxmin02 fxminhxmin20fs Joinfsx 2 fxmax hxmax20fxmaxhxmax0 f InterpolationfsxInterpolationOrder gtl If fxmin lt 0 hsx Joinfxminhxmin0fxmin2 hxmin20hs else hsx hs If fxmax gt 0 hsx Joinhsx fxmax 2hxmax20fxmaxhxmax0 h InterpolationhsxInterpolationOrder gtl lowerLim upperLim deltaT df fxminhxmin fxmaxhxmax upperLim lowerLim255 TablefttlowerLimupperLimdeltaT db TablehttlowerLimupperLimdeltaT If lowerLim lt 0 nshift Floor lowerLimdeltaT nshift dhs dh Fori0iltLengthdhidhsil CircularFFTxh 0 dhModinshiftLengthdhlF BlockNxNhNyxpadhpad FFTxpadFFThpadFFTy Nx Lengthx Nh Lengthh IfNx Nh PrintquotSignals are not same lengthquot Return Ny Nx FFTX FFTh FFTy Fourierx Fourierh FFTX FFTh y NSqrtNy InverseE ourierE E Ty ReturnReY dy CircularFFTdfdhs Plot Results of convolution makeconvnb timeAxis TablettlowerLimupperLimdeltaT Show GraphicsArray Plotfunction ListPlot TransposetimeAxisdf PlotJoined gtTrue quotFunction in Time Domainquot DisplayFunction gtIdentity PlotRange gtAll Plotkernel ListPlot TransposetimeAxisdh PlotJoined gtTrue PlotLabel gt quotImpulse Response in Time Domainquot DisplayFunction gtIdentity PlotRange gtAll Plotresult ListPlot TransposetimeAxisdy PlotJoined gtTrue PlotLabel gt quotOutput of Convolutionquot DisplayFunction gtIdentity NullPlot ListPlot lO 5105 DisplayFunction gtIdentity DisplayFunction gt DisplayFunction Function in Time Domain Impulse Response in Time Domain of Convolution 2 4 6 iGraphicsArrayi


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