Linear Sweep Synthesis
Maurice Rozenberg · Computer Music Journal · 1982
During the last 10 years, many new techniques for sound synthesis have been developed. Among them, some of the most popular are frequency modulation (FM) (Chowning 1973) and nonlinear distortion, or waveshaping (Arfib 1979; LeBrun 1979). The method presented here is well known as chirp filtering in many fields such as radar (Cook 1960), optics (Papoulis 1968), and Fourier Transform theory (Oppenheim 1969; Bluestein 1970). The basic idea is very simple. Let us take as an example a sinusoidal sound c(t) whose frequency is swept between two values fl and f2 in a linear way (Fig. 1). At each moment the amplitude of that sound is multiplied by another modulating sound r(t) (Fig. 2). The period of r(t) is identical to the time of one sweep of c(t). The result of that process is shown in Fig. 3 in the time domain and in Fig. 4 in the frequency domain. We can see from these figures that the shapes are very similar with the exception that the spectrum is curved because of the logarithmic plot. The musical application of this process lies in the possibility of designing any spectral shape F(o) and realizing it through an envelope function r(t). Some properties of this method, called linear sweep, or linear sweep FM, are as follows.