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For other uses, see Waveform (disambiguation).
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. By extension, the term "waveform" also describes the shape of the graph of any varying quantity against time.[citation needed]

Examples of waveforms[edit]

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? ]

See also[edit]


  • Yuchuan Wei, Qishan Zhang. Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis. Springer US, Aug 31, 2000 - Technology & Engineering

Further reading[edit]

External links[edit]