Translations:The shaping filter/30/en

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This is a set of N + 1 simultaneous equations with m = 0, 1, 2, …, N in the case of a causal filter and a set of 2N + 1 simultaneous equations with m = –N, –M, N + 1, … , N in the case of a noncausal filter. These are the so-called normal equations, whose solution permits us to find the filter coefficients . The known quantities in these normal equations are the autocorrelation of the input signal and the crosscorrelation of the desired output signal and the input signal. It can be shown that as N increases, the mean square error decreases (Robinson and Treitel, 2000[1]). However, the specification error starts to increase, so some optimum value of N is required so that the total of these two types of error is minimized. (Note: A mathematical model of necessity must be a simplification of the actual physical situation. The specification error is the difference between the fitted model and the actual situation. Invariably, some types of variables will be excluded from the model either by design or accident. Increasing the number of coefficients of an included variable usually cannot offset the loss of the excluded variables, and as the number of coefficients increases, it actually can make matters worse.)

  1. Robinson, E. A., and S. Treitel, 2000, Geophysical signal analysis: SEG.