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Sine, square, triangle, and sawtooth waveforms

A waveform is a variable that varies with time, usually representing a voltage or current.^[1]

Waveforms are conventionally graphed with time on the horizontal axis.

In electronics, an oscilloscope can be used to visualize a waveform on a screen. A waveform can be depicted by a graph that shows the changes in a recorded signal's amplitude over the duration of recording.^[2] The amplitude of the signal is measured on the ydisplaystyle y-axis (vertical), and time on the xdisplaystyle x-axis (horizontal).^[2]

Examples

Simple examples of periodic waveforms include the following, where tdisplaystyle t is time, λdisplaystyle lambda is wavelength, adisplaystyle a is amplitude and ϕdisplaystyle phi is phase:

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  Sine wave(t,λ,a,ϕ)=asin⁡2πt−ϕλdisplaystyle (t,lambda ,a,phi )=asin frac 2pi t-phi lambda . The amplitude of the waveform follows a trigonometric sine function with respect to time.


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  Square wave(t,λ,a,ϕ)={a,(t−ϕ)modλ<duty−a,otherwisedisplaystyle (t,lambda ,a,phi )=begincasesa,&(t-phi )bmod lambda <textduty\-a,&textotherwiseendcases. This waveform is commonly used to represent digital information. A square wave of constant period contains odd harmonics that decrease at −6 dB/octave.


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  Triangle wave(t,λ,a,ϕ)=2aπarcsin⁡sin⁡2πt−ϕλdisplaystyle (t,lambda ,a,phi )=frac 2api arcsin sin frac 2pi t-phi lambda . It contains odd harmonics that decrease at −12 dB/octave.


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  Sawtooth wave(t,λ,a,ϕ)=2aπarctan⁡tan⁡2πt−ϕ2λdisplaystyle (t,lambda ,a,phi )=frac 2api arctan tan frac 2pi t-phi 2lambda . 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.

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.

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


• Frequency domain


• Phase offset modulation


• Spectrum analyzer


• Waveform monitor


• Waveform viewer


• 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. 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

Wikimedia Commons has media related to Waveforms.

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  Collection of single cycle waveforms sampled from various sources