hardware//electronics//signal-to-noise ratio
The signal-to-noise ratio (SNR) compares the size of the signal a measurement wants with the size of everything else it picks up, and it decides whether a faint event can be told apart at all: a spike of 50 µV is easy to find over 5 µV of noise and lost under 50.
The signal-to-noise ratio (SNR) compares the size of the signal a measurement wants with the size of everything else it picks up, and it decides whether a faint event can be told apart at all: a spike of 50 µV is easy to find over 5 µV of noise and lost under 50.
Noise is any electrical variation that does not belong to the signal. It comes from the thermal agitation of charges in every resistance, from the transistors of the amplifier (whose noise grows at low frequencies), from electromagnetic interference such as the mains and nearby equipment, from movement of the sensor and, in biology, from all the other cells. In its simplest form the ratio is
SNR=AsignalAnoise,SNRdB=20log10AsignalAnoise\mathrm{SNR} = \frac{A_{\text{signal}}}{A_{\text{noise}}}, \qquad \mathrm{SNR}_{\text{dB}} = 20 \log_{10} \frac{A_{\text{signal}}}{A_{\text{noise}}}SNR=AnoiseAsignal,SNRdB=20log10AnoiseAsignal
with amplitudes; a ratio of 10 is 20 dB.
Amplification never improves the ratio; it can only keep it.
An amplifier multiplies signal and noise alike and adds noise of its own, so the first stage, the closest to the sensor, sets the best ratio the whole chain will ever have.
Bandwidth lets noise in. Thermal noise grows with the root of the bandwidth, vn=4kTR Δfv_n = \sqrt{4kTR,\Delta f}vn=4kTRΔf, so an analog filter that keeps only the frequencies of the signal raises the ratio for free.
Averaging buys ratio with repetitions. Averaging NNN recordings of the same event lowers random noise by N\sqrt{N}N, which works for a repeated stimulus and not for an event that happens once.
More bits cannot help past the noise. An analog-to-digital converter finer than the noise only records the noise in more detail, which is why the ratio, and not the resolution, is the number to quote.