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Why do we need to conjugate complex signals in autocorrelation and cross correlation

$\underline{\text{Prologue :}}$ Let me ask you another question. How will you compare two complex numbers $U$ ($a+jb$) and $V$ ($c+jd$)? By comparing magnitude? Subtract them and take real part? ...
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perfect sequences

Let $\theta_a$ and $\theta_c$ respectively denote the maximum magnitudes of the off-peak or out-of-phase periodic autocorrelation functions and the periodic crosscorrelation functions of a set of $K$ ...
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what does it mean to have a decorrelated colour space?

edit: to be clear this answer describes why Lab can be described as a decorrelated color space. This does not imply that decorrelation is the main benefit of using Lab (see many answers on why Lab is ...
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Maximum cross-correlation coefficient value for time delay estimation

As your plot shows, the second form allows for the correlation peak to be negative. Now, what does a strong negative cross correlation mean? It means the signals are very similar, except one has a ...
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How to measure the time dependent correlation of two signals

Your signals look like they have about the same ordinal scale, and little lag. Hence, you can perform local correlations: take a segment of both signals centered at a time location, you can normalize ...
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Phase shifting a noisy signal

With a real cosine a phase shift is equivalent to a time delay. If you delay the signal by $\phi_0$ then you will get the result you want. The number of samples that you will need to delay by will ...
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Why correlation property of $\mathcal Z$-transform contains a time reversal operation

Let's look at convolving: $$x_1 = [1, 2, 3];\\ x_2 = [3, 2, 2];$$ So:  Y(z) = X_1(z) X_2(z) = (1 + 2 z^{-1} + 3z^{-2})(3 + 2z^{-1} + 2 z^{-2})\\ = 3 + 2z^{-1} + 2 z^{-2} + 6z^{-1} + 4z^{-2} + 4 z^...
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This is very late, but maybe it's worth it anyway... The time-scale plane is not the same as the time-frequency plane, although it might be useful as well. Signals at different places in the time ...
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Why correlation is not associative in the context of image processing?

Subtraction is also not associative: (a-b)-c does not equal a-(b-c) in general. The order of the flipping of the sign matters, just like it does for the flipping of the kernel.
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Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$

One must be careful when asking questions about the relationships between the elements of a complex random vector. The short answer to your question is that you cannot say much for either cases ...

Why do we need to conjugate complex signals in autocorrelation and cross correlation

HINT: What is the physical meaning of the autocorrelation evaluated at lag $\tau=0$?
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Designing an efficient curve-matching algorithm

The two most obvious things you can try are: Fitting a Gaussian to your data and then clustering their parameters Estimate the similarity of waveforms directly and then try to cluster that Since you ...
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What is the time reversal convolution

I believe that h(-t) means a "time-reversed" version of h(t). Your command: 'y = conv(r,-h);' computes the convolution of 'r' and negative 'h', and you don't want that. I think you want: y = conv(r,...
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Understanding correlation in image processing using examples

As it was already posted multiple times: The problem comes from an inaccurate definition of correlation in your application. The Pearson correlation coefficient does require the data to be ...
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