$2\mathrm{.}30$ Represent the function

$e(t)=5sin31\mathrm{.}4t+2sin44t$

as a discrete set of $N=128$ numbers separated by a

time increment of $(\frac{1}{N}).$ Use an appropriate algo$-$

rithm to construct an amplitude spectrum from this

data set. $($using excel$)$

$2\mathrm{.}31$ Repeat Problem $2\mathrm{.}30$ using a data set of $256$ num$-$

bers at $t=(\frac{1}{N})$ and $t=(\frac{1}{2}N)$ seconds. Com$-$

pare and discuss the results$\mathrm{.}2\mathrm{.}30$ Represent the function e$($t$)=5$sin$31\mathrm{.}4$t$+2$sin$44$t as a discrete set of N$=128$ numbers separated by a time increment of $((1)/($N$)).$ Use an appropriate algorithm to construct an amplitude spectrum from this data set. $($Hint: A spreadsheet program or the program file DataSpect will handle this task.$)$