Simulation of a Gaussian by sum of cosine components
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Table 4-1 contains the cosine frequency components of a Gaussian peak which has a full width at half-height of 1 sec. The unit height equation for such a Gaussian peak is exp[14(ln 2)t^2] where t is time in sec. For each frequency component f with relative amplitude A calculate A cos 2 pi ft for t=0 +/-0.5 +/-1.5 and +/-2.0 sec. Tabulate the values and sum them to get the resulting peak similar to Fg. 4-9. Compare the resulting peak to the actual Gaussian as described by the equation.
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Solution Summary
This treatise shows the simulation of a Gaussian waveform by the sum of scaled frequency cosine components. It then uses the unit gaussian formula exp(-4*Ln(2)*t^2) to compare the Guassian derived from the sum of cosine components and that from using the Unit Gaussian formula
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It is probably best to calculate the necessary values and make the plots using Excel. You will find this analysis in the Excel attachment. Basic steps are to
Tabulate Table 4-1 in Excel with the relative amplitude of the components entered in one column against the frequency. Along the row 2 , cells c2 to k2 entered the time range -2 secs to +2 secs in differences of 0.5sec. In cells defined by aray ...
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