Smooth Part of a Wave

I have a 1d wave which gets noisier as the index increases. If I use the same smoothing throughout the wave, there are features at low indices that get washed out. Can I weight the smoothing to only affect the part of the wave with higher index?
You could use the Interpolate functionality which can incorporate a smoothing factor and a standard deviation wave. You'll need to make a wave with the same number of points that has an increasing "standard deviation" value as the index increases. For example if your source wave is "wave0", then you could create a "wgtWave" using Make/O/N=(numpnts(wave0)) wgtWave=p/100. Under Analysis-Interpolate, choose that wave as your Std Dev. You'll have to come up with reasonable estimates for the standard deviation scaling or play around with the smoothing factor.