- Signals and Systems Tutorial
- Signals & Systems Home
- Signals & Systems Overview
- Signals Basic Types
- Signals Classification
- Signals Basic Operations
- Systems Classification
- Signals Analysis
- Fourier Series
- Fourier Series Properties
- Fourier Series Types
- Fourier Transforms
- Fourier Transforms Properties
- Distortion Less Transmission
- Hilbert Transform
- Convolution and Correlation
- Signals Sampling Theorem
- Signals Sampling Techniques
- Laplace Transforms
- Laplace Transforms Properties
- Region of Convergence
- Z-Transforms (ZT)
- Z-Transforms Properties
- Signals and Systems Resources
- Signals and Systems - Resources
- Signals and Systems - Discussion
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)$e^{-j \omega t_d}$
$ \therefore 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
$|H(\omega)| = K \,\, \text{and} \,\,\,\,$ (amplitude response)
$ \Phi (\omega) = -\omega t_d = -2\pi f t_d \,\,\, $ (phase response)
A physical transmission system may have amplitude and phase responses as shown below:
