$(50$ pts $)$ "Voltage$\_$measurement$\_$data.xlsx$"$ contains data points with different sampling frequencies.

$($a$)(20$ pts$).$ Plot the frequency content of a signal for each sampling frequency $(18,45,77,150,290Hz).$

$($b$)(15$ pts $)$ Find a minimum sampling frequency that can avoid aliasing errors. Justify your answer using the sampling rate theorem:

$f_{\text{p}\text{e}\text{r}\text{c}\text{e}\text{i}\text{v}\text{e}\text{d}}=|f-f_s\frac{N}{\text{I}}NT(\frac{f}{f_s})|$

$($c$)(15$ pts$)$ For the sampling data measured with a sampling frequency of $290$ Hz $,$ reduce the leakage error using the Hanning windowing method. Plot the resulting FFT graph alongside the FFT result obtained in part $($a$)$ for the $290$ Hz sampling frequency, and verify the reduction in leakage.