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As someone who is new in working with filters, why do signals need to be averaged? What are the advantages, by performing filters on signals? As I know, there are different types of filters for signals, is there some sort of schema, which filter for which signal do I have to use?

I am sorry, if my question sounds somewhat ignorant, but I am having a hard time to understand it, especially since it is in another language. I am asking here on this forum, since I know there many experts here, who know more than me. If someone is able to explain it in a compact and easy way to explain, then you have my eternal gratitude.

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    $\begingroup$ Why do you think it's necessary to average signals? Why do you think that filters average signals? (Some do, others don't). The question which filter to use is not only determined by the signal itself but also by what you want to do with it. $\endgroup$ – Matt L. Feb 28 '17 at 13:46
  • $\begingroup$ From your present state of knowledge (as you outlined), I would suggest you better rephrase your question as: " What is a (digital) fllter, and how it works ? " to get much better responses. That's a too general question however and SE is not a replacement for online coursewares. Here people expect more specific questions based on existing knowledge about a particular topic. $\endgroup$ – Fat32 Feb 28 '17 at 14:06
  • $\begingroup$ @MattL., a very common class of filter, the Low-Pass Filter (it's sooo common that we use it as a prototype to design other filters) does average signals (and scales that average if the DC gain is something other than 0 dB). $\endgroup$ – robert bristow-johnson Feb 28 '17 at 20:08
  • $\begingroup$ question should be drawn out and improved, but i don't vote to close it. $\endgroup$ – robert bristow-johnson Feb 28 '17 at 20:10
  • $\begingroup$ @robertbristow-johnson: Yes, that's why I wrote in my comment "some do" (but also: "others don't"). $\endgroup$ – Matt L. Feb 28 '17 at 20:17
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An average is a summary of different values: if you have several signal processing exams, you know that both your answers and the grading person may incur some variability. On top of that, it is complicated to compare student, or the same student at different years, based on a series of grades.

So an average of grades both:

  • compacts different grades in one single number,
  • balances exam variability.

The latter is of first importance in signal processing: a signal sample may be disturbed by noise, sensor fluctuations, quantization, etc. While the signal is supposed to have some regularity, the disturbances are often chaotic, incoherent, from one sample to the other. If you average the distances alone, their amplitudes tend to diminish (not in all cases, but let us say that for now). So if close sample values are averaged, the ones from the signal don't change a lot (like a regular working student), while the disturbances reduce. Thus, the signal looks smoother, more pertinent. This is the basis for the linear filters: further, you can weight the samples differently.

The summarizing property is also important. You can average three samples, and keep the average only, and switch to the other sample triplet. This reduces the quantity of information, and is the basis for subsampling, data compression, etc. JPEG uses a lot of filtering and subsampling.

Both combined are the root of filter banks, putting several filters in parallel with subsampling. Then, you have nonlinear filters, but this is a whole new story.

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    $\begingroup$ Hello, I apologize for the late reply. A very interesting explanation you provided here. I was having trouble with understanding the concept of filtering in general, but I think, I got it. Thank you very much for helping this poor student. $\endgroup$ – CidelFastro Mar 1 '17 at 6:54
  • $\begingroup$ You can check online demos, like lifl.fr/~casiez/1euro/InteractiveDemo $\endgroup$ – Laurent Duval Mar 1 '17 at 8:34
  • $\begingroup$ @PPP Do not hesitate to upvote and accept the answer if it gave you satisfaction $\endgroup$ – Laurent Duval Mar 2 '17 at 21:03

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