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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 ...


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) ...


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).


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.


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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