(One intermediate revision by the same user not shown) | |||
Line 1: | Line 1: | ||
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)=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)) | ||
− | so z(w)=d^(-1)/dt(ax(t)*exp(-jwt)))+d^(-1)/dt( | + | so z(w)=d^(-1)/dt(ax(t)*exp(-jwt)))+d^(-1)/dt(by(t)*exp(-jwt))) |
So z(w)=ax(w)+by(w) | 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)