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Waveform

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From Wikipedia, the free encyclopedia

Shape and form of a signal

For other uses, seeWaveform (disambiguation).

Sine,square,triangle, andsawtooth waveforms.

A sine, square, and sawtooth wave at 440 Hz

A composite waveform that is shaped like a teardrop.

A waveform generated by a synthesizer

Inelectronics,acoustics, and related fields, thewaveform of asignal is the shape of itsgraph as a function of time, independent of its time andmagnitude scales and of any displacement in time.^[1]^[2]Periodic waveforms repeat regularly at a constantperiod. The term can also be used for non-periodic or aperiodic signals, likechirps andpulses.^[3]

In electronics, the term is usually applied to time-varyingvoltages,currents, orelectromagnetic fields. In acoustics, it is usually applied to steady periodicsounds — variations ofpressure in air or other media. In these cases, the waveform is an attribute that is independent of thefrequency,amplitude, orphase shift of the signal.

The waveform of an electrical signal can be visualized with anoscilloscope or any other device that can capture and plot its value at various times, with suitablescales in the time and value axes. Theelectrocardiograph is amedical device to record the waveform of the electric signals that are associated with the beating of theheart; that waveform has importantdiagnostic value.Waveform generators, 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 itstimbre.Synthesizers and modernkeyboards can generate sounds with many complex waveforms.^[1]

Common periodic waveforms

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Simple examples of periodic waveforms include the following, where $t {\displaystyle t}$ istime, $\lambda$ iswavelength, $a {\displaystyle a}$ isamplitude and $\phi$ isphase:

Sine wave: ${\textstyle (t,\lambda ,a,\phi )=a\sin {\frac {2\pi t-\phi }{\lambda }}.}$ The amplitude of the waveform follows atrigonometric sine function with respect to time.
Square wave: ${\textstyle (t,\lambda ,a,\phi )={\begin{cases}a,(t-\phi ){\bmod {\lambda }}<{\text{duty}}\\-a,{\text{otherwise}}\end{cases}}.}$ This waveform is commonly used to represent digital information. A square wave of constantperiod contains oddharmonics that decrease at −6 dB/octave.
Triangle wave: ${\textstyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arcsin \sin {\frac {2\pi t-\phi }{\lambda }}.}$ It contains oddharmonics that decrease at −12 dB/octave.
Sawtooth wave: ${\textstyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arctan \tan {\frac {2\pi t-\phi }{2\lambda }}.}$ This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as the starting point forsubtractive synthesis, as a sawtooth wave of constantperiod contains odd and evenharmonics that decrease at −6dB/octave.

TheFourier 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 theFourier transform.

Other periodic waveforms are often called composite waveforms and can often be described as a combination of a number of sinusoidal waves or otherbasis functions added together.

References

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^^a ^b"Waveform Definition".techterms.com. Retrieved2015-12-09.
^David Crecraft, David Gorham,Electronics, 2nd ed.,ISBN 0748770364, CRC Press, 2002, p. 62
^"IEC 60050 — Details for IEV number 103-10-02: "waveform"".International Electrotechnical Vocabulary (in Japanese). Retrieved2023-10-18.

External links

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Wikimedia Commons has media related toWaveforms.

Collection of single cycle waveforms sampled from various sources

v t e Timbre
Colors of noise Fundamental frequency Jivari Loudness Microinflection Noise Overtone Pitch Rustle noise Sawari Spectral envelope Sympathetic string Tonality Waveform