A measurement with a signal-to-noise ratio of 100/1 can be thought of as a signal, S, with 1% uncertainty, e. That is, the measurement is S ± e = 100 ± 1.
(a) Use the rules for propagation of uncertainty to show that, if you add two such signals, the result is total signal = 200 ± √2 , giving a signal-to-noise ratio of 200/√2 = 141/1.
(b) Show that if you add four such measurements, the signal-to-noise ratio increases to 200/1.
(c) Show that averaging √n measurements increases the signal-to-noise ratio by a factor of 1n compared with the value for one measurement.