When using an atomic force microscope, it is essential that the scope base be as stable as possible. This problem addres
Posted: Wed May 11, 2022 9:58 am
When using an atomic force microscope, it is essential that the
scope base be as stable as possible. This problem addresses two WSS
discrete-time random process models for the vibration, X(k), of the
base. a) Assume that X(K) is zero mean white noise with variance of
=9. What is the autocorrelation process Rz(m), and the PSD Sz(@for
X(K)? b) Now assume that X(K) is a zero-mean, AR process with
variance oi=9. Specifically, assume that: X(k)=0.8X(k-1)+W(k) where
MCK) is a white-noise process. Compute RalO) and Ral1). What is the
variance of the white noise process WC)? c) If you were to plot a
sample realization of both models (from parts a) and b)), which
model would you expect to vary more slowly? Explain why.
Specifically, request part c. Parts a and b are already answered
elsewhere, but not c.
scope base be as stable as possible. This problem addresses two WSS
discrete-time random process models for the vibration, X(k), of the
base. a) Assume that X(K) is zero mean white noise with variance of
=9. What is the autocorrelation process Rz(m), and the PSD Sz(@for
X(K)? b) Now assume that X(K) is a zero-mean, AR process with
variance oi=9. Specifically, assume that: X(k)=0.8X(k-1)+W(k) where
MCK) is a white-noise process. Compute RalO) and Ral1). What is the
variance of the white noise process WC)? c) If you were to plot a
sample realization of both models (from parts a) and b)), which
model would you expect to vary more slowly? Explain why.
Specifically, request part c. Parts a and b are already answered
elsewhere, but not c.