4. (10 pt) A transducer measuring pressure needs to respond to oscillations up to 3 Hz but is contaminated by 60 Hz noise. To reduce the 60 Hz noise, a student wants to design a low pass Butterworth filter having a passband of 0 to 3 Hz with 3 Hz cutoff frequency. 4-1) (5pt) If the student wants to attenuate all frequencies at and above 10 Hz by at least 30 dB, what is the required number of filter stages? Determine the minimum number of the filter stage. 4-2) (5pt) If the filter stage determined by 4-1) is used, how much is the amplitude of the 0 Hz noise attenuated? How much is the amplitude of the 60 Hz noise attenuated if the student uses a first order low-pass Butterworth filter?