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Distortion Less Transmission
Distortion Less Transmission
Transmission is said to be distortion-less if the input and output have identical wave shapes. i.e., in distortion-less transmission, the input x(t) and output y(t) satisfy the condition:
y (t) = Kx(t - td)
Where td = delay time and
k = constant.
Take Fourier transform on both sides
FT[ y (t)] = FT[Kx(t - td)]
= K FT[x(t - td)]
According to time shifting property,
= KX(w)$e^{-j omega t_d}$
$ herefore Y(w) = KX(w)e^{-j omega t_d}$
Thus, distortionless transmission of a signal x(t) through a system with impulse response h(t) is achieved when
$|H(omega)| = K ,, ext{and} ,,,,$ (ampptude response)
$ Phi (omega) = -omega t_d = -2pi f t_d ,,, $ (phase response)
A physical transmission system may have ampptude and phase responses as shown below:
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