Question

If the average of 20 measurements of a signal provide a S/N ratio of 3.30, how many measurements would be required to improve the S/N ratio to 6? Hint: Assuming a Gaussian noise distribution, the standard deviation of the mean improves with the square root of the number of measurements.

Answer 1

S/N ratio is directly proportional to square root of number of measurements

$\frac{\left ( \frac{S}{N} \right )_{2}}{\left ( \frac{S}{N} \right )_{1}}=\sqrt{\frac{n_{2}}{n_{1}}}$

$n_{2}=n_{1}\times \left [ \frac{\left ( \frac{S}{N} \right )_{2}}{\left ( \frac{S}{N} \right )_{1}} \right ]^{2}=20\times \left (\frac{6}{3.3} \right )^{2}=66.12\simeq 66$