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# Analysis of sampled output of non linear system

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The input output relation of a non linear system is y(t) = x(t)^2, the signal x(t) is band limited to Omega(max) = 2000*pi rad/s, it is shown if the output signal y(t) is band limited at all based on this scenario

Further the output y(t) is low pass filtered with magnitude of unity and cut off Omega(c) = 5000*pi rad/s. The required sampling period Ts is determined from this information

Finally an investigation is carried out to find if there is another value of for Ts that could be used to maintain the Nyquist criteria for sampling

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https://brainmass.com/engineering/electronic-engineering/analysis-of-sampled-output-of-non-linear-system-431353

#### Solution Preview

The input output relation of a non linear system is y(t) = x(t)^2, the signal x(t) is band limited to Omega(max) = 2000*pi rad/s, it is shown ...

#### Solution Summary

The input output relation of a non linear system is y(t) = x(t)^2, the signal x(t) is band limited to Omega(max) = 2000*pi rad/s, it is shown if the output signal y(t) is band limited at all based on this scenario

Further the output y(t) is low pass filtered with magnitude of unity and cut off Omega(c) = 5000*pi rad/s. The required sampling period Ts is determined from this information

Finally an investigation is carried out to find if there is another value of for Ts that could be used to maintain the Nyquist criteria for sampling

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## One-way analysis of variance (ANOVA), first with a fixed effects model, then with a random effects model. The tool for the analysis was SAS.

An experimenter wants to determine which of four seat-belt designs provide the best protection from a head-on collision. Simulated accidents are performed by four manufactures. The observations are a composite index of passenger injury. For alpha= 0.15, test for significant difference in design.

Design 1: 37, 42, 45, 49, 50, 45
Design 2: 49, 38, 40, 39, 50, 41
Design 3: 33, 34, 40, 38, 47, 36
Design 4: 41, 48, 40, 42, 38, 41

a)
1) Define linear models and corresponding assumptions (write down the formula in Greek)
2) Check (write) assumptions
3) State and test hypothesis using the S-method (Scheffe), exploratory analysis- Summarize your findings.
4) Use Tukey's method to study significance of designs. Summarize your findings.
5) Analyze the data assuming one is only interested in two planned design.

b) Re-analyze the given data assuming the treatments are sampled from a population of treatments. (One way random ANOVA model)
Review model assumptions, state model, analyze the data and perform post hoc analysis.

NOTE: I need only explanations, hypothesis, model, etc. to be written down. The calculation parts needs to be done in SPSS (or SAS), and I need SPSS (or SAS) outputs, (and SAS codes) too.

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