At work we were smoothing a signal by convolving with either
f1=[0.2000 0.2000 0.2000 0.2000 0.2000]
f2=[0.1111 0.2222 0.3333 0.2222 0.1111].
A colleague noticed that f1 smoothed "stronger" than f2 and suggested a new filter:
f3=[0.2727 0.1818 0.0909 0.1818 0.2727]
His reasoning was that this should smooth even "stronger" than f1, and therefore be better.
My answer to this was that
if he wanted "stronger" smoothing he should instead increase the size of the filter
a good smoothing filter should always approach zero at the start and beginning
My motivation for 2. was Gaussian filters which are often used for noise reduction in image analysis.
Is 2. correct?
Also because of the periodic nature of DFT does not f3 have the same frequency response as
f4=[0.0909 0.1818 0.2727 0.2727 0.1818],
which in turn should have a very similar frequency response as f2?
Edit: I followed Jim Clay's suggestion and zero padded and the result shows that f3 has terrible stop band ripple while f2 is quite OK in this respect:
Thanks in advance for any answers!