Rectilinear projection

Distortion

[dih-stawr-shuhn]

A distortion is the alteration of the original shape (or other characteristic) of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted. In some fields, distortion is desirable, such as electric guitar (where distortion is often induced purposely with the amplifier or an electronic effect to achieve the electric guitar's desired, electrifying, aggressive sound). The slight distortion of analog tapes and vacuum tubes is considered pleasing in certain situations. The addition of noise or other extraneous signals (hum, interference) is not considered to be distortion, though the effects of distortion are sometimes considered noise.

Electronic signals

In telecommunication and signal processing, a noise-free "system" can be characterised by a transfer function, such that the output y(t) can be written as a function of the input x as

y(t) = F(x(t))

When the transfer function comprises only a perfect gain constant A and perfect delay T

y(t) = Acdot x(t-T)

the output is undistorted. Distortion occurs when the transfer function F is more complicated than this. If F is a linear function, for instance a filter whose gain and/or delay varies with frequency, then the signal will experience linear distortion. Linear distortion will not change the shape of a single sinuosoid, but will usually change the shape of a multi-tone signal.

This diagram shows the behaviour of a signal (made up of a square wave followed by a sine wave) as it is passed through various distorting functions.

  1. The first trace (in black) shows the input. It also shows the output from a non-distorting transfer function (straight line).
  2. A high-pass filter (green trace) will distort the shape of a square wave by reducing its low frequency components. This is the cause of the "droop" seen on the top of the pulses. This "pulse distortion" can be very significant when a train of pulses must pass through an AC-coupled (high-pass filtered) amplifier. As the sine wave contains only one frequency, its shape is unaltered.
  3. A low-pass filter (blue trace) will round the pulses by removing the high frequency components. All systems are low pass to some extent. Note that the phase of the sine wave is different for the lowpass and the highpass cases, due to the phase distortion of the filters.
  4. A slightly non-linear transfer function (purple), this one is gently compressing as may be typical of a tube audio amplifier, will compress the peaks of the sine wave. This will cause small amounts of low order harmonics to be generated.
  5. A hard-clipping transfer function (red) will generate high order harmonics. Parts of the transfer function are flat, which indicates that all information about the input signal has been lost in this region.

The transfer function of an ideal amplifier, with perfect gain and delay, is only an approximation. The true behavior of the system is usually different. Nonlinearities in the transfer function of an active device (such as vacuum tubes, transistors, and operational amplifiers) are a common source of non-linear distortion; in passive components (such as a coaxial cable or optical fiber), linear distortion can be caused by inhomogeneities, reflections, and so on in the propagation path.

Amplitude distortion

Amplitude distortion is distortion occurring in a system, subsystem, or device when the output amplitude is not a linear function of the input amplitude under specified conditions.

Frequency distortion

This form of distortion occurs when different frequencies are amplified by different amounts, mainly caused by combination of active device and components. For example, the non-uniform frequency response curve of RC-coupled cascade amplifier is an example of frequency distortion.

Phase distortion

This form of distortion mostly occurs due to the reactive component, such as capacitive reactance or inductor capacitance. Here, all the components of the input signal are not amplified with the same phase shift, hence causing some parts of the output signal to be out of phase with the rest of the output.

Group delay distortion

Can be found only in dispersive media. In a waveguide, propagation velocity varies with frequency. In a filter, group delay tends to peak near the cut-off frequency, resulting in pulse distortion. When analog long distance trunks were commonplace, for example in 12 channel carrier, group delay distortion had to be corrected in repeaters.

Correction of distortion

As the system output is given by y(t) = F(x(t)), then if the inverse function F-1 can be found, and used intentionally to distort either the input or the output of the system, then the distortion will be corrected.

An example of such correction is where LP/Vinyl recordings or FM audio transmissions are deliberately pre-emphasised by a linear filter, the reproducing system applies an inverse filter to make the overall system undistorted.

Correction is not possible if the inverse does not exist, for instance if the transfer function has flat spots (the inverse would map multiple input points to a single output point). This results in a loss of information, which is uncorrectable. Such a situation can occur when an amplifier is overdriven, resulting in clipping or slew rate distortion, when for a moment the output is determined by the characteristics of the amplifier alone, and not by the input signal.

Teletypewriter or modem signaling

In binary signaling such as FSK, distortion is the shifting of the significant instants of the signal pulses from their proper positions relative to the beginning of the start pulse. The magnitude of the distortion is expressed in percent of an ideal unit pulse length. This is sometimes called 'bias' distortion.

Telegraphic distortion is a similar older problem, distorting the ratio between "mark" and "space" intervals.

Audio distortion

In this context, distortion refers to any kind of deformation of a waveform, compared to an input. Clipping, compression, non-linear behavior of electronic components, modulation, aliasing, and mixing phenomena or power supply inefficiencies can cause distortion.

In most fields, distortion is characterized as unwanted change to a signal.

Optics

In optics, image distortion is a divergence from rectilinear projection caused by a change in magnification with increasing distance from the optical axis of an optical system.

Map projections

In cartography, a distortion is the misrepresentation of the area or shape of a feature. The Mercator projection, for example, distorts Greenland because of its high latitude, in the sense that its shape and size are not the same as those on a globe.

See also

References

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