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 fall off at −6 dB/octave.
- Triangle wave: (t − 2 floor ((t + 1) /2)) (−1)floor ((t + 1) /2). It contains odd harmonics that fall off 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 fall off 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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