Sentence examples for by the difference equation from inspiring English sources
This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model.
This is quite obvious by the difference equation (4.1) with forward differences.
As a toy example, which is supposed to fail for illustrative purposes, a single-pole system, described by the difference equation y(n)=-a y n-1)+x(n), (7). is presented.
Fermat polynomials can be generated by the difference equation mathcal{F}_{i+2}(t)=3 t mathcal{F}_{i+1}(t -2 mat -2l{F}_{i}(t), qquadmathcal{F}_{i}(t)=0,qquadmathcal{{F}_{1}(t)=1, quad igeq0}
The system model defined by the difference equation (2) can be, easily, converted to a description by a discrete transfer function G z) from the control input U z) to the output V z) in the z -domain, given below: G z = V z U z = b 1 z + b 2 z 2 − a 1 z − a 2 (3).
The mutational process is described by the difference equation (1) Solving equation (1), we obtained (2) In the case of haploid organisms such as E. coli, the selection process is described by (3) where q n ′ is the frequency of a after selection.
The integral part was then rewritten to its approximate summation form and by using the difference equation, the final expression was simplified to obtain the mask.
Thus, by applying the difference equation of the classical Bernoulli polynomials B n ( x + 1 ) − B n ( x ) = n x n − 1 for non-negative integer n (see, e.g., [26]) to (2.21), the desired result follows immediately.
In practice, the sequence u can be obtained by integrating the difference equation (1) based on an associated "quantization rule," q n = Q ( u n - 1, u n - 2,..., x n, x n - 1,... ) (2).
By solving the difference equation in (1) with the boundary conditions, x[ 0]=ξ and x[N]=0, we obtain A N ξ+Φ u=0 with Phi triangleq left[begin{aligned} A^{N-1}boldsymbol{b}&, A^{N-2}boldsymbol{b}&ldots&~Aboldsymbol{b}&boldsymbol{b} end{aligned}right].
