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VLSI_Class_Notes_1_Statistical_Analysis_for_ICs

VLSI_Class_Notes_1_Statistical_Analysis_for_ICs - EEL 5322...

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EEL 5322 W.R. Eisenstadt STAT, 1 Statistical Analysis for ICs: Review (hopefully) Arithmetic Mean, μ (measure of tendency) = = 1 0 ) ( 1 N n n x N μ Where x (n) is a sampled data set n= 0, 1, 2, 3,…, N-1 Standard Deviation, σ (measure of uncertainty) [ ] = = 1 0 2 ) ( 1 N n n x N μ σ Variance, σ ² - square of standard deviation For an IC process with many inputs with different standard deviations, total standard deviation, σ Total becomes: Input 1 = σ 1 Input 2 = σ 2 Input n = σ n Total variance, σ ² Total = σ ² 1 + σ ² 2 + … + σ ² n Total Standard Deviation, σ Total 2 2 2 2 1 ... n Total σ σ σ σ + + + = For a signal with the DC component subtracted. [ ] = = 1 0 2 ) ( 1 N n n x N RMS Signal Page 1 of 3
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EEL 5322 W.R. Eisenstadt STAT, 1 Probabilities and Probability Density Functions Central Limit theorem: Distribution of a set of random variables; statistically independent, becomes large (N>30) tends toward a Gaussian distribution. Happens whether or not the individual distributions are Gaussian.
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