Linear Filters for Removing Impulsive noise

[Master1022]

Homework Statement

Explain briefly why a linear filter would not be appropriate for removing impulsive noise in a signal, and suggest an alternative filter.

Relevant Equations

Linear Filters

Hi,

I was working on the following homework problem and just wanted to check whether my thoughts were along the right lines:
"Explain briefly why a linear filter would not be appropriate for removing impulsive noise in a signal, and suggest an alternative filter."

Attempt:
When we use a linear filter, which can be represented as a linear combination of a neighborhood of points, we are retaining information from the (impulsive) noise instead of completely removing it. <-- Is this the right reason why this isn't the right filter. The reason I think that is similar to why a gaussian filter isn't useful when dealing with salt and pepper noise in image processing.

It would instead be better to use a median filter. <-- Similarly, I just recall that median filters are optimal for removing salt and pepper noise due to the nature of the noise, and thus reasoned that they are best suited to this scenario as well. Is there a better filter for this purpose?

Does my reasoning seem like it is along the right lines?

Thanks in advance.

 

[tech99]

I should have thought that the filter has somehow to distinguish an impulse from an ordinary signal, and then try to reduce it. Maybe it could restrict the maximum rate-of-change between samples?

 

[rude man]

Depends on the freqency of the signal.
The response to even a 1st order linear filter is $e^-t/RC)$. So if the signal frequency were such that 1/f >>RC then theat filter would be fine.
So, my answer is the question has to be contextually elaborated.