a. Provide a rough estimate of the heart rate in bpm based on this diagram QRS 0

Question

a. Provide a rough estimate of the heart rate in bpm based on this diagram QRS 05 P -0.5 0 6 10 Time (s) b. Assuming that the noise is white noise (broadband) and the frequency content of the QRS complex (the sharpest, biggest peaks as labelled above) extends from 10-30 Hz, describe in words how you might approach improving the signal quality to improve your ability to locate heartbeat peaks. c. If the noise were not white noise, but were instead interference from nearby fluorescent lights and were focused at 120 Hz, what other options might you use for filtering out these artifacts? d. Design your filters from b. and c. in MATLAB and plot the impulse response for both. Plot the magnitude and phase response. Explain all design choices you made.

Explanation / Answer

You can generate band-limited Gaussian noise. I'm not sure what you mean by "...signal ranging from 0 to 3 with a frequency of 0-6Hz", so I'll assume that you want a passband of 0 to 6 Hz. You did not tell us your sampling frequency, I'll assume 100 Hz.

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance 2cn(t)cn2(t) and you want sample it at rate of fsfs you should generate discrete noise samples with variance of fs2cnfscn2.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of fs/2fs/2.

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