1912:
582:
1592:
151:
1584:
1904:
45:
956:
1618:
2004:
745:
2047:, then the waveform may never actually reach the theoretical high and low levels, and if the system is underdamped, it will oscillate about the high and low levels before settling down. In these cases, the rise and fall times are measured between specified intermediate levels, such as 5% and 95%, or 10% and 90%. The
1566:
2027:
As already mentioned, an ideal square wave has instantaneous transitions between the high and low levels. In practice, this is never achieved because of physical limitations of the system that generates the waveform. The times taken for the signal to rise from the low level to the high level and back
1899:{\displaystyle {\begin{aligned}x(t)&={\frac {4}{\pi }}\sum _{k=1}^{\infty }{\frac {\sin \left(2\pi (2k-1)ft\right)}{2k-1}}\\&={\frac {4}{\pi }}\left(\sin(\omega t)+{\frac {1}{3}}\sin(3\omega t)+{\frac {1}{5}}\sin(5\omega t)+\ldots \right),&{\text{where }}\omega =2\pi f.\end{aligned}}}
2018:
For a reasonable approximation to the square-wave shape, at least the fundamental and third harmonic need to be present, with the fifth harmonic being desirable. These bandwidth requirements are important in digital electronics, where finite-bandwidth analog approximations to square-wave-like
571:
1435:
1268:
951:{\displaystyle {\begin{aligned}x(t)&=\operatorname {sgn} \left(\sin {\frac {2\pi t}{T}}\right)=\operatorname {sgn}(\sin 2\pi ft)\\v(t)&=\operatorname {sgn} \left(\cos {\frac {2\pi t}{T}}\right)=\operatorname {sgn}(\cos 2\pi ft),\end{aligned}}}
268:
1929:
600:
348:
2145:
2019:
waveforms are used. (The ringing transients are an important electronic consideration here, as they may go beyond the electrical rating limits of a circuit or cause a badly positioned threshold to be crossed multiple times.)
1930:
1358:
1995:
An ideal mathematical square wave changes between the high and the low state instantaneously, and without under- or over-shooting. This is impossible to achieve in physical systems, as it would require infinite
1428:
1579:
The six arrows represent the first six terms of the
Fourier series of a square wave. The two circles at the bottom represent the exact square wave (blue) and its Fourier-series approximation (purple).
598:
1003:
1623:
1008:
750:
1928:
1576:
445:
2137:
599:
635:
between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions between minimum and maximum are instantaneous.
395:
681:
Square waves are universally encountered in digital switching circuits and are naturally generated by binary (two-level) logic devices. They are used as timing references or "
182:
1561:{\displaystyle {\frac {2}{\pi }}\arctan \left(\tan \left({\frac {\pi ft}{2}}\right)\right)+{\frac {2}{\pi }}\arctan \left(\cot \left({\frac {\pi ft}{2}}\right)\right)}
1279:
689:
circuits at precisely determined intervals. However, as the frequency-domain graph shows, square waves contain a wide range of harmonics; these can generate
294:
1931:
642:
which allows arbitrary durations at minimum and maximum amplitudes. The ratio of the high period to the total period of a pulse wave is called the
716:. They also make up the "beeping" alerts used in many household, commercial, and industrial contexts. Additionally, the distortion effect used on
1363:
2051:
of a system is related to the transition times of the waveform; there are formulas allowing one to be determined approximately from the other.
591:
720:
clips the outermost regions of the waveform, causing it to increasingly resemble a square wave as more distortion is applied.
1984:
in non-ideal square waves can be shown to be related to this phenomenon. The Gibbs phenomenon can be prevented by the use of
109:
2210:
1921:
81:
958:
which will be 1 when the sinusoid is positive, −1 when the sinusoid is negative, and 0 at the discontinuities. Here,
566:{\displaystyle x(t)={\frac {4}{\pi }}\sum _{k=1}^{\infty }{\frac {1}{2k-1}}\sin \left(2\pi \left(2k-1\right)t\right)}
128:
88:
66:
2048:
1997:
1263:{\displaystyle {\begin{aligned}x(t)&=2\left-1\\&=2\sum _{n=-\infty }^{\infty }\left-1.\end{aligned}}}
95:
2015:
effects similar to those of the Gibbs phenomenon or ripple effects similar to those of the σ-approximation.
1432:
Using the fourier series (below) one can show that the floor function may be written in trigonometric form
62:
1615:, an ideal square wave with an amplitude of 1 can be represented as an infinite sum of sinusoidal waves:
735:
The square wave in mathematics has many definitions, which are equivalent except at the discontinuities:
698:
361:
263:{\displaystyle x(t)=4\left\lfloor t\right\rfloor -2\left\lfloor 2t\right\rfloor +1,2t\notin \mathbb {Z} }
77:
2060:
708:
In musical terms, they are often described as sounding hollow, and are therefore used as the basis for
17:
690:
662:
2283:
2235:
2203:
982:
628:
55:
406:
713:
2065:
2007:
Animation of the additive synthesis of a square wave with an increasing number of harmonics
1989:
993:
670:
287:
8:
1985:
724:
658:
102:
2278:
2196:
343:{\displaystyle \mathbb {R} \setminus \left\{{\tfrac {n}{2}}\right\},n\in \mathbb {Z} }
2182:
1981:
686:
654:
416:
2012:
1977:
963:
2003:
1591:
717:
709:
2173:
Interactive demo of square wave synthesis using sine waves, from GeoGebra site.
2119:, a musical instrument that produces odd overtones approximating a square wave.
1973:
1600:
1273:
438:
426:
2011:
Square waves in physical systems have only finite bandwidth and often exhibit
1937:
220 Hz square wave created by harmonics added every second over sine wave
1583:
697:
or errors. To avoid this problem in very sensitive circuits such as precision
2272:
2255:
2245:
2105:
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2080:
739:
431:
163:
159:
1353:{\displaystyle x(t)=2\left(2\lfloor ft\rfloor -\lfloor 2ft\rfloor \right)+1}
32:
This article is about the waveform. For the type of ocean surface wave, see
682:
1575:
650:
693:
or pulses of current that interfere with other nearby circuits, causing
646:. A true square wave has a 50% duty cycle (equal high and low periods).
2240:
2070:
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1946:
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2170:
1595:
Graph showing the first 3 terms of the
Fourier series of a square wave
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702:
632:
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33:
44:
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2090:
1955:
354:
2176:
1954:
The ideal square wave contains only components of odd-integer
685:", because their fast transitions are suitable for triggering
2095:
694:
2188:
2022:
150:
2179:
Interactive demo of square wave synthesis using sine waves.
1423:{\displaystyle x(t)=\left(-1\right)^{\lfloor 2ft\rfloor }.}
705:
are used instead of square waves as timing references.
981:
A square wave can also be defined with respect to the
311:
1621:
1438:
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1282:
1006:
748:
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185:
970:
is its frequency, which are related by the equation
69:. Unsourced material may be challenged and removed.
1898:
1560:
1422:
1352:
1262:
950:
565:
389:
342:
262:
2270:
2108:, a square-wave stripe target used in imaging.
1272:A square wave can also be generated using the
631:in which the amplitude alternates at a steady
2204:
1992:to help the sequence converge more smoothly.
1412:
1400:
1336:
1324:
1318:
1309:
2211:
2197:
2023:Characteristics of imperfect square waves
1976:representation of the square wave is the
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129:Learn how and when to remove this message
2002:
1590:
1587:(Odd) harmonics of a 1000 Hz square wave
1582:
1574:
638:The square wave is a special case of a
606:5 seconds of square wave at 220 Hz
14:
2271:
2171:Fourier decomposition of a square wave
1972:A curiosity of the convergence of the
649:Square waves are often encountered in
2192:
2148:from the original on 22 January 2023
67:adding citations to reliable sources
38:
1570:
390:{\displaystyle \left\{-1,1\right\}}
24:
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2177:Square Wave Approximated by Sines
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1945:Problems playing this file? See
1926:
738:It can be defined as simply the
629:non-sinusoidal periodic waveform
614:Problems playing this file? See
596:
149:
43:
54:needs additional citations for
29:Type of non-sinusoidal waveform
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2061:List of periodic functions
282:Domain, codomain and image
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1958:frequencies (of the form
691:electromagnetic radiation
663:digital signal processing
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277:Electronics, synthesizers
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592:Square wave sound sample
983:Heaviside step function
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2138:"Partial sum formula"
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1990:Lanczos sigma factors
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1603:with cycle frequency
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714:subtractive synthesis
712:sounds created using
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274:Fields of application
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2142:www.wolframalpha.com
2066:Rectangular function
1922:Additive square demo
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1364:
1280:
1004:
994:rectangular function
746:
725:Rademacher functions
671:two-state trajectory
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63:improve this article
659:digital electronics
172:General information
2009:
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2043:If the system is
1988:, which uses the
1982:Ringing artifacts
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1601:Fourier expansion
1571:Fourier analysis
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16:(Redirected from
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1978:Gibbs phenomenon
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1986:σ-approximation
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742:of a sinusoid:
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710:wind instrument
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677:Origin and uses
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2284:Fourier series
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2236:Non-sinusoidal
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2165:External links
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1274:floor function
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439:Fourier series
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427:Antiderivative
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401:Basic features
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2256:Triangle wave
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2246:Sawtooth wave
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2106:Ronchi ruling
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2101:Multivibrator
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2086:Sawtooth wave
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2081:Triangle wave
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119:December 2019
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78:"Square wave"
75:
74:Find sources:
68:
64:
58:
57:
52:This article
50:
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41:
40:
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27:
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2250:
2185:Square wave.
2150:. Retrieved
2141:
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61:Please help
56:verification
53:
26:
2251:Square wave
1871:where
731:Definitions
651:electronics
625:square wave
144:Square wave
2273:Categories
2124:References
2071:Pulse wave
2045:overdamped
1947:media help
1609:over time
1276:directly:
703:sine waves
667:stochastic
644:duty cycle
640:pulse wave
616:media help
158:, square,
89:newspapers
18:Squarewave
2279:Waveforms
2231:Sine wave
2220:Waveforms
2112:Cross sea
2076:Sine wave
2049:bandwidth
2037:fall time
2031:rise time
1998:bandwidth
1884:π
1875:ω
1857:…
1845:ω
1836:
1811:ω
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476:∑
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304:∖
253:∉
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166:waveforms
34:Cross sea
2146:Archived
2117:Clarinet
2091:Waveform
2055:See also
2034:and the
1956:harmonic
355:Codomain
234:⌋
223:⌊
212:⌋
206:⌊
164:sawtooth
160:triangle
2013:ringing
962:is the
103:scholar
2152:9 July
1599:Using
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1450:arctan
964:period
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627:is a
417:Period
407:Parity
288:Domain
162:, and
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2096:Sound
695:noise
110:JSTOR
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2154:2023
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661:and
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