The Magic of Convolution and Correlation | MATLAB | Animation | Engineeing Concepts | Signals

"𝐓𝐡𝐞 𝐌𝐚𝐠𝐢𝐜 𝐨𝐟 𝐂𝐨𝐧𝐯𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐚𝐧𝐝 𝐂𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧!"

"Biomedical Engineering students require a solid grasp of these mathematical concepts, as they have far-reaching applications from Biosignal Processing to Computer-Aided Diagnostics"

The Basic difference between Correlation and convolution is:-

𝑪𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒊𝒐𝒏 is a measurement of the similarity between two signals/sequences.
𝑪𝒐𝒏𝒗𝒐𝒍𝒖𝒕𝒊𝒐𝒏 is a measurement of the effect of one signal on the other signal.

Graphically, the convolution of two signals is obtained by flipping and then shifting one of the signals over the other while multiplying and adding common elements (for continuous: it is integration of overlapping area). The mathematical calculation of Correlation is the same as a convolution in the time domain, except that the signal/kernel is not reversed, before the multiplication process. We engineers have to understand that generally convolution is used to modify signals (e.g., filtering, enhancing features), while correlation is used to detect patterns and measure similarity. In Biosignal processing, if we have a filter and a signal and want to get the response of the filter, we will use the convolution operator. Correlation can be used for noise analysis in CT/ Ultrasound X-ray images and for numerous other purposes.
In summary, both correlation and convolution are sliding inner products, used to project one thing onto another as they vary over space or time. Convolution is used when order is important, and is typically used to transform the data. Correlation is typically used to find a smaller thing inside of a larger thing, i.e. to match.

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