Waveform

In the domains of electronics, acoustics, and allied disciplines, the waveform of a signal denotes the graphical representation of its amplitude over time, irrespective of its temporal and magnitude scaling or any temporal displacement. Periodic waveforms exhibit consistent repetition over a fixed period. This terminology also extends to non-periodic or aperiodic signals, such as chirps and pulses.

Within electronics, this term typically refers to time-variant voltages, currents, or electromagnetic fields. Conversely, in acoustics, it commonly describes stable periodic sounds, which are characterized by pressure fluctuations in air or other mediums. In both contexts, the waveform constitutes an inherent characteristic that remains distinct from the signal's frequency, amplitude, or phase shift.

The waveform of an electrical signal can be graphically represented using an oscilloscope or other instruments capable of capturing and plotting its instantaneous values over time, provided appropriate scaling for the temporal and amplitude axes. The electrocardiograph, a medical instrument, records the waveforms of electrical signals linked to cardiac activity, with these waveforms possessing significant diagnostic utility. Waveform generators, which produce periodic voltages or currents with diverse waveform shapes, are indispensable instruments in electronics laboratories and workshops.

The timbre of a stable periodic sound is directly influenced by its waveform. Contemporary synthesizers and electronic keyboards are capable of producing sounds characterized by a wide array of intricate waveforms.

Common Periodic Waveforms

The subsequent list presents fundamental examples of periodic waveforms, where ${\displaystyle t}$ represents time, ${\displaystyle \lambda }$ denotes wavelength, ${\displaystyle a}$ signifies amplitude, and ${\displaystyle \phi }$ indicates phase:

• Sine wave: ${\textstyle (t,\lambda ,a,\phi )=a\sin {\frac {2\pi t-\phi }{\lambda }}.}$ The amplitude of this waveform varies according to a trigonometric sine function over time.
• Square wave: ${\textstyle (t,\lambda ,a,\phi )={\begin{cases}a,(t-\phi ){\bmod {\lambda }}<{\text{duty}}\\-a,{\text{otherwise}}\end{cases}}.}$ This waveform is frequently employed for the representation of digital information. A square wave with a constant period comprises odd harmonics that attenuate at a rate of −6 dB per octave.
• The triangle wave, represented by the formula ${\textstyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arcsin \sin {\frac {2\pi t-\phi }{\lambda }}.}$
• The sawtooth wave, defined by the equation ${\textstyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arctan \tan {\frac {2\pi t-\phi }{2\lambda }}.}$

The Fourier series provides a mathematical framework for decomposing periodic waveforms, illustrating that any such waveform can be constructed from the summation of a potentially infinite array of fundamental and harmonic constituents. Conversely, non-periodic waveforms possessing finite energy are amenable to sinusoidal analysis through the application of the Fourier transform.

Additional periodic waveforms are commonly referred to as composite waveforms, frequently characterized as a superposition of multiple sinusoidal waves or other fundamental basis functions.

Arbitrary waveform generator

• Arbitrary waveform generator
• Carrier wave
• Crest factor
• Continuous waveform
• Envelope (music)
• Frequency domain
• Phase offset modulation
• Spectrum analyzer
• Waveform monitor
• Waveform viewer
• Wave packet

References

Wei, Yuchuan, and Qishan Zhang. Common Waveform Analysis: A New and Practical Generalization of Fourier Analysis. Springer US, August 31, 2000.

• Yuchuan Wei, Qishan Zhang. Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis. Springer US, Aug 31, 2000
• He, Hao, Jian Li, and Petre Stoica. Waveform Design for Active Sensing Systems: A Computational Approach. Cambridge University Press, 2012.
• Golomb, Solomon W., and Guang Gong. Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar. Cambridge University Press, 2005.
• Jayant, Nuggehally S., and Peter Noll. Digital Coding of Waveforms: Principles and Applications to Speech and Video. Englewood Cliffs, NJ, 1984.
• Soltanalian, M. Signal Design for Active Sensing and Communications. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.
• Levanon, Nadav, and Eli Mozeson. Radar Signals. Wiley.com, 2004.
• Li, Jian, and Petre Stoica, editors. Robust Adaptive Beamforming. John Wiley, New Jersey, 2006.
• Gini, Fulvio, Antonio De Maio, and Lee Patton, editors. Waveform Design and Diversity for Advanced Radar Systems. Institution of Engineering and Technology, 2012.
• Benedetto, J. J., Konstantinidis, I., and Rangaswamy, M. (2009). "Phase-Coded Waveforms and Their Design." IEEE Signal Processing Magazine, 26(1): 22. Bibcode:2009ISPM...26...22B. doi:10.1109/MSP.2008.930416.A compilation of single-cycle waveforms acquired from diverse origins.
  • Collection of single cycle waveforms sampled from various sources