Discrete Lanczos derivatives of noisy data

Timothy J. McDevitt, Elizabethtown College


Finite differences are frequently used to differentiate empirical functions, but standard differences tend to amplify the random error that is present in almost all empirical data. This paper uses higher-order Lanczos derivatives and discretized Legendre polynomials to generate minimum variance finite differences to approximate ordinary derivatives of all orders for a fixed discretization error magnitude. The resulting differences can be implemented as finite impulse response filters and are therefore very fast on a computer. © 2012 Taylor & Francis Group, LLC.