Audio Signal Processing and Coding

9.5 FM SYNTHESIS

The HILN algorithm seeks to optimize coding efficiency by making combined use of three distinct source models. Although the HILN harmonic sinusoid object has been shown to facilitate increased coding gain for certain signals, it is possible that other object types may offer opportunities for greater efficiency when representing spectrally complex harmonic signals. This notion motivated a recent investigation into the use of frequency modulation (FM) synthesis techniques [Chow73] in low-rate sinusoidal audio coding for harmonically structured single instrument sounds [Wind98]. In this section, we first review the basic principles of FM synthesis, and then present an experimental audio codec that makes use of FM synthesis operators for low-rate coding.

9.5.1 Principles of FM Synthesis

FM synthesis offers advantages over other harmonic coding methods (e.g., [Ferr96b] [Edle96c]) because of its ability to model with relatively few parameters harmonic signals that have many partials. In the simplest FM synthesis, for example, the frequency of a sine wave (carrier) is modulated by another sine wave (modulator) to generate a complex waveform with spectral characteristics that depend on a modulation index and the parameters of the two sine waves. In continuous time, the FM signal is given by

where A is the amplitude, f_c is the carrier frequency, f_m is the modulation frequency, ...