Engineering Linear Filters for Removing Impulsive noise

AI Thread Summary
Linear filters are ineffective for removing impulsive noise because they retain information from the noise rather than eliminating it, similar to the limitations of Gaussian filters with salt and pepper noise. A median filter is recommended as it is optimal for this type of noise due to its ability to distinguish between impulse and ordinary signals. The discussion highlights the importance of context in selecting the appropriate filter, suggesting that the effectiveness of a filter can depend on the signal's frequency and characteristics. The need for a filter that can manage the maximum rate of change between samples is also mentioned. Overall, the conversation emphasizes the necessity of understanding the nature of the noise and the signal when choosing a filtering method.
Master1022
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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.
 
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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?
 
Depends on the freqency of the signal.
The response to even a 1st order linear filter is ## e^-t/RC) ##. So if the signal frequecy were such that 1/f >>RC then theat filter would be fine.
So, my answer is the question has to be contextually elaborated.
 
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