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The frequency-dependent imbalance are modeled by FIR filters with the following impulse response: and for the branch 1, and and.
In the time domain, the filter is defined by the following impulse response: g ( t ) = a t n - 1 cos 2 π f c t + ϕ e - 2 π bt, (1).
In wireless communications, the multi-path, fading channel with Doppler frequency-shifts may be modeled as a linear time-varying system with the following impulse response [14 16]: (1).
Consider the following impulse differential inequalities: begin{aligned}& omega'(t) leq geq), p(t)omega(t)+q(t),quad tneq t_{k}, & omegabigl(t_{k}^bigr) leq geq), d_{k} omega(t_{k})+b_{k},quad t=t_{k},kin N, end{aligned} where (p(t),q(t)in C(R_,R)), (d_{k}geq0), and (b_{k}) are constants.
Consider the following impulse differential inequalities: textstylebegin{cases} u'(t)leq geq) a(t)u(t)+c(t), & tneq t_{k}, u(t^_{k})leq geq) b_{k}u(t_{k})+d_{k}, & t=t_{k}, kin N, end{cases} where (a(t),c(t)in C(R_,R)), (b_{k}geq0), and (d_{k}) are constants.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com