Next, we will show a series of loss functions using interpolating polynomials that approximate the ideal low-pass window (Brick Wall) by other functions, each one with its particular characteristics; some will have a better behavior in the pass band; others will have a better behavior in the attenuated band; others in the transition slope rate; and others in their time behavior. The reader should be able to choose from among all the possibilities shown, the alternative that best suits his needs, even proposing his own polynomials or a modification of the existing ones. The higher the order of the chosen filter, the closer the filter response will be to a brick wall. With the tools provided in Chap. 1 , you will be able to predict its behavior before its development.

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Loss Function Modeling

  • Carlos Fernández Marzalo

摘要

Next, we will show a series of loss functions using interpolating polynomials that approximate the ideal low-pass window (Brick Wall) by other functions, each one with its particular characteristics; some will have a better behavior in the pass band; others will have a better behavior in the attenuated band; others in the transition slope rate; and others in their time behavior. The reader should be able to choose from among all the possibilities shown, the alternative that best suits his needs, even proposing his own polynomials or a modification of the existing ones. The higher the order of the chosen filter, the closer the filter response will be to a brick wall. With the tools provided in Chap. 1 , you will be able to predict its behavior before its development.