If the SNR is 1:2, averaging 64 responses will improve the ratio to what?

When considering the improvement of the Signal-to-Noise Ratio (SNR) through averaging, it is essential to understand how averaging impacts both the signal and the noise levels. The original SNR of 1:2 indicates that the signal is half the magnitude of the noise, which can be expressed as a numerical ratio of 0.5.

When averaging 'n' responses, the noise is effectively reduced, as it adds up across the measures while the signal remains approximately constant. The improvement factor in the SNR through averaging is generally proportional to the square root of the number of averages taken.

In this case, if 64 responses are averaged, the noise is reduced by a factor of the square root of 64, which is 8. Therefore, the improvement in SNR can be calculated as follows:

1. Start with the original SNR of 0.5 (1:2).

2. When you average 64 responses, the noise level decreases by a factor of 8.

3. Hence, the new SNR becomes 0.5 * 8 = 4.

This translates into an SNR of 4:1, signifying that the signal has become four times stronger relative to the noise after