electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...

, acoustics, and related fields, the waveform of a

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

is the shape of its

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

as a function of time, independent of its time and

magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...

scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics'', 2nd ed., , CRC Press, 2002, p. 62 In electronics, the term is usually applied to periodically varying

voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...

current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...

s, or electromagnetic fields. In acoustics, it is usually applied to steady periodic

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

s—variations of

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

in air or other media. In these cases, the waveform is an attribute that is independent of the

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

, or

phase shift In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it ...

of the signal. The term can also be used for non-periodic signals, like chirps and

pulse In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the n ...

s. The waveform of an electrical signal can be visualized in an oscilloscope or any other device that can capture and plot its value at various times, with a suitable

scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number w ...

in the time and value axes. The electrocardiograph is a

medical Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care practic ...

device to record the waveform of the electric signals that are associated with the beating of the

heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to t ...

; that waveform has important

diagnostic Diagnosis is the identification of the nature and cause of a certain phenomenon. Diagnosis is used in many different disciplines, with variations in the use of logic, analytics, and experience, to determine " cause and effect". In systems engin ...

value.

Waveform generator A signal generator is one of a class of electronic devices that generates electrical signals with set properties of amplitude, frequency, and wave shape. These generated signals are used as a stimulus for electronic measurements, typically used ...

s, that can output a periodic voltage or current with one of several waveforms, are a common tool in electronics laboratories and workshops. The waveform of a steady periodic sound affects its

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...

. Synthesizers and modern

keyboards Keyboard may refer to: Text input * Keyboard, part of a typewriter * Computer keyboard ** Keyboard layout, the software control of computer keyboards and their mapping ** Keyboard technology, computer keyboard hardware and firmware Music * Musi ...

can generate sounds with many complicated waveforms.

Examples

Simple examples of periodic waveforms include the following, where

t

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...

\lambda

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...

a

and

\phi

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

: * Sine wave:

(t, \lambda, a, \phi) = a\sin \frac

. The amplitude of the waveform follows a

trigonometric Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...

sine function with respect to time. * Square wave:

(t, \lambda, a, \phi) = \begin
a, & (t-\phi) \bmod \lambda < \text \\
-a, & \text
\end

. This waveform is commonly used to represent digital information. A square wave of constant

period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...

contains odd harmonics that decrease at −6 dB/octave. *

Triangle wave A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, ...

(t, \lambda, a, \phi) = \frac \arcsin \sin \frac

. It contains odd harmonics that decrease at −12 dB/octave. *

Sawtooth wave The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called ...

(t,\lambda, a, \phi) = \frac \arctan \tan \frac

. This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as the starting point for

subtractive synthesis Subtractive synthesis is a method of sound synthesis in which partials of an audio signal (often one rich in harmonics) are attenuated by a filter to alter the timbre of the sound. While subtractive synthesis can be applied to any source audio ...

, as a sawtooth wave of constant

contains odd and even harmonics that decrease at −6 dB/octave. The Fourier series describes the decomposition of periodic waveforms, such that any periodic waveform can be formed by the sum of a (possibly infinite) set of fundamental and harmonic components. Finite-energy non-periodic waveforms can be analyzed into sinusoids by the Fourier transform. Other periodic waveforms are often called composite waveforms and can often be described as a combination of a number of sinusoidal waves or other

basis functions In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be repres ...

added together.

References

External links

Collection of single cycle waveforms
sampled from various sources {{Waveforms

Examples

See also

References

Further reading

External links