Distortion - Electronic Signals

Electronic Signals

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

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