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What is the mathematics needed to delve in signal processing?

I don't know if it correct to dig toward purism downwards or stay at the applied level. Specifically, in complex analysis I find the $\varepsilon-\delta$ definition and limits.

I don't know whether am going to use them for next concepts in the book or not. I found that the word neighborhood has specific meanings in topology and analysis. do I need some pure math?

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    $\begingroup$ Welcome to the site! You asked in quite rapid succession several related questions. It might be better to wait a bit longer for answers and feedback before asking a new question. If you want to expand or clarfiy a question you can edit them. $\endgroup$
    – quid
    Commented Oct 8, 2014 at 21:53
  • $\begingroup$ How deep do you want to delve into signal processing? Some engineering courses sidestep most theoretical issues and rely mostly on calculus. $\endgroup$
    – J W
    Commented Oct 9, 2014 at 16:35
  • $\begingroup$ to understand limits and precise definition of limits and neighborhoods ... convergence , conformal mapping ..etc $\endgroup$
    – Eng_Boody
    Commented Oct 9, 2014 at 16:40
  • $\begingroup$ Is your choice of topics based on the answers to your question at dsp.stackexchange.com/questions/18280/study-signal-processing? $\endgroup$
    – J W
    Commented Oct 9, 2014 at 16:55
  • $\begingroup$ You may also wish to look at math.stackexchange.com/questions/617625/… on MSE. $\endgroup$
    – J W
    Commented Oct 9, 2014 at 16:58

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An important mathematical tool for signal processing is differential equations. Other necessary forms of math derive from this, including difference equations, transform theory, linear algebra, functional analysis, etc.

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