FM synthesis - how it works
FM synthesis is a basic sound synthesis method that is difficult to predict in terms of its results. In this practical tip, we explain the basics of FM synthesis and show you some sound examples.
What is FM synthesis?
Basically, you should know the following about FM synthesis:
- FM synthesis is a sound synthesis process that creates artificial sounds or modifies natural sounds.
- The "FM" in FM synthesis stands for "Frequency Modulation".
- FM synthesis was invented by John Chowning in the early 1970s.
- In a technical article and his book, he explains the parameters precisely and gives initial instructions on how to reproduce natural instrument sounds using FM synthesis.
- FM synthesis is used in many keyboards and synthesizers, such as the Yamaha DX7 and the FM7 from Native Instruments.
- Other sound synthesis methods include additive synthesis, as can be heard in this YouTube video, as well as wavetable and granular synthesis, subtractive synthesis, amplitude modulation or ring modulation, physical modeling or waveshaping with lookup tables.
This is how FM synthesis works
In principle, FM synthesis works using a formula that can be easily implemented in both analog circuits and digital programming to produce complex sounds. In the following we explain the basic terms of FM synthesis. Time series and spectra as well as links to YouTube videos that also contain the resulting sounds can be found in the following picture gallery.
- FM synthesis basically begins with a formula consisting of a carrier frequency and a modulation frequency: A cos (2 π fc t + β cos (2 π fm t))
- The spectrum is constructed symmetrically around the carrier frequency or carrier frequency fc. These symmetrical frequencies are called "sidebands".
- The modulation frequency fm gives you the repetition rate of the frequency modulation. Low values are a low frequency oscillator (LFO) and vibrato can be heard. At higher frequencies, the modulation is so fast that a complex sound impression is created.
- The modulation index β determines the bandwidth, the fullness of the sound. It specifies the depth of modulation. The number of sidebands is approx. 2 × (β + 2).
- The frequencies of the sidebands are fc + k fm, where k is a positive or negative integer.
- If frequencies become too high for the sample rate, aliasing occurs: a frequency of 10000 + 1000 becomes 10000 - 1000 etc.
- "Negative" frequencies are also reflected, namely at 0 Hz. -10 Hz becomes 10 Hz, but out of phase by 180 °.
- If you keep the ratio of fc to fm and the modulation index β constant, the waveform will be transposed when you change the carrier frequency. This is how you can create an "instrument" with a homogeneous timbre.
- In order for fc to be the fundamental frequency of the sound, fm must be at least twice as large as fc, as this is the only way that all frequencies below the carrier become "negative" frequencies and, after mirroring, are 0 Hz higher than fc itself. Exception: fm = fc
In further CHIP online practical tips, we will explain how you can connect your electric piano to a PC and what General MIDI is all about.
Latest videos
A low modulation frequency produces a [[//youtu.be/I-Uo27R-OKw|Vibrato effect]]. The larger the modulation index here, the greater the depth of modulation, i.e. the frequency range of the frequency modulation.
From a modulation frequency of 20 to 30 Hz, the modulation is so fast that the impression of a [[//youtu.be/Ng9zfpN9Bzs| complex sound]] is created.
In digital systems, frequencies above the Nyquist frequency generate aliasing frequencies that are "mirrored" at the Nyquist frequency. Likewise, "negative" frequencies generate aliasing frequencies mirrored at 0 Hz.
In combination with an envelope, you can roughly recreate natural instrument sounds, such as the sound of brass instruments.
Incidentally, the carrier and modulator functions do not have to be cosine functions. A [[//youtu.be/R1tGy5JqXA0|Bessel function]] or a [[//youtu.be/e5KNJIuy7_M|Areasinus hyperbolic function]] is also possible.
