You are building a heartbeat detector using a sensor that produces a voltage when the heart moves during a contraction. The circuit you are using to amplify the signal from this sensor has significant noise at 60 Hz (due to pick-up from the power lines). You decide to add a low pass filter to decrease the amplitude of this noise, so you can better resolve heartbeats in your signal. (a) At what frequency should you set the cutoff frequency of the low pass filter to achieve a 100 X reduction in the amplitude of the 60 Hz noise? [2 points] (b) If the fundamental period of the heartbeat signal is -1 s, by how much will this filter attenuate the fundamental frequency of the heartbeat signal? If the sensor produces a signal of about 1 V amplitude with each heartbeat, and you need the final signal, after filtering, to be greater than 0.25 V, is this filter attenuating the signal too much? [2 points] (c) To decrease the amount of attenuation at 1 Hz, you decide to use a two-poll low-pass filter. Your circuit now has a low pass filter, followed by an op-amp follower (buffer), and then a second low pass filter with the same values of R and C as the first filter. Draw a schematic of this circuit. Calculate the magnitude of for the whole circuit as a function of the values of R and C, and the frequency. [5 points] (d) Now, at what frequency should you set the cutoff frequency of this two-poll low pass filter to achieve a 100 X reduction in the amplitude of the 60 Hz noise? [2 points] (e) Now, at what frequency should you set the cutoff frequency of this two-poll low pass filter to achieve a 100 X reduction in the amplitude of the 60 Hz noise? [2 points] (f) If the fundamental period of the heart beat signal is ~1 s, by how much will this two-poll filter attenuate the fundamental frequency of the heart beat signal? If the sensor produces a signal of about 1 V amplitude with each heart beat and you need the final signal, after filtering, to be greater than 0.25 V, is this filter attenuating the signal too much? [2 points