91Ó°ÊÓ

• The signal-to-noise ratio (SNR) is calculated by dividing the mean value of a signal (S) by the background standard deviation (N).
• When S/N falls below 2 or 3, the signal becomes impossible to see.

(a)

When it combine two of these signals, it get:

$100Â\pm 1+100Â\pm 1-200Â\pm √2$

where the uncertainty is determined:

$$\begin{gathered} e=\sqrt{e_1^2+e_2^2} \\ e=\sqrt{1^2+1^2} \\ =\sqrt{2} \end{gathered}$$

The signal-to-noise ratio is calculated as follows:

$\frac{200}{\sqrt{2}}=\frac{141}{1}$

(b)

When four of these measurements are added together, it get:

$100Â\pm 1+100Â\pm 1+100Â\pm 1+100Â\pm 1-400Â\pm 2$

where there is uncertainty:

$$\begin{gathered} \mathrm{e}=\sqrt{{\mathrm{e}}_1^2+{\mathrm{e}}_2^2+{\mathrm{e}}_3^2+{\mathrm{e}}_4^2} \\ \mathrm{e}=\sqrt{1^2+1^2+1^2+1^2} \\ =2 \end{gathered}$$

The signal-to-noise ratio is calculated as follows:

$\frac{400}{2}=\frac{200}{1}$

(c)

The signal to noise ratio of the initial measurement is:

$\frac{100}{1}$

As a result, the average signal is as follows:

role="math" localid="1663653596294" $\frac{\mathrm{n}×100}{\mathrm{n}}×100$

The average amount of noise is:

$\frac{\sqrt{\mathrm{n}}}{\mathrm{n}}=\frac{1}{\sqrt{\mathrm{n}}}$

The average signal to average noise ratio is:

$\frac{100}{\sqrt{\mathrm{n}}}=100×\sqrt{\mathrm{n}}$