Fundamental frequency

The term fundamental frequency, even fundamental or root, is a concept from the theory of vibrations, acoustics, electrical engineering, refers to the lowest (bottom ) frequency in a harmonic frequency mixture. Under frequency refers to the number of oscillations per time. The fundamental frequency describes how often takes place such a pattern repeat.

Importance

Sees a periodic signal in which a specific pattern is repeated for a certain period, it describes the fundamental frequency, as often occurs a pattern repeat. In acoustics, auditory determination is made in general. In reality, periodic oscillations are always fraught with a certain amount of spurious emissions or harmonics, this is true not only with respect to sound waves. The medium is in motion can be different, electrons in conductors or vacuum mass particles in the air or other media.

Will apply the notion of the fundamental frequency

• In the field of signal processing and communications technology, in order to describe the behavior and the characteristics of vibrations.
• In the field of music, to describe with what pitch a musical tone of an instrument is perceived by a listener.
• In the field of pattern recognition, in order to describe periodicities.
• In the language used to describe the frequency swing with the vocal cords during voiced speech.

Signal Analysis

Each discrete time signal can be described in sum with a finite number of sinusoidal partials of the Fourier series.

Periodic signals are primarily composed of vibrations in which the higher-frequency components are an integer multiple of the basic frequency. Refers to the length of the repeating pattern over a given period of the periodic signal as a period of time, this results in the fundamental frequency of the reciprocal value of this period. Higher-frequency components of the oscillations are also referred to as harmonics, partials, partials, harmonics or overtone or in certain contexts as distortion. According to the psychoacoustics are in the acoustic tones in most cases very complex. A distinction between purely harmonic and inharmonic complex tones is practically based on physical criteria hardly or only with a certain probability possible. Generally referred to as harmonic complex tones those which are periodic and corresponds to the root of the principal perceived pitch.

The knowledge of the fundamental frequency of a signal to many methods of communication equipment (e.g., in the transmission technique ) and signal processing (for example in speech recognition ) is important.

Music

In the field of music, the fundamental frequency describes the pitch at which an instrument is perceived.

For example, come with a guitar string several types of vibrations at the same time before. On the one hand swings the entire guitar string identical over the entire length strings. In addition, there are oscillations in which both halves of the string with the double frequency vibrate against each other, vibration frequency tripled to 1/3 of the string, etc. The oscillation of the lowest frequency ( similar oscillation of the entire string ) here is the fundamental frequency, the other vibration harmonics.

There are also musical sounds used, in which an analysis of the time signals would result in no detectable period. For example, drum sounds have very strong noise components themselves ( non-periodic ) narrow-band noise can be used as a musical tone. Generally, musical sounds a tone and thus a fundamental frequency associated with when a listener can assign a sound pitch.

Pattern Recognition

In methods of pattern recognition is often sought after periodicities in signals, for example by autocorrelation. Again, there is the concept of fundamental frequency in a more extended form than repetitiveness of basic patterns.

See also: wavelet transform

Language

In the area of ​​language, the term fundamental frequency, the frequency at which the vocal cords vibrate during voiced speech. Determining the fundamental frequency of an individual the speaker will appear as a simple signal processing task. In reality, the fundamental frequency determination since the beginning of the research, however, is in this area in the early 20th century, an unsolved problem. In the second half of the 20th century, numerous efforts have been made to determine the fundamental frequency of a speaker. Hundreds of algorithms for determining the fundamental frequency ( GFB ) algorithms have been developed. Hess ( 1983) are to the most comprehensive overview of this subject and comes to the conclusion that there is no one GFB algorithm. Hess is one of the fundamental frequency determination " to the most difficult problems of speech signal processing " and concludes with the remark: "None [ of the algorithms ] works for all conditions properly ".

Hess cites five reasons why the fundamental frequency determination is difficult:

The range used is different from speaker to speaker and depends, inter alia, also depends on whether the speaker reads a text or acquits. Investigations show that in read speech the fundamental frequency range of an octave is not exceeded.