Is There Any Filtering Technique with Element Wise Product Only Instead of Convolution? 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.
Classic filteration is indeed done using convolution.
Though I have seen broader definition of filtering as shaping the signal in its frequency domain which can be done in many other methods as well.

Of course you can create meaningful operations using element wise operations and even specifically multiplication.

Think of the case you have a noise with the following properties:


It is non negative.
It is signal dependent.


Then operation like thresholding would make sense and it is applied using element wise multiplication. This case is very similar to $ {L}_{1} $ Denoising.

Pay attention that in this case the filter depends on the data.