What does convolution mean?

[bals]

sir,
i wish to know the meaning of the word convolution?
what is the need for convolution?
what is the main difference between DFT and DTFT..explain interms of periodicity..[/b]

 

[helios]

about convolution

convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. A convolution is a kind of very general moving average, as one can see by taking one of the functions to be an indicator function of an interval.




pfff

you must read books...rather than asking here

 

[Dmitrij]

Re: about convolution

The need for convolution is very actual. If you have a filter with the known impulse response and the input signal is given (it doesn't matter whether you work with discrete-time or continious-time signals) then the output signal is the convolution of the input one and the frequency response:

S_ou(t) = S_in(t)*h(t), where * - convolution, h(t) - impulse response of the system (the reaction for Dirac impulse)

You must distinguish linear convolution (described above) and cyclic convolution, which is often computed in Fourier analysis. Cyclic convolution is used in processing periodic signals, when the computation procedure is done on period's duration only. Linear convolution is the expression of the algorithm of signal's filtration.

Also, convolution is used for smoothing signals, contaminated by noise. This operation decreases the harmful influence of the noisy component, which often presents in the mixture with the main signal. The often used kernels are Gaussian function, Lorentz function and Moffat function. While regulating the available parameters of these functions you obtain more or less smoothed representation.

Concerning the differences of DFT and DTFT, frankly speaking, i use them as synonims. It's unlikely that any essential difference exists between these terms.

With respect,

Dmitrij