Signal Processing Techniques to Improve Precision of Spectral Fit Algorithm

6.1 Growing Window Averaging The first signal processing technique investigated was a simple extension of the Spectral Fit algorithm where the estimates for any given window size were the average of the estimates for smaller window sizes. In the algorithm, the averaging was restricted to window lengths greater than 2 mm. Furthermore, because scatterer size estimates of less than 1 μm were not physically reasonable for the range of frequencies used in the evaluation, any estimates giving a scatterer size smaller than 1 μm were also excluded from the averaging. Because estimates for window lengths have already been found for the basic Spectral Fit algorithm in Chapter 5, the same data were re-evaluated using this new algorithm. As a result, the spectra were still averaged in the log domain and the convolution effects of windowing remained uncompensated. Despite these limitations, the general performance of the algorithm could still be evaluated. Also, the choice of limiting the window length in the averaging to 2 mm was somewhat arbitrary. Hence, other limits may have slightly different performances, but the general behavior should not be drastically affected. A plot showing the errors in the estimated total attenuation and scatterer size for the halfspace with an attenuation of 0.3 dB/cm/MHz for the attempted window lengths is shown in Figure 6.1. Because scatterer estimates of less than 1 μm were automatically excluded from the averaging, not all 40 of the independent waveform groups yielded an estimate as is shown in Figure 6.1c. Also, when comparing the results shown in Figure 6.1 to the previous results given