$(20$ points$)$ Design a lowpass Butterworth filter with the following specifications:

A desired peak passband ripple $R_p$ of $3$ dB $,$ the minimum stopband attenuation $R_s$ of $50$ dB $,$ the passband edge frequency ${}_p$ of $2000ra\frac{d}{sec},$ and stopband edge frequency ${}_s$ of $3300ra\frac{d}{sec}.$

$($a$)$ Estimate the order for this filter.

$($b$)$ Find the range of the cut$-$off frequency for this filter. please don't use ai