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Strain-Based Measurement Introduction:FIGURE 1-7. The Transfer Function:Qw(t) X H(w) = Q o (w)InputQ i (t)H 1 (w)H 2 (w)H 3 (w)H n (w)Outputf 1+ f 2 + f 2 =f nMagnitude H(w) = H 1 (w) X H 2 (w)........H n (w)And where the Phase Response is given by:Phase j(w) = j 1 (w) + j 2 (w) +........... j n (w)The total output of the measuring system is therefore:F out ( w) = H( w)F in ( w)(EQ 1-5)and the total Phase Response is given by:j out ( w) = j( w) + j in ( w)(EQ 1-6)Although convolution defines a specific mathematical operation in time andfrequency domain analysis, equation 1-5 (Figure 1-8) can be thought of as theconvolution of the input signal with the transfer function of the sensor system.The reverse process, where the output function of the system is divided by thetransfer function, can be thought of as deconvolution and is expressed as:F in (w) = F out (w)/ H(w)CHAPTER 1-22 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-6:and where:j in (w) = j out (w) - j(w)FIGURE 1-8. Convolution and Deconvolution:F in(w)H(w)F out (w)CONVOLUTION:F out(w) = H(w) X F in (w)DECONVOLUTION:(Data Reduction)F in (w)=F out (w)H(w)Convolution occurs during the process of measurement and deconvolution is theprocess of the data reduction. Most data reduction difficulties come from thedeconvolution of collected data with the defined transfer function of the measurementsystem.The convolution function applied to spectral analysis of data is a very well-definedcomplex mathematical process where convolution in the time domain is equivalentto multiplication in the frequency domain. The relationship between convolutionand multiplication in the two domains allows the use of the convolution function tocompute transfer functions and time domain outputs of digitally-implemented signalfiltering routines.The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-23
Page 1 and 2: The Art of Practical andPrecise Str
Page 3 and 4: Special Credits:Mrs. Helen Pierson,
Page 5 and 6: Table of ContentsBy James G. Pierso
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Page 10: ContentsCHAPTER 8Electrical Conside
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