Harmonic

A harmonic in the physics and technology of a vibration whose frequency is an integer multiple of a fundamental frequency. A harmonic above the fundamental frequency is also harmonic, sometimes harmonic and called in music overtone.

As a function of time, the harmonic describes a purely sinusoidal oscillation. Harmonics play a role in music as well as in mechanics, electronics and optics.

Designations

There are the following names: The fundamental oscillation frequency f is called the first harmonic vibration at double the frequency (2f ) as second harmonic or first harmonic. In general, the oscillation with the frequency n times the fundamental frequency ( nf) the n harmonics, ie, the (n- 1). Harmonic. As higher harmonics all harmonics are referred to except the 1st harmonic.

The root is the first harmonic, an octave above the 2nd harmonic, which is the first overtone. The overtone is numerically always one number less than the harmonic. Even harmonics are odd harmonics and vice versa.

Basics

The FFT and DFT can be any periodic waveforms that are generated by a musical instrument as a sound or an oscillator as an electric audio signal or other signal, for example, decomposed into its frequency spectrum. Technically, this analysis can be performed with a spectrum analyzer.

For any periodic signal shows that in a sinusoidal fundamental frequency f and disassemble many more sinusoidal harmonic frequencies with integer multiples of the fundamental frequency f 2, f 3, f 4 and so can this. In the analysis, any periodic waveforms prove sum of infinitely many may sinusoidal signals. The reversal of this situation for the synthesis of periodic signals is also possible, however, by analysis and subsequent synthesis no longer be absolutely accurately restores the original. In contrast to the analysis of periodic waveforms of the decomposition of a non- periodic signal results in a continuous frequency range, which can include all frequencies.

In harmonic complex tones, the frequencies are between them and the fundamental frequency in integer ratio. In music simultaneously sounding pitches with such frequency ratios are perceived as harmonious sound and refers to the harmonics as overtone. Therefore, the term in the more general context described here stems. At approximately harmonic complex tones higher frequency components have a non- exact integer reference to the fundamental frequency, and already have a non-negligible proportion of inharmonicity on. At low harmonic complex tones have sound signals on Teiltonfrequenzen, which already differ significantly from the harmonic pattern. This includes all the sounds which are produced by striking of bells, bars or tubes or membrane-like bodies.

In the music signal is a sound. Each sound is made up of the fundamental tone and the overtones. Here determine the relative strengths, physically the amplitude ratios of the harmonics, the timbre of the sound. In terms such as partials, partials or harmonic frequencies of the fundamental frequency is counted in audio engineering. Speaking of overtones, the fundamental frequency is not counted and considered only the multiples of the fundamental frequency. In the literature there are also terms such as sub-harmonic tone series, which is inspired to see the mathematical definitions subharmonic function.

In electrical and communication equipment, the proportion of signals determined by harmonic frequencies to arrive at the passage through a system (for example, amplifiers or transmission path ) to the original signal, the extent of this sinusoidal input signal is distorted ( the fundamental frequency ) in the passage. These distortions are measured as total harmonic distortion. The resulting integer multiples of the fundamental frequency are superposed at the output of the system of the fundamental frequency. In power electronics form, generated for example by rectifier, harmonic frequencies interfering reactions on the operated with AC voltage public supply network. The occurring harmonic frequencies above the mains frequency can be reduced by the power factor correction.

Terms

Often the terms harmonic harmonic and harmonics are used synonymously for vibration with an integer multiple of a fundamental frequency verwendet.Im general terms are further differentiated, so that the first harmonic of the vibration at the fundamental frequency (fundamental wave ) and the first harmonic of the oscillation represents at twice the fundamental frequency. Thus, in general corresponds to the nth harmonic of the ( n -1). Harmonic.

Harmonic and harmonics can be distinguished in two ways:

• If you (ie vibrations ) talks about the processes involved in sending the signal, ie the corresponding concept harmonic " vibration of the transmitter with a harmonic ( vibrational ) frequency " - not to be confused with harmonic oscillation. Summarizing the carrier of the signal, such as air for sounds, the electromagnetic field for radio signals, etc., in the eye, then one speaks of harmonics.
• A harmonic is a higher harmonic of the periodic function of a quantity at the time. A harmonic is the higher harmonics of the periodic dependence of a value in place.

For example, pitch a ' and the first four harmonics

This table shows the root a '( this is the pitch at the fundamental frequency f = 440 Hz ) and its first three harmonics n with their order and their frequencies. The nth harmonic has generally the frequency n · f