In electronics, the term is usually applied to time-varying
voltages,
currents, or
electromagnetic fields. In acoustics, it is usually applied to steady periodic
sounds — variations of
pressure in air or other media. In these cases, the waveform is an attribute that is independent of the
frequency,
amplitude, or
phase shift of the signal.
The waveform of an electrical signal can be visualized in an
oscilloscope or any other device that can capture and plot its value at various times, with suitable
scales in the time and value axes. The
electrocardiograph is a
medical device to record the waveform of the electric signals that are associated with the beating of the
heart; that waveform has important
diagnostic value.
Waveform generators, that can output a periodic voltage or current with one of several waveforms, are a common tool in electronics laboratories and workshops.
The waveform of a steady periodic sound affects its
timbre.
Synthesizers and modern
keyboards can generate sounds with many complicated waveforms.[1]
Common periodic waveforms
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.
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.
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.