(A formal derivation of Equations 3.8 and 3.9 are given in Appendix A-2.) Equations that calculate the Fourier series coefficients from x(t) are termed “analysis equations.” Equation 3.5 works in the other direction, generating x(t) from the a's and b's, and is known as the “...
The derivation of a transfer function for system involves making assumptions about the physical model, e.g. springs, masses and damping, that can be used to represent the system. We can derive the frequency response of systems from a knowledge of their transfer functions. Thus the validity of...
21 、While for thesinusoidalapproximation method, a detail derivation of the amplitude of eachsinusoidalfunction is re-derived for completeness.───为完整性,文中亦详细推导正弦函数近似法中各个频率之振幅。 22 、DPO will be asinusoidalDPO by improving the circuit. A good quality FSK output are ea...
Koizumi, H., Whitten, W.B., Reilly, P.T.A., Koizumi, E.: Derivation of mathematical expressions to define resonant ejection from square and sinusoidal wave ion traps. Int. J. Mass Spectrom. 286, 64-69 (2009)H. Koizumi, W.B. Whitten, P.T.A. Reilly, E. Koizumi, Derivation of ...
In this paper, we thus describe and discuss two methods to estimate parameters of LIF models with the added complexity of a time-varying input current. We assume that the time-varying current is a sinusoidal wave, but we believe that the approaches generalize to an arbitrary periodic forcing ...
In this paper, we thus describe and discuss two methods to estimate parameters of LIF models with the added complexity of a time-varying input current. We assume that the time-varying current is a sinusoidal wave, but we believe that the approaches generalize to an arbitrary periodic forcing ...
In this paper, we thus describe and discuss two methods to estimate parameters of LIF models with the added complexity of a time-varying input current. We assume that the time-varying current is a sinusoidal wave, but we believe that the approaches generalize to an arbitrary periodic forcing ...
The Fokker–Planck equation allows for approximate maximum likelihood estimation. We chose an alternative loss function, though, because it marginally appeared more robust, possibly because a numerical derivation step is avoided. This is further investigated by simulations in the supplementary online materi...
Appendix. Derivation of the plasma oscillator mathematical model equation Eq. (1) used in this work to represent the dynamics of a plasma oscillator can be derived from a simple fluid plasma model considering an ion-sound instability. The basic equations for the positive ion fluid are the contin...
The step-by-step derivation of Equation (1) is given in [18] (pp. 349–350). Figure 1. General electronic diagram of voltage-controlled oscillator on the basis of an impedance converter. In Reference [15,16,17], one of the impedances Z0, Z1, or Z2 is capacitive, and the other...