Smoothing a discrete function with point wise variances
Other then the endpoints, this is really just an FIR filter. You can easily assess the impact of smoothing on the spectrum by looking at the Fourier Transform of the impulse response of the filter . In this case it's a notch filter which seems like an odd choice.

In general smoothing is in many cases similar or equivalent to a lowpass filter operation and will in general decrease high frequency content of the signal. The "best" choice of low-pass will always depend on your specific application and requirements.