I am following this slide on FFT. On the last page, it says:


I would like to ask where $a = A(2)$ comes from. Thanks.

  • 5
    $\begingroup$ That's the definition of the binary expansion. $\endgroup$
    – Randall
    Jun 9 at 14:34
  • $\begingroup$ What are your thoughts? $\endgroup$ Jun 9 at 14:38

In base two, a number $b = b_{n-1}\dots b_0$ stands for $b = \sum_{i=0}^{n-1} b_i 2^i$.

Defining the polynomial $B(X) =\sum_{i=0}^{n-1} b_i X^i$, you have $b = B(2)$.

Note : in base $\beta$, the number $b = b_{n-1}\dots b_0$ is $B(\beta)$.

  • $\begingroup$ Thanks!!! This clarifies everything. I was wondering what happens if I swap $2$ with something else. $\endgroup$
    – CaTx
    Jun 9 at 14:47

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