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The statement is: eliminating all points where the difference between $x$ and $i$ is at least $r$ so eliminate those points for which $$ |x - i | \gt r \tag{1}$$ Isn't that correct? One could argue whether the words say $$ |x - i | \ge r $$ instead, which might be problematic at the border, but using (1) the statement seems OK to me. The text after the ...


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Are there situations in signal processing where one would like to identify e.g. a time-domain signal from only it's power spectrum? Well, your described optical algorithm doesn't "only" depend on the power spectrum, but on the power spectrum under different phase shifts – which is a way of estimating the Fourier transform of the time (or spatial) ...


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If you implement the Goertzel algorithm P times to detect P different spectral samples, Goertzel is more efficient (fewer multiplies) than the N-point FFT when P < log2(N).


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You can use the Prime-factor FFT algorithm recursively, since $100 = 5 \cdot 5 \cdot 2 \cdot 2$, you only have to implement the radix-5 and radix-2 reductions.


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If your sequences are uncorrelated, then for the sum of the sequences, the variance becomes $$ \mathrm{Var}\left(\sum_i^N X_i\right) = \sum_i^N \mathrm{Var}(X_i) $$ and it is easy to solve the minimum problme. If they are unfortunately correlated, the variance is $$ \mathrm{Var}\left(\sum_i^N X_i\right) = \sum_i^N \mathrm{Var}(X_i) + \sum_{i\neq j}\mathrm{...


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