GoldExI : FAQ : Turbo Averaging Filter

Question

You say Turbo Averaging acts as a filter. What is its amplitude-frequency characteristic?

Answer

The amplitude-frequency characteristic can be easily calculated. But is it not as simple as for usual filters. For all spectral components which have a period of a signal which is not a multiple of the averaging period, the TA result will depend on the phase of the wave. Since all phases have equal probability, we can calculate the probability of corresponding amplitude after TA-filter. The plot for T=100ms looks as follows.

Probability of A(f)

We suppose that on the input of TA-filter we applied while noise with the amplitude of each component equal to unity. The intensity of the green shows the probability of corresponding amplitude of spectral component of frequency f. For f=10 Hz, 20 Hz, etc., the probability of zero amplitude is 1, i.e. these frequencies are cut off completely, independently on phase. For other frequencies the amplitude on the output of TA-filter can be in some range with different probabilities but the sum of probabilities is always 1 (integral along A from 0 to 1 for fixed f).