Test results for leveled inverse interpolation

Figures 14 and 15 show the same example as in Figures and . What is new here is that the proper PEF is not given but is determined from the data. Figure 14 was made with a three-coefficient filter (1,a₁,a₂) and Figure 15 was made with a five-coefficient filter (1,a₁,a₂,a₃,a₄). The main difference in the figures is where the data is sparse. The three-coefficient filter can fit only a single sinusoid and it does that. The five-coefficient filter can fit only two sinusoids and it does something like that, a high-frequency sinusoid on the left and a lower one on the right. The data points in Figures , 14 and 15 are samples from a sinusoid.

 

subsine390 Figure 14 Interpolating with a three-term filter. The interpolated signal is fairly monofrequency.

 

subsine590 Figure 15 Interpolating with a five term filter. A low frequency component grows towards the right.

Comparing Figures and to Figures 14 and 15 we conclude that by finding and imposing the prediction-error filter while finding the model space, we have interpolated beyond aliasing in data space.