Using the Parametric Time-Varying Analog Filter to Average-Evoked Potential Signals

Analytical Synthesis of Parameter-Varying Filter of Constant Component with Application to Switching Systems

“…where: x(t) and y(t) are respectively the input and output of the filter and T(t) is a time-varying function of time constant T. In order to examine the properties of the time-varying filter let us assume the following form of function T(t) [8] …”

“…However, it is known from the analysis of systems with constant parameters that damping of the harmonic components with α-accuracy is many times shorter than working out the constant component. One should then estimate whether the introduction of the time-varying parameters can shorten the transient of the filter [8].…”

“…In [8], it has been proved that a time-varying filter may be regarded as a traditional time-invariant filter when its parameters settle to steady values with time. The so-called ''time of operation'' can be calculated either considering the settling time t s1 of the step response h(t) fulfilling the following relation:…”

“…For instance, in [6,7], a parameter-varying lowpass filter was used to eliminate the oscillatory response exhibited by load cells used in weighting applications. Another parameter-varying filter was used in [8,9] to reduce the time employed in the acquisition of evoked potentials generated through auditive stimuli. Moreover, the parameter-varying technique was used to reduce the transients of delay-equalized lowpass filters [10][11][12][13] and analog and digital notch filters [14,15].…”

Modelling of the First-Order Time-Varying Filters with Periodically Variable Coefficients

“…Many theoretical works [1][2][3][4][5] as well as practical applications have been devoted to these systems. In particular, LTV systems can be applied in signal processing [6][7][8][9][10][11], especially in sampling systems [12], signal filtering and noise reduction [7,8,[13][14][15][16][17], and current compensators in power networks [18,19], amplifiers [5,20], chaos generators [21], electromagnetic launchers [22], and medical devices [23]. The main advantages of LTV system application include improvement of the dynamic properties of systems and reduction of the transient state [16,24].…”