Linear distortion and equalization
Linear Distortion
In the output signal of a physical LTI system, there is always a certain amount of distortion present. It can be either continuous-time or discrete-time depending on the deviation in the frequency response of the system from the ideal conditions. There are two components of linear distortion and they can be distinguished easily by transmitting a signal through an LTI system.
The two components are:
Amplitude distortion:
The frequency components of the input signal are transmitted through the system with different amounts of gain. This is done whenever the magnitude response of the system is not constant inside the present frequency bands. This phenomenon is known as amplitude distortion.
Phase distortion:
The second form of linear distortion is phase distortion, it arises when the phase response of the system is not linear with the frequency inside the frequency band of interest. If the input signal is divided into a set of components, each component will occupy a narrow band of frequencies. These components are subject to different delays when passing through the system. Phase distortion is also known as delay distortion.
An LTI system is said to be dispersive if there is linear distortion present in it. In this case, the frequency components of the input signal show phase characteristics that are different from the original input signal after it is transmitted through the system. An example of a dispersive system is a telephone channel.
It is also important to emphasize the difference between a constant delay and a constant phase shift. In the case of continuous-time LTI systems, a constant delay means a linear phase response, while on the other hand, a constant phase shift means arg{H(jw)} is equal to some constant for all w.
These two cases have different implications, as constant delay is a requirement for distortionless transmission, and constant phase shift causes the signal to be distorted.
Equalization
To overcome linear distortion, a network known as an equalizer can be used. It is connected vertically in series with the required system. In the equalizer, the overall magnitude and phase responses inside the frequency band can approximate the conditions for distortionless transmission within the prescribed limit.
In practical use, the equalizer is designed to match the ideal value for the frequency response as closely as possible to reduce linear distortion to a satisfactory level.
The ideal value is represented as follows,
Heq (jw) = e^-jwt0/ Hc (jw)
It is also possible to design an equalizer with an analog filter, though the preferred method is to design in discrete-time using a digital filter. As with the discrete-time method, the channel output can be sampled before the equalization. And depending on the application, the equalizer can also give an output that is converted back to a continuous-time signal or left in the discrete-time, as required. Tapped delay line equalizer or the FIR digital filter is well suited for the equalization.
Reference