1. The figures in this question are extracts from a US Patent for a wearable heart rate monitor'. a) Referring to the text highlighted in Figure Q1a, and using suitable illustrations to support your answer, explain why a notch filter is employed. (0) 90. The function of this block is to remove high and low 35 bandpass fl frequency noise from the digital samples. The digital filtering steps represented by block 90 comprises, in the preferred embodiment, a first step of low pass filtering the incoming digital data with a low pass filter 40 having a notch at 60 Hertz and then passing the resulting filtered data through a bandpass filter which amplifies the signals in a frequency range from 10-40 Hertz and has a notch at 60 Hertz. The reason a low pass filtering step is used prior to passing the data through the low pass filter is to 45 remove remaining high frequency components in the incom- ing data prior to passing the signals through the bandpass filter for amplification and further filtering. FIG. 8 represents the frequency response of the preferred embodiment for the digital low pass filter implemented by so the preferred embodiment of the digital filtering step 90 in G7. This digital filtering is achieved by implementing a filter response frequency thereb also that although 97 at the low freq rolloff at the low i at the low frequ response is only 2 low frequency con data. Returning to the processing repres performed, two dil EKG signal in the only the enhance block 92 is perfo matching or cross native results whic 5 Figure Qla b) Referring to the highlighted ECG signal in Figure Q1b, suggest a suitable value for the fundamental frequency, and suggest an appropriate sampling rate to digitise and display the ECG signal. Show how the original continuous time signal could be recovered. N.B. the numbers on the axes in Figure Q1b are not in units of time. 5 FIG. 6C FIG. 6D FIG. 6E Figure Q1b Use suitable sketches and explanations throughout to provide a coherent answer. c) Referring to the text highlighted in Figure Q1c, use your understanding of autocorrelation to explain how it could be applied to a discrete time signal to estimate the signal's fundamental frequency. 5 is autocorrelation as exemplified in U.S. Pat. No. 5.365.934. In this patent, the EKG signal is sensed by probes which are typically mounted on the handles of exercise equipment 35 which the user grabs while exercising. The signals sensed by these probes, which contain the EKG signal. are passed through an autocorrelator which performs a correlation calculation between a piece of the signal represented by one buffer's worth of digital samples and an adjacent portion of 40 the signal in time represented by another set of samples. Signal indication logic monitors the output of the autocor- relator for the presence of a periodic signal and generates a synthetic candidate heart rate signal that has the same frequency as the periodic signal in the output of the auto- 45 correlator. The difficulty with this approach is that the EMG signals are also periodic and will cause peaks in the auto- correlator output that do not represent periodic EKG signal. In one embodiment, the signal indication logic has logic hich detects a pulse in the autocorrelation signal which has 50 heart rate is characteristics learned by correl with a prestored signal. A paramet to examine the o represents a ORS (ORS is a term of signal), an interv recognitions of Ol consistent with w interval judge out average interval ti averages the rate i Righter also te user how good or based upon the si Also, the center fre Figure Q1c d) Use your understanding of autocorrelation to explain how it could be used to estimate the energy of a discrete time energy signal. 5 e) Use your understanding of system properties to characterise the two systems expressed mathematically in the highlighted section Figure Qle, in terms of causality, linearity, time invariance, and memory. 5 4 FIG. 15. C FIG 16. Figure Que