DAFX: Digital Audio Effects, Second Edition

3.2 Modulators

3.2.1 Ring Modulator

In the ring modulation (RM), the audio signal x(n) is multiplied by a sinusoid m(n) with carrier frequency fc, as in Figure 3.1. While difficult in the analog domain, the multiplication is straightforward to realize in the digital domain [Ste87]. The input signal is called the modulator x(n) and the second operand is called the carrier m(n), giving the output signal

3.1

If m(n) is a sine wave of frequency fc, the spectrum of the output y(n) is made up of two copies of the input spectrum: the lower side band (LSB) and the upper side band (USB). The LSB is reversed in frequency and both side band are centered around fc (see Figure 3.2). Depending on the width of the spectrum of x(n) and on the carrier frequency, the side bands can be partly mirrored around the origin of the frequency axis. If the carrier signal comprises several spectral components, the same effect happens with each component. Although the audible result of a ring modulation is fairly easy to comprehend for elementary signals, it gets very complicated with signals having numerous partials. The carrier itself is not audible in this kind of modulation. When carrier and modulator are sine waves of frequencies fc and fx, one hears the sum and the difference frequencies fc + fx and fc − fx [Hal95].

Figure 3.1 Ring modulation of a signal x(n) by a sinusoidal carrier signal m(n).