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.
Examples of waveforms
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.
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- Collection of single cycle waveforms sampled from various sources