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I assume I have the length of such vector $y$ is $N$. In the first time I divide that vector into two columns and then sum them point-wise summation. The second time, I divide the same vector $y$ into four columns and then sum them. Then, I divide $y$ into eight columns and sum them. I need to mathematically find the number of additions for that operation in function of $N$ and number of divisions. Assume that number of divisions is $l$.

Example

The vector $y$ with length $N= 64$, and $l = 4$.

$l = 1$, $y$ will be divided into two vectors of length $32$ and number of additions are 32;

$l = 2$, $y$ will be divided into four vectors of length $16$ and number of additions are 48;

$l = 3$, $y$ will be divided into eight vectors of length $8$ and number of additions are 56;

$l = 4$, $y$ will be divided into sixteen vectors of length $4$ and number of additions are 60;

So how can I express the total number of real addition mathematically in function of $l$ and $N$

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    $\begingroup$ I’m voting to close this question because it does not seem to be about signal processing. $\endgroup$
    – MBaz
    Jul 4 at 13:48

1 Answer 1

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The number of additions is just the length of the individual vectors times their number minus $1$:

$$\textrm{number of additions}=N\cdot\frac{2^l-1}{2^l}$$

Of course we assume that $N$ is a power of $2$, and $2^l\le N$.

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