# why adding noise enhances the accuracy sometimes?

I am applying simple FFT to estimate the frequencies of the oscillations. The real values of frequencies are known to me as I made a synthesis signal for simulation.Thus, I can calculate the error simply. The signal contains 4 different frequencies. FFT can estimate these components fairly accurate.
when, the noise is added to the signal it is expected to see an increase in estimation errors. also increasing the noise strength must increase the error size naturally.
The question is this, in most case the error is increased in with noise. But for some cases,'one or two modes out of four', the error is decreased and better accuracy is obtained in noisy environment. why this is happening.
please provide some rational reasons with some references to this unexpected phenomenon.
Thanks in the best way
P.S The added noise is zero mean Guassian

• When you say "some cases", do you mean that, for a given noise power, you obtain different results for different noise sequences? – Deve Sep 6 '14 at 11:05
• yes, for example for 10db-SNR (strong noise) the estimation error for a certain frequency is less than the estimation error which is obtained for 30 db SNR(light noise). It is only happens for 1 or 2 frequency components of a signal. for other embedded frequencies the estimation error is natural as the error is increased while the SNR decreased(getting stronger) @Deve – Electricman Sep 6 '14 at 12:49
• What happens if you keep the SNR constant at, say 10 dB, and change the noise sequence (change the seed of your random number generator)? Is the behaviour the same? – Deve Sep 6 '14 at 12:57
• not always, but sometimes it behaves same way. its kinda depend on the generated noise as it is random . – Electricman Sep 6 '14 at 13:09
• That's normal, and you just gave the explanation yourself ;) The noise is random so for a specific noise sequence it might happen that the estimation is better than for another noise sequence with lower noise power. – Deve Sep 6 '14 at 13:13