How do we calculate the correlation of 2 discrete signals (real or complex)?

What is the formula? Can you explain with an example (take discrete signals of length 10)?

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This answer was edited.Correlation:Correlation is the measure of similarities between two signals.Auto-correlation

Cross-correlation

This answer was edited.Correlation describes the mutual relationship which exists between the two or more things.The same definition which holds good in the case of signals.Correlation between signals indicates the measure up to which the given signal resembles the another signal.

Auto correlation of discrete time signal is expressed as

and cross correlation of discrete time signals is expressed as

This answer was edited.Cross correlation of two signals is

This answer was edited.It is a measure of similarity between two signals or signals with itself.

Auto-correlation of discrete time signal is expressed as

and cross-correlation of discrete time signals is expressed as

Example: Given

The cross correlation yields the output.

which can also be shown according to the plot generated given below.

This answer was edited.## Correlation:

correlation is the measure of similarity between a time shifted signal and its original signal.

We will calculate the correlation of two discrete signals using the formula :

Let us consider an example with 2 discrete sequences as :

after correlating the above sequence we get result as ;

This answer was edited.Correlation: Correlation is defined as measure of similarity or relationship between two signals.

Autocorrelation: The correlation between the two same discrete sequences.

Auto correlation of discrete time signal is expressed as

Cross correlation:The correlation between two different discrete sequences.

cross-correlation of discrete time signals is expressed as

Example:

The cross correlation of the above sequences gives the output as follows:

This answer was edited.The correlationof two signals is the convolution between one signal with the functional inverse version of the other signal.If the two signals are the same then it is autocorrelation otherwise it is cross-correlation.

Example: let us take the two discrete sequences as

The output of the correlation of these two signals is

This answer was edited.Correlation is a mathematical tool that measures the amount of similarity present between two signals. In communications, it is widely used at the receiver side to detect the required signals and discard the unwanted signals.

If correlation is performed in between same signals, it is termed as

“Autocorrelation”. It are calculated as follows:If correlation is performed between two different sequences, it is termed as

“Cross Correlation”. It are calculated as follows:As an example, consider the two sequences each of length 10

Then the autocorrelation of the first sequence with itself is

Then the crosscorrelation of the two sequences is

This answer was edited.Correlation is the measure of similarity between two signals.

Correlation between two discrete signals x[n] and y[n] is denoted by Rxy[k]. It is calculated by using following formula.

If the correlation is between same signal, it is called Auto-Correlation.

If correlation is between two different signals, it is called Cross-Correlation

Example:

x[n] = { 1,0,2,0,1,1,3,2,1,2}

y[n] = {2,0,1,2,3,4,3,2,1,2}

Cross correlation: {2 , 1, 6, 5, 10, 12, 19, 19, 21, 29, 27, 31, 23, 20, 12, 11, 6, 2, 4}

This answer was edited.When we have two distinct signals a[n] and b[n] , we calculate correlation of them using

Correlation is of two types:

For real and discrete signals a[n] and b[n] :

Auto correlation is

Cross correlation is

For complex and discrete signals a[n] and b[n] :

Auto correlation is

Cross correlation is

Example :

The cross correlation of a[n] and b[n] is

This answer was edited.Correlationrefers to the similarity or relationship between two signals. It measures how similar two signals are in terms of shape or pattern.Cross-correlation: This type of correlation measures the similarity between two signals as a function of the time lag between them. It is commonly used in signal processing to detect patterns or features in a signal or to filter the unwanted noiseWhere Rxy(k) is the cross-correlation at lag k, x(n) is the value of the first signal at time n, y(n) is the value of the second signal at time n, and k is the time lag.

Auto-correlation: This type of correlation measures the similarity between a signal and a time-shifted version of itself. It is used to detect periodic patterns in a signal or to find statistical properties of the signalWhere Rxx(k) is the auto-correlation at lag k, x(n) is the value of the signal at time n, and k is the time lag.

Here i took two discrete signal each of length 10 element

The cross-correlation of x[n] and y[n] is

correlationdescribe the relationship between two signals.it is measure of similarities and degree of similarities between two signals.it has two type of correlation

1.auto correlation

2.cross correlation

auto correlationthe autocorrelation function is defined as the measure of similarity between a signal and its time delayed version.The auto correlation between two same signals or waveforms.

cross correlationthe cross correlation function is defined as the measure of similarity between a signal and its time delayed version.The cross correlation between two different signals or waveforms.

ExampleIn this example i have taken two sequence x1(n) and X2(n) with length of 10 elements.

x(n)=[1,1,1,1,1,2,2,2,2,2]

Y(n)=[3,3,3,3,3,4,4,4,4,4]

take x(n) sequence itself and invert y(n) sequence and perform convolution between two sequence it results correlation.

If the same sequence perform this operation it results auto correlation.

Rxx(n) =[2,4,6,8,10,13,16,19,22,25,22,19,16,13,10,8,6,4,2]

If the different sequence perform this operation it results cross correlation.

Rxy(n) = [4,8,12,16,20,27,34,41,48,55,50,45,40,35,30,24,18,12,6]

Given two discrete-time real signals (sequences) x[n] and y[n] .

The autocorrelation and crosscorrelation functions are respectively defined by

Autocorrelation of x[n]

Autocorrelation of y[n]

Crosscorrelation of x[n] and y[n]

Crosscorrelation of y[n] and x[n]

Let us understand using an example;

Example:Find the Correlation of the given below given two sequences

x[n]={1,2,1,5,4,3,1,2,6,8}

p[n]={2,2,4,5,3,6,1,1,2,2}

We can use the above formula or we can also write MATLAB code for correlation.

MATLAB code:

This answer was edited.Correlation :A signal operation similar to signal convolution, but with completely different physical meaning, is signal correlation. The signal correlation operation can be performed either with one signal (autocorrelation) or between two different signals (cross correlation). Physically, signal autocorrelation indicates how the signal energy (power) is distributed within the signal, and as such is used to measure the signal power. Applications of signal autocorrelation are in radar, sonar, satellite, and wireless communications systems. There are also many applications of signal cross correlation in signal processing systems, especially when the signal is corrupted by another undesirable signal (noise) so that the signal estimation (detection) from a noisy signal has to be performed. Signal can be also considered as a measure of similarity of two signals.Formula :Given two discrete-time real signals (sequences) and . The autocorrelation and cross correlation functions are respectively defined by

is the auto correlation of x[n]

is the auto correlation of y[n]

is the cross correlation of x[n] and y[n]

is the cross correlation of y[n] and x[n]

Example :let x[n] and y[n] are two discrete time signals

Correlation: Correlation is a simple mathematical operation to compare two functions or signals or waveforms. It is defined as the measure of similarity between those signals. There are two types of correlations −

Cross-correlation: It is the measure of similarity or coherence between one signal and the time-delayed version of another signal.

Autocorrelation: It is the measure of similarity or coherence between a signal and its time delayed version.

Both cross-correlation and autocorrelation is also defined separately for energy (or aperiodic) signals and power (periodic) signals.

autocorrelation:

cross-correlation:

Ex: let X[n] and Y[n] are two discrete time signals

X[n]=[1,2,3,4,0,4,3,2,1,0]

Y[n]=[5,4,3,2,1,0,1,2,3,4]

The cross-correlation of X[n] and Y[n] is

R[n]=[4,11,20,30,20,28,32,35,37,45,42,45,40,30,40,26,14,5,0].

This answer was edited.Correlation:to compare two signals.Cross CorrelationAuto CorrelationCross Correlation:This is a kind of correlation, in which the signal in-hand is correlated with another signal so as to know how much resemblance exists between them.Auto Correlation:Autocorrelation, also known as serial correlation, refers to the degree of correlation of the same variables between two successive time intervals.Example : x(n) = { 1 , 0 , 1 , 2 , 1 , 0 , 3 , 1 , 1 , 2}

y(n) = { 0 , 0 , 1 , 1 , 2 , 0 , 3 , 0 , 1 , 0}

The cross correlation of a[n] and b[n] is :

z(n) = {0 , 0 , 1 , 1 , 3 , 3 , 8 , 5 , 9 , 10 , 12 , 7 , 14 , 7 , 6 , 7 , 1 , 2 , 0}