Simplified block diagram of adaptive signal averaging.
Adaptive linear predictor used in the adaptive signal averaging technique. Note that the desired signal is replaced with the unfiltered, conventional average.
(a) Reduction in noise power for both the unfiltered and filtered averages as a function of scan for different values of the exponential weighting factor. The range of λ is 0.55 ≤ λ ≤ 0.95 with 0.05 increments. (b) Reduction in noise power for both the unfiltered and filtered averages as a function of scan for different values of the turn on time L. The turn on time was varied from 2 ≤ L ≤ 40 at increments of 4 scans.
(a) The top plot illustrates the desired simulated signal and the bottom plot illustrates a representative noise sequence u(n) that was added to create x(n). The three smaller signals to the left are enlarged in a few of the plots in the figure to better visualize results of the simulation. (b) The bottom plot illustrates the 100th individual unfiltered scan and the top figure illustrates its filtered version using the average of 100 unfiltered scans as the desired signal in the ALP. Note that only two of six line shapes are apparent in the individual unfiltered trace, while five of the six line shapes are revealed in an individual filtered trace. (c)The top plot illustrates the average of 85 filtered scans and the bottom figure illustrates the average of 100 unfiltered scans. Note that all 6 line shapes are almost completely resolved in the filtered average. (d) The top plot illustrates the average of 985 filtered scans and the bottom figure illustrates the average of 1000 unfiltered scans. Note that even now, the conventional average still does not match the SNR achieved when averaging 85 filtered scans.
(a) Histogram of the 85th sequence of prediction errors v(n) with a superimposed Gaussian fit. This figure justifies the assumption made earlier about the prediction error distribution being Gaussian. (b) Histogram of the averaged (985 scans) prediction errors v 985(n) with superimposed Gaussian fit. This close correspondence is expected as suggested by the central-limit theorem.
The top plot illustrates the reduction in noise power for both unfiltered and filtered averages as a function of scan. The bottom plot illustrates the noise reduction factor between these two variance levels as a function of scan. Note that the filtered average maintained a noise power level that was consistently 10 times lower than that of the unfiltered average. This would correspond to a SNR improvement by a factor of more than 3.
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