How can we reduce noise in analog signal?
The best way to remove white noise from an analog signal is with bandwidth reduction. This is equivalent to reducing the measurement time for a signal and gathering more measurements, followed by averaging results. In terms of analog signals sent to an amplifier circuit, you should opt for a lower bandwidth amplifier.
How Fourier transform helps in reducing noisy signals?
Using information of the Fourier transform of trigonometric functions, dominant components can be distinguished from the noisy data. After filtering out weaker components we can compute IDFT of the remaining coefficients resulting in a filtered signal in the time domain.