# Waveform

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 -axis (vertical), and time on the -axis (horizontal).^{[2]}

## Examples[edit]

Simple examples of **periodic waveforms** include the following, where is time, is wavelength, is amplitude and is phase:

- Sine wave. The amplitude of the waveform follows a trigonometric sine function with respect to time.
- Square wave. 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. It contains odd harmonics that decrease at −12 dB/octave.
- Sawtooth wave. 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[edit]

- AC waveform
- Arbitrary waveform generator
- Crest factor
- Frequency domain
- Phase offset modulation
- Spectrum analyzer
- Waveform monitor
- Waveform viewer
- Wave packet

## References[edit]

**^**David Crecraft, David Gorham,*Electronics*, 2nd ed., ISBN 0748770364, CRC Press, 2002, p. 62- ^
^{a}^{b}"Waveform Definition".*techterms.com*. Retrieved 2015-12-09.

## Further reading[edit]

- 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[edit]

Wikimedia Commons has media related to .Waveforms |

- Collection of single cycle waveforms sampled from various sources