9/14/2001
CS
461, Copyright G.D. Hager
The Gaussian Filter: A Better Noise Reducer
•Ideally, we would like an averaging
filter that removes (or at least attenuates) high frequencies beyond a
given range
•It is not hard to show that the FT of a
Gaussian is again a Gaussian.
Hence, it operates as a low pass filter.
•Note that in general, we truncate --- a
good general rule is that the width (w) of the filter is at least such that w
> 5 s. Alternatively we
can just stipulate that the width of the filter determines s (or vice-versa).
•Note that in the discrete domain, we
truncate the Gaussian, thus we are still subject to ringing like the box filter.
