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Triangle wave
 
 
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A triangle wave is a non-sinusoidal waveform
Waveform

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form....
 named for its triangular shape.








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Is triangular wave even or odd function








Encyclopedia


A triangle wave is a non-sinusoidal waveform
Waveform

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form....
 named for its triangular shape.

Triangle Td and Fd
Like a square wave
Square wave

A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels....
, the triangle wave contains only odd harmonic
Harmonic

In acoustics and telecommunication, a harmonic of a wave is a component frequency of the Signalling that is an integer multiple of the fundamental frequency....
s. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse), and so its sound is smoother than a square wave and is nearer to that of a sine wave
Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
.

One simple definition of a triangle wave is

It is possible to approximate a triangle wave with additive synthesis
Additive synthesis

Additive synthesis is a technique of audio synthesis which creates musical timbre.The timbre of an instrument is composed of multiple harmonics or partials, in different quantities, that change over time....
 by adding odd harmonics of the fundamental, multiplying every (4n-1)th harmonic by -1 (or changing its phase by ), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental
Fundamental frequency

The fundamental tone, often referred to simply as the fundamental and abbreviated f0 or F0, is the lowest frequency in a harmonic series ....
.

This infinite Fourier series converges to the triangle wave:

Synthesis Triangle
It is also possible to express a triangle wave with abs and floor:

Or with modulo:

where % is the modulo operator, e.g., x%y means x modulo y.

See also

  • Triangle function
  • Sine wave
    Sine wave

    The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
  • Sawtooth wave
    Sawtooth wave

    The sawtooth wave is a kind of non-sinusoidal waveform. It is named a sawtooth based on its resemblance to the teeth on the blade of a saw.The convention is that a sawtooth wave ramps upward and then sharply drops....
  • Square wave
    Square wave

    A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels....
  • Wave
    Wave

    A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
    s
  • Sound
    Sound

    Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....