Waveform
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 generated by a synthesizer
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
Contents
1 Examples
2 See also
3 References
4 Further reading
5 External links
Examples
Simple examples of periodic waveforms include the following, where tdisplaystyle t
Sine wave(t,λ,a,ϕ)=asin2πt−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.
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.
Triangle wave(t,λ,a,ϕ)=2aπarcsinsin2πt−ϕλdisplaystyle (t,lambda ,a,phi )=frac 2api arcsin sin frac 2pi t-phi lambda. It contains odd harmonics that decrease at −12 dB/octave.
Sawtooth wave(t,λ,a,ϕ)=2aπarctantan2πt−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
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ISBN 0748770364, CRC Press, 2002, p. 62
^ ab "Waveform Definition". techterms.com. Retrieved 2015-12-09.
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. |
Collection of single cycle waveforms sampled from various sources
