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Question: 1 numrical derivative since the time of bernoulli differentiation has...

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1. Numrical derivative: Since the time of Bernoulli, differentiation has been approximated using sampled signals. Consider a difference equation appearing in the American Journal of Cardiology, 1991; 67: 965 975 Let (seconds) be the period between uniformly-spaced samples. Data, {리지), are post-processed to approximate a derivative. Quoting from the paper: The dcrivative at timc nT is approximated by a wcighted sum of finite diffcrcnccs: onc-half timcs the difference of the values one sample ahead minus one sample behind, plus one-eighth times the difference of values two samples ahead minus two samples behind (a) Write an input-output relationship rclating the approximate derivative, vin], to the input, n. (b) Is the system relating r[n] and vn linear? (e) Is the system relating rin) and vinl) time-invariant? (d) Is the system causal? (c) Is the system stablc? (f) What is the system impulse response? (g) What is the zero state response of the system for the input 50n - 2]?

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