(HW 3.3 - Xiaodian Xie_ECE301_Summer2009) |
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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)) | ||
| − | 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)
