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Derivation of Linearity for CT signals by Xiaodian Xie | Derivation of Linearity for CT signals by Xiaodian Xie | ||
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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)) | 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)) | ||
Revision as of 18:02, 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(ay(t)*exp(-jwt)))
So z(w)=ax(w)+by(w)
