If your initial signal amplitude is 0.5 uV inside a background noise level of 2 uV, what will the signal-to-noise ratio (SNR) be after 400 averages?

To determine the signal-to-noise ratio (SNR) after averaging, it’s important to understand how averaging affects both signal and noise levels. The SNR is calculated as the ratio of the signal amplitude to the noise level. Initially, you have a signal amplitude of 0.5 microvolts (uV) and a background noise level of 2 uV.

When averaging the data, the noise level decreases, while the signal remains unchanged. The noise reduction via averaging is determined by the square root of the number of averages taken. Specifically, as you average more samples, the noise is reduced according to the formula:

Noise after averaging = initial noise level / √(number of averages)

In this case, with 400 averages, the noise will be reduced to:

Noise after 400 averages = 2 uV / √400 = 2 uV / 20 = 0.1 uV

Now we can calculate the SNR after 400 averages:

SNR = Signal amplitude / Noise after averaging

SNR = 0.5 uV / 0.1 uV = 5

This results in a signal-to-noise ratio of 5, making the correct answer the choice that reflects this