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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 is the shape of its graph 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 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 ...
s, currents, or
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
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 ...
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 a ...
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 of the signal. The term can also be used for non-periodic signals, like chirps and pulses. 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 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 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 ca ...
; 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 enginee ...
value. Waveform generators, 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.
Synthesizer A synthesizer (also spelled synthesiser) 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 complicated waveforms.


Examples

Simple examples of periodic waveforms include the following, where t is
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
, \lambda is
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, tr ...
, a is
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 ...
and \phi is phase: *
Sine wave A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...
: (t, \lambda, a, \phi) = a\sin \frac. The amplitude of the waveform follows a trigonometric 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 contains odd
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
s that decrease at −6 dB/octave. * Triangle wave: (t, \lambda, a, \phi) = \frac \arcsin \sin \frac. It contains odd
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
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 ...
: (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, as a sawtooth wave of constant period contains odd and even
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
s that decrease at −6 dB/octave. The
Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or '' ...
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 A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...
. 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.


See also

* AC waveform * Arbitrary waveform generator * Crest factor * Continuous waveform * Envelope (music) * Frequency domain * Phase offset modulation * Spectrum analyzer * Waveform monitor *
Waveform viewer A waveform viewer is a software tool for viewing the signal levels of either a digital or analog circuit design.Janick Bergeron, ''Writing Testbenches: Functional verification of HDL Models'', Kluwer Academic Publishers, 2000 Waveform viewers come ...
* Wave packet


References


Further reading

*Yuchuan Wei, Qishan Zhang. ''Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis.'' Springer US, Aug 31, 2000 * Hao He, Jian Li, and
Petre Stoica Petre is a surname and given name derived from Peter. Notable persons with that name include: People with the given name Petre * Charles Petre Eyre (1817–1902), English Roman Catholic prelate * Ion Petre Stoican (circa 1930–1990), Romanian vi ...

Waveform design for active sensing systems: a computational approach
Cambridge University Press, 2012. * Solomon W. Golomb, and Guang Gong
Signal design for good correlation: for wireless communication, cryptography, and radar
Cambridge University Press, 2005. * Jayant, Nuggehally S and Noll, Peter. ''Digital coding of waveforms: principles and applications to speech and video''. Englewood Cliffs, NJ, 1984. * M. Soltanalian
Signal Design for Active Sensing and Communications
Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014. * Nadav Levanon, and Eli Mozeson. Radar signals. Wiley. com, 2004. * Jian Li, and Petre Stoica, eds. Robust adaptive beamforming. New Jersey: John Wiley, 2006. * Fulvio Gini, Antonio De Maio, and Lee Patton, eds. Waveform design and diversity for advanced radar systems. Institution of engineering and technology, 2012. * John J. Benedetto, Ioannis Konstantinidis, and Muralidhar Rangaswamy.
Phase-coded waveforms and their design
" ''IEEE Signal Processing Magazine'', 26.1 (2009): 22–31.


External links


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