﻿ Frequency modulation synthesis

# Frequency modulation synthesis

Frequency modulation synthesis, abbreviated as FM synthesis, refers to a technical modulation method based on the frequency modulation. The first frequency is frequency modulated directly by the frequency of the second oscillator in the simplest case by means of two oscillators.

In contrast to the frequency modulation used in radio and communication equipment as a transmission system, the two frequencies in the FM synthesis are spectrally close to each other. The motivation is the extraction of complex waveforms that are not going to win with the individual oscillators. The individual fundamental frequencies move for applications in the field of electronic music and sound in the human audible frequency range.

## Mathematical Background

Frequency modulation synthesis is part of the non-linear analog synthesis techniques and can easily simulate digitally when taking into account the sampling theorem does not exceed the so-called Nyquist frequency for the generated harmonics.

The following applies:

With the amplitude of the carrier angular frequency, for the frequency modulation circuit for the modulation index and on the time.

## Simple frequency modulation synthesis

Core of a simple FM synthesis is a pair of oscillators, the so-called operators. The frequency of the first oscillator can be controlled by the second oscillator. The first oscillator, the carrier and the second modulator. This principle is known from the FM radio transmission for some time. At slow modulation to 10 Hz vibrato is produced; in modulation of the carrier with a frequency in the audible range (ie, from 20 Hz upwards) is heard no more vibrato instead come to the root of the carrier added more overtones.

## Complex frequency modulation synthesis

FM synthesis of complex is referred to with the use of a plurality of modulators which modulate a single carrier. In this case, the resulting frequency spectrum is principally composed of the individual spectra of each modulator carrier pair.

### Parallel connection of the modulators

Modulator 1, and at least one other modulator 2 is modulated, and the latter then applied to the carrier. The final signal is composed of the frequency spectrum modulator 1, 2 modulator and carrier together so that it corresponds to an addition of the spectra of modulator 1 carrier and modulator 2 carrier.

### A cascade circuit of the modulators

When cascading the modulator pair 1 2 as a modulator -carrier pair in series acts. Each Teilsinuston now modulates the carrier. In principle, this results in a parallel circuit very similar frequency spectrum. It is added only that the sidebands of modulator 2 omitted in most of interconnection possibilities.

## History

The theoretical basis of the frequency modulation were based on the considerations Jean Baptiste Joseph Fourier, 1922 by John Renshaw Carson developed for the purpose of telecommunications. 1967 discovered the American John Chowning at Stanford University in the modulation of two sinusoids the emergence extremely overtone spectra. He patented and published the results of his research 1973. 1974 Yamaha licensed the company the patent. In 1982, Yamaha introduced the synthesizer GS1 and GS2, who worked for the first time with this technique.

The most popular FM synthesizer is the 1983 Yamaha introduced the DX7, which is available even today in virtual form as a plug- in from Native Instruments called FM8. Although the DX7 so that was for many users become synonymous with the FM technique, he does not actually do exactly taken with this method. Is used here, however, the related phase modulation that works mathematically integration.

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