I want to figure out how much of my total noise is getting through my filter. To see this, I generated a noise vector, applied the filter, and measured the output variance. However, the output variance changes if I scale my filter (as would be expected). I suspected that I needed to normalize the DC gain to be one, but I'm not sure if that is the right approach. Here's my code:
noiseVector = randn(1,1e6); varOrig=var(noiseVector) filterCoeff = rcosdesign(0.2,10,12); filteredNoise1 = conv(noiseVector,filterCoeff); var1=var(filteredNoise1) filteredNoise2 = conv(noiseVector, filterCoeff/sum(filterCoeff)); var2=var(filteredNoise2)
There's a big difference between var1 ($\approx 1.00$) and var2 ($\approx 0.08$). Var1 would indicate that essentially all of the noise power was getting through the filter, but var2 would say that most of the noise is filtered out.
For my purpose of characterizing how much noise is getting through the filter, should I be using the normalized one (and is that normalization factor the right one)?