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# 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 Preview

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 ...

#### 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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