Distortion

Graph of a waveform and some distorted versions of the same waveform

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

${\displaystyle y(t)=F(x(t))}$

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

${\displaystyle y(t)=A\cdot x(t-T)}$

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, the signal suffers linear distortion. Linear distortion does not introduce new frequency components to a signal but does alter the balance of existing ones.

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) distorts 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) rounds 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 gently compresses the peaks of the sine wave, as may be typical of a tube audio amplifier. This generates small amounts of low order harmonics.
5. A hard-clipping transfer function (red) generates 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.

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 is corrected.

An example of a similar 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 produces an uncorrectable loss of information. Such a situation can occur when an amplifier is overdriven—causing clipping or slew rate distortion when, for a moment, the amplifier characteristics alone and not the input signal determine the output.

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 and older problem, distorting the ratio between mark and space intervals.[2]

In the art world, a distortion is any change made by an artist to the size, shape or visual character of a form in order to express an idea, convey a feeling, or enhance visual impact. Such distortions or "abstractions" primarily refer to purposeful deviations from photorealistic perspective or from realistic proportionality. Examples include "The Weeping Woman" by Picasso and "The Adoration of the Shepherds" by El Greco, whose human subject matters are irregularly and (as is often with physical distortions) asymmetrically proportioned in a way that is not possible in standard perspective.

A graph of a waveform and the distorted version of the same waveform

With respect to audio, distortion refers to any kind of deformation of an output waveform compared to its input, usually clipping, harmonic distortion, or intermodulation distortion (mixing phenomena) caused by non-linear behavior of electronic components and power supply limitations.[3] Terms for specific types of nonlinear audio distortion include: crossover distortion and slew-induced distortion (SID).

Other forms of audio distortion are non-flat frequency response, compression, modulation, aliasing, quantization noise, wow and flutter from analog media such as vinyl records and magnetic tape. The human ear cannot hear phase distortion, except that it may affect the stereo imaging.

In most fields, distortion is characterized as unwanted change to a signal. Distortion in music is often intentionally used as an effect when applied to an electric guitar signal in styles of rock music such as heavy metal and punk rock.

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

In cartography, a distortion is the misrepresentation of the area or shape of a feature. The Mercator projection, for example, distorts by exaggerating the size of regions at high latitude.

 This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).

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