What are the real life applications of correlation and convolution

i am interested in knowing the real life application of convolution and correlation

Answer 1

[Image Analyst]

Way too many to list. I took a whole graduate level course in them and Fourier analysis. I can give one example. If you have colimated light hitting an infinitely long slit you'll get a sinc function on a plane infinitely past the slit. This is the Fourier transform of the slit. If you have the light hit a circular aperture you get a sombrero function (Fourier transform of a disc). Now if you have a bunch of slits or circles, you essentially are convolving the aperture shape with a comb function (array of Dirac delta functions). Now the Fourier transform of a comb function is a comb function so you get an array of points multiplied by the Fourier transform of the aperture. Here's the math F(circle) = sombrero, and F(comb) = comb. So if input = comb**circle, where means convolution, then at infinity you'll get F(comb**circle). Because the Fourier transform is a linear system, you can say that F(A**B) = F(A)*F(B), or in other words convolution in one domain (either one) is the same as multiplication in the other domain. So F(comb**circle) = F(comb)*F(circle) = comb * sombrero, which is an array of dots whose intensity is modulated by a sombrero function. It's used all the time in optics because the diffraction pattern (pattern of light at infinity after scattering through some plane with a pattern of apertures on it) is the Fourier Transform of the pattern on the plane with the aperture pattern on it. It's also used with lenses, electrical theory and all kinds of other things.