Generally we apply a filter to reduce noise from signal. For example if the received signal is $S$ we would get a signal $Y$ with reduced noise applying a filter $W$ with the operation Y= convolution(S,W). In other words filter is nothing but convolution. Is there a known method or example of getting a useful $Y$ such that $Y=S.*W$ where $.*$ means element wise multiplication. An example of element wise multiplication is demodulation.
Can anyone give an insight if element wise multiplication can be used to reduce noise under some circumstances?
Edit: Yes, product in time domain means convolution in frequency domain. Still the question under what situation convolution in frequency domain or product in time domain can reduce noise? Is there any such application? Did anyone used such a method?
Edit: There may be a situation where it is much easier to find a vector $W$ such that the element wise multiplication does reduce noise. It may difficult to find the corresponding filter.