A voltage signal is produced by a transducer. The signal contains its strongest frequency component at 50 Hz (amplitude = 5.0 V), plus a weaker component at the second harmonic (100 Hz) with amplitude 2.0 V. In addition, there is noise at 60 Hz with amplitude 0.50 V, and some overall low-amplitude background noise at all frequencies. The voltage signal is measured with a digital data acquisition system. The sampling frequency is 80 Hz.
(a) Sketch the frequency spectrum that would be generated under these conditions. Be careful to add numbers to the frequency scale and voltage scale, and label each spike in the spectrum, explaining the origin of each spike.
(b) If a 6th-order low-pass Butterworth filter is used to attenuate the 100 Hz component, with a cut off frequency of 60 Hz, by how many dB will the 100 Hz component be attenuated?