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1

Your first formula in your question is generally wrong, that's why you can't prove it. The correct formula is $$\sum_{n=-\infty}^{\infty}x[n]y^*[n]=\frac{1}{2\pi}\int_{-\pi}^{\pi}X(e^{j\omega})Y^*(e^{j\omega})d\omega\tag{1}$$ which is just Parseval's theorem. If $x[n]$ and $y[n]$ are real-valued, $(1)$ can be written as $$\sum_{n=-\infty}^{\infty}x[n]y[n]... 4 Two codewords c_1 and c_2 of length n, with elements in \lbrace +1, -1 \rbrace, and Hamming distance d, have a cross-correlation given by$$(n-d) -d = n-2d. The reason is that there are $n-d$ bits that are equal and their product is $1$, and $d$ bits that are different and their product is $-1$. Note that: The larger the distance $d$, the ...

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Well, as you can easily verify, these two criteria aren't the same if you define "minimum correlation" to mean that the absolute value of the correlation coefficient is minimized (i.e. 0): In $\mathbb F_2^N$, the vector that's the farthest away from any given vector $v$ is its bit-wise inverse $\overline v$ (using Hamming distance) Using your mapping, the ...

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Figures that the same day I post a bounty I answer my own question. The answer to this question is dead/speckle like pixels. For a fixed number of dead pixels of a given brightness, the smaller the relative shift between the two images, the fewer dead pixels that are needed to cause the (0,0) pixel to spike. It can take fewer brighter dead pixels to have ...

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