In which real case scenarios a convolution or deconvolution operation is useful ?
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Any real instrument will have some impulse response. The measured signal is the convolution of the source signal with this impulse response. For example, if you aim a telescope at a point source, you will see not a point source but the point source convolved with the point spread function (2D impulse response) of the telescope. Some kind of (usually approximate) deconvolution is applied to correct this and better estimate the source signal. |
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This is a very general topic to discuss, (I'm not sure there's a right answer here), but I think it's very much worth pointing out the convolution theorem. It's not a "practical" application per se, but it's a very useful method, since Fourier analysis enters physics in so many areas. Anywhere where you encounter spectrum analysis, convolutions will quite possibly come into play somewhere. The convolution theorem states: $$\mathcal{F}\{f*g\} = \mathcal{F}\{f\} \cdot \mathcal{F}\{g\}$$ $$\mathcal{F}\{f \cdot g\}= \mathcal{F}\{f\}*\mathcal{F}\{g\}$$ where $\mathcal{F}$ represents the Fourier transform operator. These are remarkably useful identities when performing Fourier transforms. Since Fourier transforms can in fact be used for solving some differential equations, they have a notable application there too. |
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Solving the Fresnel diffraction integral, to find the amplitude and phase of waves near a source: http://en.wikipedia.org/wiki/Fresnel_diffraction#Convolution |
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