Convolution vs correlation? [duplicate]

1. Is correlation same as convolution?
2. Why use convolution instead of correlation?
3. Under what condition is convolution equivalent to correlation?
4. How is correlation related to convolution and what is the need to study of correlation?

Is correlation same as convolution?

Convolution is just like correlation, except we flip over the filter before correlating. Figure 7. Convolution Operation in 1-D. In the case of 2D convolution, we flip the filter both horizontally and vertically.

Why use convolution instead of correlation?

Which one you use depends on the application. If you are performing a linear, time-invariant filtering operation, you convolve the signal with the system's impulse response. If you are "measuring the similarity" between two signals, then you cross-correlate them.

Under what condition is convolution equivalent to correlation?

Convolution is only a measure of similarity between two signals if the kernel is symmetric, making the problem equivalent to correlation.

How is correlation related to convolution and what is the need to study of correlation?

The convolution and correlation are closely related. In order to obtain the crosscorrelation of two real signals 𝑥₁(𝑡) and 𝑥₂(𝑡), we multiply the signal 𝑥₁(𝑡) with function 𝑥₂(𝑡) displaced by τ units. Then, the area under the product curve is the cross correlation between the signals 𝑥₁(𝑡) and 𝑥₂(𝑡) at 𝑡 = 𝜏.