Signals in Noise:

Let us now consider a weak information signal that is to be amplified by a noisy amplifier. The signal-to-noise ratio (SNR), usually expressed in decibels, becomes an important system performance measure. It is given by

where the amplified signal power is P_out = GP_in in the numerator, which includes source and amplifier noise given by Equation; P_in is the average power of the input signal; and the denominator Nout is the total output noise power given by Equation. Notice that the amplifier's power gainG does not appear in the final result of the SNR. Alarge SNR indicates that the signal is strong enough to mask the noise and possibly make the noise inconsequential. For example, with SNR ≥ 20 dB, intelligible voice communication results; otherwise, "static" in the voice signal; with SNR ≥ 50 dB, noisefree television image results; otherwise, "snowy" TV picture. For a good system performance, Equation suggests a large value of Pin and/or small values for T + T_a and B. However, one should be reminded here that the amplifier's bandwidth B should not be less than the signal bandwidth W. That simply means that with large-bandwidth signals, one would expect noise to be more troublesome.