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Window shape (included in An_aadf_pitch_estimator and written in company of Enrique Tomás)
All the windows developed for spectrum estimation by means of Fourier Transform is valid in our method. Smoother windows produces smoother functions, ada in our case. The reason is obvious: if the streams of the window are small, the changing of moment t where our function is calculated change little the values of the samples included in the calculation. Think in the rectangular window, changing t drop suddenly some samples in others appear with their actual value.
Using a triangular window with head samples that are gradually the window because their waves are diminishing little by little until they disappear.
Therefore continuous windows with small extremes are good windows for ada analysis. Hamming, Hanning, Bartlett and Blackman, will behave well in our analysis.
In order to reduce the amount of calculation involved in ADA analysis we can, in big windows used for a great tau (delay between the two windows) using less samples: we can use samples sparsely, something like a decimation in time. An implementation of this philosophy consist on using compact windows for the minimum tau, one sample and not the other for double tau and so on. Empirically the ada functions behave similarly that with the compact windows and the amount of calculation is reduced.
We can also achieve a similar result concentrating the used samples in the center and using less and less for extremes. In this way we reduce calculation time, simulate small extremes and suppress multiplications, though some calculations is needed to choose the right samples in each window size..
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