electronics Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

, and related fields, the waveform of a

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

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 discret ...

as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics'', 2nd ed., , CRC Press, 2002, p. 62 '' Periodic waveforms'' repeat regularly at a constant period. The term can also be used for non-periodic or aperiodic signals, like

chirp A chirp is a signal in which the frequency increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser syste ...

s and

pulse In medicine, the pulse refers to the rhythmic pulsations (expansion and contraction) of an artery in response to the cardiac cycle (heartbeat). The pulse may be felt ( palpated) in any place that allows an artery to be compressed near the surfac ...

s. In electronics, the term is usually applied to time-varying

voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...

s, currents, or

electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...

s. 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 br ...

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 eve ...

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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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 of the signal. The waveform of an electrical signal can be visualized with an

oscilloscope An oscilloscope (formerly known as an oscillograph, informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing i ...

or any other device that can capture and plot its value at various times, with 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 ...

in the time and value axes. The electrocardiograph is a

medical Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, ...

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

heart The heart is a muscular Organ (biology), organ found in humans and other animals. This organ pumps blood through the blood vessels. The heart and blood vessels together make the circulatory system. The pumped blood carries oxygen and nutrie ...

; that waveform has important

diagnostic Diagnosis (: diagnoses) is the identification of the nature and cause of a certain phenomenon. Diagnosis is used in a lot of different academic discipline, disciplines, with variations in the use of logic, analytics, and experience, to determine " ...

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, which 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 of a musical note, sound or tone. Timbre distinguishes sounds according to their source, such as choir voices and musical instrument ...

Synthesizer A synthesizer (also synthesiser or synth) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis a ...

s and modern keyboards can generate sounds with many complex waveforms.

Common periodic waveforms

Simple examples of periodic waveforms include the following, where

t

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

\lambda

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

a

and

\phi

is phase: *

Sine wave A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...

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

The amplitude of the waveform follows a trigonometric sine function with respect to time. *

Square wave Square wave may refer to: *Square wave (waveform) A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same ...

(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 contains odd

harmonic In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...

s that decrease at −6 dB/octave. * Triangle wave:

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

It contains odd

s 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 a ...

(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 Harmonic_series_(music)#Partial.2C_harmonic.2C_fundamental.2C_inharmonicity.2C_and_overtone, overtones of an audio signal are attenuated by a audio filter, filter to alter the timbre of ...

, as a sawtooth wave of constant period contains odd and even

s that decrease at −6 dB/octave. The

Fourier series A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems ...

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 In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

. 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 added together.

References

External links

Collection of single cycle waveforms
sampled from various sources {{Authority control

Common periodic waveforms

See also

References

Further reading

External links