Question

The RMS random noise in a biosignal from a single measurement is 10.0mV. What the RMS noise would be in the averaged signal obtained from 16 repeated measurements of the same signal?

x_rms = [ Σ (x_n²) ]^(1/2), where n=1 to N

Answer 1

The RMS noise in the averaged signal obtained from 16 repeated measurements of the same signal can be calculated using the formula x_rms_avg = sqrt((1/N^2) * Σ(x_rms^2)), where x_rms is the RMS noise in a single measurement and N is the number of repeated measurements. In this case, N = 16 and x_rms = 10.0mV. Plugging in the values, the RMS noise in the averaged signal is 2.5mV.

Step-by-step explanation:

The root mean square (RMS) noise in the averaged signal obtained from 16 repeated measurements of the same signal can be calculated using the formula:

x_rms_avg = sqrt((1/N^2) * Σ(x_rms^2))

where x_rms is the RMS noise in a single measurement and N is the number of repeated measurements. In this case, N = 16 and x_rms = 10.0mV. Plugging in the values, the RMS noise in the averaged signal is:

x_rms_avg = sqrt((1/16^2) * 16 * (10.0mV)^2) = 2.5mV