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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/06/07 23:03:17」(JST)

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Sine, square, triangle, and sawtooth waveforms

A sine, square, and sawtooth wave at 440 Hz

A composite waveform that is shaped like a teardrop.

A waveform is the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.

In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term "waveform" refers to the shape of a graph of the varying quantity against time or distance. An instrument called an oscilloscope can be used to pictorially represent a wave as a repeating image on a screen.

To be more specific, a waveform is a set graph that represents an audio signal or recording which shows the changes in amplitude over a certain period of time.^[1] The amplitude of the signal is measured on the y-axis (vertical), as time is measured below on the x-axis (horizontal).^[1]

Most programs show waveforms to give the user a visual aid of what has been recorded by imagery.^{[clarification needed]} If the waveform is low, the recording was most likely soft.^[1] If the waveform is large and covering most of the image, the recording may have been recorded with the levels high.^[1] Waveforms can vary, they may be small when there is just a vocalist singing, but may become much larger when the drums and guitar come in. ^[1]

Examples of waveforms

Common periodic waveforms include (t is time):

Sine wave: sin (2 π t). The amplitude of the waveform follows a trigonometric sine function with respect to time.
Square wave: saw(t) − saw (t − duty). This waveform is commonly used to represent digital information. A square wave of constant period contains odd harmonics that decrease at −6 dB/octave.
Triangle wave: (t − 2 floor ((t + 1) /2)) (−1)^{floor ((t + 1) /2)}. It contains odd harmonics that decrease at −12 dB/octave.
Sawtooth wave: 2 (t − floor(t)) − 1. 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 harmonics that decrease at −6 dB/octave.

Other 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.

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.^{[relevant? – discuss]}

References

Yuchuan Wei, Qishan Zhang. Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis. Springer US, Aug 31, 2000 - Technology & Engineerin
Waveform Definition [1]

^ ^a ^b ^c ^d ^e "Waveform Definition". techterms.com. Retrieved 2015-12-09.

External links

Collection of single cycle waveforms sampled from various sources

UpToDate Contents

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English Journal

Temporal and spatial properties of arterial pulsation measurement using pressure sensor array.

Hu CS, Chung YF, Yeh CC, Luo CH.SourceDepartment of Electrical Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
Evidence-based complementary and alternative medicine : eCAM.Evid Based Complement Alternat Med.2012;2012:745127. Epub 2011 Jun 30.
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Determination of nonlinear medium parameter B/A using model assisted variable-length measurement approach.

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Japanese Journal

Modified Reset Waveform for High Speed Address under High Ambient Temperature in AC Plasma Display Panel

Jang Soo-Kwan,Park Hyung Dal,Tae Heung-Sik,Shin Bhum Jae,Seo Jeong Hyun
Jpn J Appl Phys 50(9), 096201-096201-6, 2011-09-25
… As a result, the proposed reset waveform with the ramp-up holding part optimized according to the subfield conditions was able to minimize the wall voltage variation during the address period, achieving a fast and stable address discharge under a high ambient temperature of +65 °C in a 50-in. …
NAID 150000057917

Model for Effects of RF Bias Frequency and Waveform on Si Damaged-Layer Formation during Plasma Etching

Eriguchi Koji,Takao Yoshinori,Ono Kouichi
Jpn J Appl Phys 50(8), 08JE04-08JE04-5, 2011-08-25
… However, we found that, owing to the stochastic effect on the ion-projected range, the effects of bias frequency and the waveform were suppressed, i.e., the thickness of the damaged layer and the density of residual defect sites are weakly dependent on IEDFs under the same average incident ion energy. …
NAID 150000057800