Analysis of Controlled Digital Recursive High-Pass Filters Structures with Infinite Non-Negative Impulse Response

Abstract

Digital signal processing is widely used in modern technology, including robotics, medical technology, etc. Thus, high-pass filters are used to eliminate the constant component of the output signal at the output of an analog-to-digital converter. This also reduces the low-frequency interference level spread out on the frequency axis to the left of the lower boundary of the signal spectrum. In the case of a dynamic change in the signal and interference spectra, controlled digital filters are used, the coefficients of which explicitly depend on the cutoff frequency. A non-negative impulse response, which corresponds to a flat transient response, is required. For example, in the case of determining the presence of a negative signal against the background of a positive pulse of a much larger amplitude. Or, conversely, to determine the presence of a positive signal against the background of a negative pulse. As this takes place, a signal pass is allowed, but a false detection is not allowed. False detection can be caused by undershoot or fluctuations in the step response ($SR$) of the high-pass filter. The paper investigates the structures of high-pass filters based on a parallel connection of a direct pass and a cascade connection of first order low-pass filters, which are obtained by the method of invariant transformation of the impulse response. The disadvantage of some of the studied structures is the presence of an overshoot on the amplitude-frequency response in the vicinity of the cutoff frequency. The conditions under which the negative impact of this emission decreases, are analyzed.