Harmonics and non-linearities

When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom. Conversely, a system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, at least one even harmonic will be produced (and probably also odd).Symmetry (from Greek symmetrein "to measure together") has two meanings. The first is a vague sense of harmonious and beautiful proportion and balance.[1][2] The second is the exact mathematical "patterned self-similarity" with the rules of a formal system, such as in geometry or physics. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.[2][3] Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations such as scaling, reflection, and rotation; through other kinds of functional transformations;

4] and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[5][6] This article describes these notions of symmetry from four perspectives. The first is symmetry in geometry, which is the most familiar type of symmetry for many people. The second is the more general meaning of symmetry in mathematics as a whole. The third describes symmetry as it relates to science and technology. In this context, symmetries underlie some of the most profound results found in modern physics, including aspects of space and time. The fourth discusses symmetry in the humanities, covering its rich and varied use in history, architecture, art, and religion. The opposite of symmetry is asymmetry.Distortion (or warping) is the alteration of the original shape (or other characteristic) of something, such as an object, image, sound or waveform. Distortion is usually unwanted, and often efforts are to lessen it. In some fields, however, distortion may be desirable; such is the case with electric guitar distortion. The addition of noise or other outside signals (hum, interference) is not deemed to be distortion, though the effects of quantization distortion are sometimes deemed noise. A quality measure that explicitly reflects both the noise and the distortion is the Signal-to-noise-and-distortion (SINAD) ratio.