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sobek
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Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$$R(\tau)=\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}t$$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

$$(f \star g)(\tau) = \int_{-\infty}^{\infty}\! f(t)g(t-\tau)\,\mathrm{d}t$$

In case of the cross correlation $\tau$ has no significance over periodicity of the single signals but if for a given $\tau$ the correlation is high, $\tau$ indicates the phase shift between the signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$$R(\tau)=\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}t$$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$$R(\tau)=\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}t$$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

$$(f \star g)(\tau) = \int_{-\infty}^{\infty}\! f(t)g(t-\tau)\,\mathrm{d}t$$

In case of the cross correlation $\tau$ has no significance over periodicity of the single signals but if for a given $\tau$ the correlation is high, $\tau$ indicates the phase shift between the signals.

That was only one equation...
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jojeck
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Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}x$

$$R(\tau)=\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}t$$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}x$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$$R(\tau)=\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}t$$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

formula added
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sobek
  • 151
  • 8

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}x$

For varying $\tau$, the autocorrelationautocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

Usually this refers to the autocorrelation coefficient.

Consider any 1D signal with periodicity $\pi$.

Now let's look at the autocorrelation integral:

$\int_{-\infty}^{\infty}\! f(t)f(t-\tau)\,\mathrm{d}x$

For varying $\tau$, the autocorrelation will have a maximum for $\tau$ equalling $\pi$ and its multiples. Thus autocorrelation can be used to study the periodicity of a signal.

This is often sort of colloquially used to indicate that certain parts of a signal are very similar or even identical.

The analogue for two different signals would be the cross correlation. It can be used to study the similarity of two separate signals.

When speaking about equations it's good to add them, isn't it?
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jojeck
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  • 75
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sobek
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