Fundamental frequency , also fundamental wave or fundamental tone called, is a term used in the vibrational, acoustic , or electrical , the lowest (lowest) frequency in a mixture of harmonic frequencies , respectively.
Frequency is the number of oscillations per time. The basic frequency describes how often such a pattern repetition takes place.
If you consider a periodic signal in which a certain pattern is repeated over a certain period of time, the fundamental frequency describes how often the pattern is repeated per unit of time. An auditory determination is generally made in acoustics . In reality, periodic oscillations are always associated with a certain amount of secondary or harmonic oscillations . This not only applies to sound waves , the moving medium can be different: electrons in conductors or in a vacuum , mass particles in the air or other media.
The term basic frequency is used
- in the field of signal processing or communications technology to describe the behavior and characteristics of vibrations.
- in the field of music , to describe the pitch with which a musical tone of an instrument is perceived by a listener.
- in the field of pattern recognition , to describe periodicities .
- in the realm of speech, to describe the frequency at which the vocal cords vibrate during voiced speech.
Every discrete time signal can be described as the sum of a finite number of sinusoidal oscillations of the Fourier series . Periodic signals are composed primarily of those vibrations whose higher-frequency components are in an integer ratio to the fundamental frequency; the higher-frequency components are referred to as harmonics or as harmonics or, in certain contexts, also as partial tones, partials, overtones or distortion. The temporal length of the pattern of the periodic oscillation that is repeated over a certain period is referred to as period duration ; the basic frequency is the reciprocal of the period.
According to psychoacoustics , sounds are in most cases very complex in acoustics. A distinction between purely harmonic and in-harmonic complex tones is practically impossible or only possible with a certain probability on the basis of physical criteria. In general, tones are said to be harmonically complex that are periodic and whose root corresponds to the primary perceived pitch .
If a listener can assign a pitch to a musical sound or instrument, the perceived pitch is described by the fundamental tone and thus the fundamental frequency.
For example, several types of vibrations occur simultaneously in a guitar string: on the one hand, the entire string vibrates in the same way over its entire length; In addition, there are vibrations in which both halves of the string vibrate against each other at double frequency, vibrations with triple frequency on 1/3 of the string, etc. The vibration with the lowest frequency (similar vibration of the entire string) is the fundamental frequency here, the others Vibrations harmonics.
However, there are also sounds used musically for which an analysis of the time signals would not reveal a period. Such sounds have no fundamental frequency, so no pitch can be assigned to them. For example, drum tones have very high levels of noise , even (non-periodic) narrow-band noise can still be used as a musical tone.
In methods for pattern recognition, periodicities in signals are often searched for, for example by autocorrelation . Here, too, there is the term basic frequency in a more extended form as the repetition frequency of basic patterns.
See also: wavelet transformation
Determining the fundamental frequency of an individual speaker appears to be a simple signal processing task. In reality, however, the determination of the fundamental frequency has been an unsolved problem since research began in this area at the beginning of the 20th century. In the second half of the 20th century, numerous efforts were made and hundreds of algorithms for fundamental frequency determination (GFB algorithms) were developed. In what is probably the most comprehensive overview of this topic, Hess (1983) comes to the conclusion that there is no such thing as a GFB algorithm. He counts the determination of the fundamental frequency "one of the most difficult problems in speech signal processing" and concludes with the remark: "None [of the algorithms] works perfectly for all circumstances".
Hess gives five reasons why it is difficult to determine the fundamental frequency:
- Language is not stationary . The current articulation position of the vocal tract can change quickly, which leads to drastic changes in the temporal structure of the signal.
- Due to the many sensible articulation positions in the vocal tract and the diversity of human voices, there is a large number of time structures in the speech signal.
- The frequency range to be examined is up to four octaves . However, this does not mean that the range of the voice is four octaves, but that the spectrum of formants , which are important for determining the fundamental frequency, extends over this range.
- The excitation signal can be irregular.
- Voice transmission systems distort or band limit the signal.
The range used differs from speaker to speaker and may vary. a. also depends on whether the speaker reads a text out loud or speaks freely: Studies show that the fundamental frequency range of one octave is not exceeded when speech is read.
- Acoustic communication: Basics with audio examples, Ernst Terhardt, 1998, ISBN 3-54063-408-8 .
- Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harri Deutsch, Frankfurt am Main 2000, ISBN 3-8171-1628-4 .
- Gregor Häberle, Heinz Häberle, Thomas Kleiber: Expertise in radio, television and radio electronics. 3rd edition, Verlag Europa-Lehrmittel, Haan-Gruiten 1996, ISBN 3-8085-3263-7 .
- Thomas Görne: Sound engineering. 1st edition, Carl Hanser Verlag, Leipzig 2006, ISBN 3-446-40198-9
- Thomas Görne: Microphones in theory and practice. 8th edition, Elektor-Verlag, Aachen 2007, ISBN 978-3-89576-189-8 .
- Wolfgang Hess: Pitch Determination of Speech Signals 1st edition, Springer, Berlin 1983, ISBN 3-540-11933-7 .