Improvement of Signal to Noise Ratio?

Question

Discuss how a signal to noise ratio might be improved by the use of:
i) Filtering
ii) Averaging

Answer 1

If the frequency spectrum of the noise is different from the frequency spectrum of the signal, S/N ratio is improved by filtering those frequencies in the noise spectrum. In many applications, noise spectrum is very broad while signal occupies a narrow band. Filtering out those frequencies not in the signal band improves S/N.

Averaging is a form of filtering useful for reducing random noise whose average value is zero over short intervals of time while signal amplitudes change more slowly. Averaging is equivalent to removing high-frequency components, and if the signal does not include those frequencies, the S/N is improved.