State the applications of linear convolution?

Convolution and related operations are found in many applications of engineering and mathematics. * In statistics, as noted above, a weighted moving average is a convolution. * In probability theory, the probability distribution of the sum of two independent random variables is the convolution of their individual distributions. * In optics, many kinds of "blur" are described by convolutions. A shadow (e.g. the shadow on the table when you hold your hand between the table and a light source) is the convolution of the shape of the light source that is casting the shadow and the object whose shadow is being cast. An out-of-focus photograph is the convolution of the sharp image with the shape of the iris diaphragm. The photographic term for this is bokeh. * Similarly, in digital image processing, convolutional filtering plays an important role in many important algorithms in edge detection and related processes. * In linear acoustics, an echo is the convolution of the original sound with a function representing the various objects that are reflecting it. * In artificial reverberation (digital signal processing, pro audio), convolution is used to map the impulse response of a real room on a digital audio signal (see previous and next point for additional information). * In electrical engineering and other disciplines, the output (response) of a (stationary, or time- or space-invariant) linear system is the convolution of the input (excitation) with the system's response to an impulse or Dirac delta function. See LTI system theory and digital signal processing. * In time-resolved fluorescence spectroscopy, the excitation signal can be treated as a chain of delta pulses, and the measured fluorescence is a sum of exponential decays from each delta pulse. * In physics, wherever there is a linear system with a "superposition principle", a convolution operation makes an appearance. * This is the fundamental problem term in the Navier Stokes Equations relating to the Clay Institute of Mathematics Millennium Problem and the associated million dollar prize. * In digital signal processing, frequency filtering can be simplified by convolving two functions (data with a filter) in the time domain, which is analogous to multiplying the data with a filter in the frequency domain