Note that unlike the sinusoid it makes little sense to talk about a peak
amplitude when describing gaussian noise. This is because there are many peak
amplitudes and any one is not representive of the amplitude of the noise
overall. How should we measure the amplitude of a gaussian noise? We can't
take the average of the instantaneous amplitudes since negative and positive
values always cancell yielding an average value of zero. To prevent this we square each amplitude making all values positive. We then take the
square root of the average of the squared values to get back to an amplitude
measure. The resultant measure is refered to as the root-mean-square or RMS
amplitude. The RMS amplitude is a more commonly accepted measure of amplitude
because it applies to periodic sounds like sinusoids as well as to noise. The
computational formula for RMS is
where, p refers to an instantaneous amplitude or pressure value, and N refers to the number of these values in the time waveform.
Alright - don't panic, there's a simple way to remember how to compute RMS. Just remember the letters and work backwards.
Step 1: S - square, square all values of amplitude.
Step 2: M - mean, take the mean of the squared values.
Step 3: R - root, take the square-root of the mean.
We'll do a problem in class.