(New page: Derivation of Linearity for CT signals by Xiaodian Xie Suppose z(t) = {ax(t)+by(t)}, then the fourier transform of z is z(w)=\int\limits_{-\infty}^{\infty}(ax(t)+by(t))e^{(-\jmath wt)}dt ...) |
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Derivation of Linearity for CT signals by Xiaodian Xie | Derivation of Linearity for CT signals by Xiaodian Xie | ||
− | Suppose z(t) = {ax(t)+by(t)}, then the fourier transform of z is z(w)= | + | |
− | z(w)= | + | |
− | + | ||
− | + | Suppose z(t) = {ax(t)+by(t)}, then the fourier transform of z is z(w)=d^(-1)/dt((ax(t)+by(t))*exp(-jwt)) | |
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+ | so z(w)=d^(-1)/dt(ax(t)*exp(-jwt)))+d^(-1)/dt(by(t)*exp(-jwt))) | ||
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+ | So z(w)=ax(w)+by(w) |
Latest revision as of 18:03, 8 July 2009
Derivation of Linearity for CT signals by Xiaodian Xie
Suppose z(t) = {ax(t)+by(t)}, then the fourier transform of z is z(w)=d^(-1)/dt((ax(t)+by(t))*exp(-jwt))
so z(w)=d^(-1)/dt(ax(t)*exp(-jwt)))+d^(-1)/dt(by(t)*exp(-jwt)))
So z(w)=ax(w)+by(w)