How could we remove noise from signals as show in in attached pictures, Thanks
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There are no pictures attached except for one embedded above your sentence. And I'm not sure what you consider to be the noise in that curve.
There are a variety of noise reduction filters, probably the most common are median filter, sliding mean filter, Savtizky-Golay filter, and wiener filter, though there are tons of others.
Last I heard, the best noise reduction filter isBM3D. That's what everyone seems to be trying to beat in papers published these days. I haven't seen anything beat it across the board. There are other good ones like non-local means, UINTA, K-LLD, K-SVD, etc. The bilateral filter is probably better than simple filters like median, averaging, etc. but the aforementioned ones are better, though a lot more complicated. Non-local means is in the File Exchange - maybe some of the others are too. MATLAB code for BM3D is on the link I gave you:http://www.cs.tut.fi/~foi/GCF-BM3D/
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