The finite numerical resolution of digital number representation has an impact on the properties of filters. Much effort has been done to develop efficient digital filters investigating the effects in the frequency response. However, it seems that there is less attention to the influence in the entropy by digital filtered signals due to the finite precision. To contribute in such a direction, this manuscript presents some remarks about the entropy of filtered signals. Three types of filters are investigated: Butterworth, Chebyshev, and elliptic. Using a boundary technique, the parameters of the filters are evaluated according to the word length of 16 or 32 bits. It has been shown that filtered signals have their entropy increased even if the filters are linear. A significant positive correlation (p < 0.05) was observed between order and Shannon entropy of the filtered signal using the elliptic filter. Comparing to signal-to-noise ratio, entropy seems more efficient at detecting the increasing of noise in a filtered signal. Such knowledge can be used as an additional condition for designing digital filters.

The classical theory of signal processing assumes that the designed IIR filters are continuous and have infinitely accurate coefficients. However, when developing filters for real-world digital signal processing tasks, it is necessary to take into account the finite precision of the coefficients representation, especially considering the fixed-point arithmetic. In this paper, we propose a new approach, which we call the interval size approach, making it easy to evaluate the actual digital filter response for various fixed-point arithmetic parameters. We provide Illustrative examples to demonstrate the frequency response bounds evolution as an order, cutoff frequency, and signal frequency are varying. We show that the interval size can be used as a well-suited accuracy factor of a digital filter.

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