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I was reading circular convolution topic from Digital Signal Processing Using Matlab 3rd Ed,by Proakis. I came across a strange term/symbol; I have highlighted it in attached snapshot

Update:Pg150; same chapter,same book(just before example 5.4) contains this notation and mentions that it is a rectangular window of length N

I have also attached snap of eq 5.24,in 2nd snap, where this RN(n) symbol appears also:

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    $\begingroup$ Can you give a little more context on the topic being explained here? By looking at just this I can only imagine that this term represents $n^{th}$ component of a Vector in N dimension, usually represented as $\mathcal{R}^N$ $\endgroup$
    – DSP Rookie
    Jun 20, 2020 at 11:44
  • $\begingroup$ Proakis / edited multiple books, in multiple revisions. Which one is this, which page? $\endgroup$
    – Marcus Müller
    Jun 20, 2020 at 11:53

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This symbol denotes a rectangular pulse of length $N$:

$$\mathcal{R}_N(n)=\begin{cases}1,&0\le n\le N-1\\0,&\textrm{otherwise}\end{cases}$$

I'm not sure where it is defined for the first time, but this definition is clear from the equation above Eq. $(5.24)$ on page $130$ of the 3rd edition of Digital Signal Processing Using Matlab by V.K. Ingle and J.G. Proakis.

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  • $\begingroup$ I have attached snap of eq 5.24 ,but sorry for that equation is bit different from your $\endgroup$
    – DSP_CS
    Jun 20, 2020 at 14:09
  • $\begingroup$ @engr: I don't see how it's different. If you interpret $\mathcal{R}_N(n)$ as in my answer, it matches exactly the equation given in the book. $\endgroup$
    – Matt L.
    Jun 20, 2020 at 14:49
  • $\begingroup$ Because apparently the equation involves product of RN(n) & X(k) . Beacuse RN(n) is not alone $\endgroup$
    – DSP_CS
    Jun 20, 2020 at 17:06
  • $\begingroup$ @engr: That's right, but from the equation you can infer what is meant by that symbol. $\endgroup$
    – Matt L.
    Jun 20, 2020 at 17:11
  • $\begingroup$ Yes, i understood, that is why, i clicked accept answer $\endgroup$
    – DSP_CS
    Jun 20, 2020 at 17:31

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