The sawtooth wave (or saw wave) is a kind of basic non-sinusoidal waveform. It is named a sawtooth based on its resemblance to the teeth on the blade of a saw. A sawtooth wave can be created by an instrument such as an oboe. Non-sinusoidal waveforms are waveforms that are not sine waves. ... Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ... Look up saw, SAW in Wiktionary, the free dictionary. ... The oboe is a double reed musical instrument of the woodwind family. ...

The usual convention is that a sawtooth wave ramps upward as time goes by and then sharply drops. However, there are also sawtooth waves in which the wave ramps downward and then sharply rises. The latter type of sawtooth wave is called a 'reverse sawtooth wave' or 'inverse sawtooth wave'. The 2 orientations of sawtooth wave sound identical when other variables are controlled.

A bandlimited sawtooth wave pictured in the time domain (top) and frequency domain (bottom). The fundamental is at 220 Hz (A2).

The piecewise linear function bandlimited sawtooth wave shown in time and frequency domains File links The following pages link to this file: Sawtooth wave Categories: Images with unknown source ... bandlimited sawtooth wave shown in time and frequency domains File links The following pages link to this file: Sawtooth wave Categories: Images with unknown source ... A function (blue) and a piecewise linear approximation to it (red). ...

based on the floor function of time t, is an example of a sawtooth wave with period 1. The floor and fractional part functions In mathematics, the floor function of a real number x, denoted or floor(x), is the largest integer less than or equal to x (formally, ). For example, floor(2. ... Wiktionary has related dictionary definitions, such as: period Wiktionary has related dictionary definitions, such as: periodic Period and periodic may refer to: Period (music) Period (rhetoric) Historical period Menstrual cycle, relating to the reproductive system Full stop, also known as a period, that marks the end of a sentence Science...

A more general form, in the range −1 to 1, and with period a, is

This sawtooth function has the same phase as the sine function. To meet Wikipedias quality standards, this article or section may require cleanup. ...

A sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency. Because it contains all the integer harmonics, it is one of the best waveforms to use for constructing other sounds, particularly strings, using subtractive synthesis. In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. ... The fundamental tone, often referred to simply as the fundamental, is the lowest frequency in a harmonic series. ... Subtractive synthesis is a method of sound synthesis characterised by the application of an audio filter to a source signal. ...

A sawtooth can be constructed using additive synthesis. The infinite Fourier series Additive synthesis is a technique of audio synthesis which creates musical timbre. ...

converges to a sawtooth wave. In digital synthesis, the series is only summed over k such that the highest harmonic, N_max, is less than the Nyquist frequency (half the sampling frequency). This summation can generally be more efficiently calculated using the Fast Fourier transform. If the waveform is digitally created directly in the time domain using a non-bandlimited form, such as y = x - floor(x), infinite harmonics are sampled and the resulting tone contains aliasing distortion. A digital system is one that uses discrete values (often electrical voltages), especially those representable as binary numbers, or non-numeric symbols such as letters or icons, for input, processing, transmission, storage, or display, rather than a continuous spectrum of values (ie, as in an analog system). ... The Nyquist frequency, named after Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system. ... The sampling frequency or sampling rate defines the number of samples per second taken from a continuous signal to make a discrete signal. ... A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. ... A bandlimited signal is a deterministic or stochastic signal (e. ... The floor and fractional part functions In mathematics, the floor function of a real number x, denoted or floor(x), is the largest integer less than or equal to x (formally, ). For example, floor(2. ... On statistics, signal processing, and related disciplines, aliasing is an effect that causes different continuous signals to become indistinguishable (or aliases of one another) when sampled. ...

Animation of the additive synthesis of a sawtooth wave with an increasing number of harmonics

An audio demonstration of a sawtooth played at 440 Hz (A4) and 880 Hz (A5) and 1760 Hz (A6) is available below. Both bandlimited (non-aliased) and aliased tones are presented. Image File history File links Synthesis_sawtooth. ... Image File history File links Synthesis_sawtooth. ... A440 is the 440 Hz tone that serves as the standard for musical pitch. ...

Image File history File links Sawtooth-aliasingdemo. ... Software development stages In computer programming, development stage terminology expresses how the development of a piece of software has progressed and how much further development it may require. ...

Applications

• The sawtooth wave is a base of almost all typical "synth" sounds in VA and analog synthesisers.
• The sawtooth wave is the form of the vertical and horizontal deflection signals used to generate a raster on CRT-based television or monitor. Oscilloscopes also use a sawtooth wave for their horizontal deflection, though they typically use electrostatic deflection.
  • On the wave's "ramp", the magnetic field produced by the deflection yoke drags the electron beam across the face of the CRT, creating a scan line.
  • On the wave's "cliff", the magnetic field suddenly collapses, causing the electron beam to return to its resting position as quickly as possible.
  • The voltage applied to the deflection yoke is adjusted through various means (transformers, capacitors, center-tapped windings) so that the half-way voltage on the sawtooth's cliff is at the zero mark, meaning that a negative voltage will cause deflection in one direction and a positive voltage will produce deflection in the other direction, allowing the whole screen to be covered by a center-mounted deflection yoke. Frequency is 15.75 kHz on NTSC, 16.75 kHz for PAL and SECAM)
  • The vertical deflection system operates the same way as the horizontal, though at a much lower frequency (60 Hz on NTSC, 50 Hz for PAL and SECAM).
  • The ramp portion of the wave must be perfectly linear - if it isn't, it's an indication that the voltage isn't increasing linearly, and therefore that the magnetic field produced by the deflection yoke won't be linear. As a result, the electron beam will accelerate during the non-linear portions. On a television picture, this would result in the image being "squished" to the direction of the non-linearity. Extreme cases will show obvious brightness increases, since the electron beam spends more time on that side of the picture.
  • Most TV sets used to have manual adjustments for vertical and/or horizonal linearity though they have generally disappeared due to the greater temporal stability of modern electronic components.

Analog Modeling Synthesizer, also referred to as Virtual Analog or VA is a synthesizer that emulates the sounds of traditional analog synthesizers using digital signal processing high quality samples of analog sound waves. ... Subtractive synthesis is a method of sound synthesis characterised by the application of an audio filter to a source signal. ... [[ Deflection happens when an object hits a plane surface In physics In physics deflection is the event where an object collides and bounces against a plane surface. ... Suppose the smiley face in the top left corner is an RGB bitmap image. ... CRT can mean: Cathode Ray Tube, in electronics, a display device (such as those used in one type of television) C Run-Time, in computing Charitable Remainder Trust, in Law Chinese Remainder Theorem, in mathematics Corneal Refractive Therapy, in medicine Criterion-referenced test, in U.S. schools Critical race theory... A Tektronix model 475A portable analogue oscilloscope, a very typical instrument of the late 1970s. ... Electrostatics is the branch of physics that deals with the force exerted by a static (i. ... The electron is a fundamental subatomic particle that carries an electric charge. ... A scanline is a line on a CRT tube, made up of dots. ... NTSC is the analog television system in use in Canada, Japan, South Korea, the Philippines, the United States, and some other countries, mostly in the Americas (see map). ... PAL, short for phase-alternating line, phase alternation by line or phase alternation line, is a colour encoding system used in broadcast television systems in large parts of the world. ... SÉCAM (Séquentiel couleur à mémoire, French for sequential colour with memory) is an analog color television system first used in France. ... NTSC is the analog television system in use in Canada, Japan, South Korea, the Philippines, the United States, and some other countries, mostly in the Americas (see map). ... PAL, short for phase-alternating line, phase alternation by line or phase alternation line, is a colour encoding system used in broadcast television systems in large parts of the world. ... SÉCAM (Séquentiel couleur à mémoire, French for sequential colour with memory) is an analog color television system first used in France. ...

See also

Sine, square, triangle, and sawtooth waveforms

• Sine wave
• Triangle wave
• Square wave
• Wave
• Sound
• Sawtooth distortion