$1.$ Design a first order, low pass active filter with a cutoff frequency of $\backslash (10\backslash$mathrm$\{$krad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Determine reasonable values for the resistor and capacitor $-$ elements that you can purchase or find easily. Obtain the transfer function and show a circuit schematic for your filter. Find the Bode plot for your filter using Matlab.

$2.$ Cascade three of the filters designed in part $1$ and repeat the instructions for part $1.$

$3.$ Now, make corrections to your design to account for the shift in cutoff frequency due to higher order filters. What is the new design and new transfer function to obtain your design cutoff $(\backslash (10\backslash$mathrm$\{$krad$\}/\backslash$mathrm$\{$sec$\}\backslash ))$ from part $1$ with a third order filter? Find the Bode plot for the new filter

$4.$ The Butterworth filter has several advantages over the cascaded $\backslash (3^\{\backslash$text $\{$rd $\}\}\backslash )$ order filter. Design a third order Butterworth filter with the same cutoff frequency. Show the transfer function, the circuit schematic for your filter. Model the filter on Matlab. Compare with the filter in part $2$ by plotting both Bode plots on the same plot.