q4_additivity_soln

q4_additivity_soln - 16.881 – Robust System Design...

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Unformatted text preview: 16.881 – Robust System Design Solution to Quiz #4 S/N Ratios & Additivity 1) (25%) An increase in 6dB in the nominal-the-best S/N ratio always indicates a) A reduction by about 50% in the standard deviation of the response. b) A reduction by about 50% in the variance of the response. c) An increase by about 400% in the mean of the response. d) An approximate four fold increase in the ratio of mean squared and variance. d is the correct answer. The nominal the best signal to noise ratio is defined as η = 10log 10 µ 2 σ 2 where µ is the mean of the response and σ is the standard deviation of the response. Let’s say we have a product with a signal to noise ratio of η 1 a mean of µ 1 and a standard deviation on σ 1 . Let’s also say that, through robust design, the signal to noise ratio was increased by 6dB and that this robust product has a mean of µ 2 and a standard deviation on σ 2 . η 1 = 10log 10 µ 1 2 2 η 1 + 6 = 10log 10 µ 2 2 2 σ 1 σ 2 Subtracting the first equation from the second gives 2 6 = 10log 10 µ 2 2 2 − 10log 10 µ 1 2 2 = 10log 10 µ 2 2 σ 2 σ 2 σ 1 µ 1 2 σ 1 2 Therefore 2 2 6 µ 2 2 σ 2 2 = 10 10 ≅ 4 µ 1 σ 1 So, the ratio of mean squared and variance must increase by a factor of approximately...
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q4_additivity_soln - 16.881 – Robust System Design...

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