Single sideband modulation

Figure 8.31: Using an all-pass filter network to make a frequency shifter.

As described in Section 8.4.3, a pair of all-pass filters can be constructed to give roughly $\pi /2$ phase difference for positive frequencies and $-\pi/2$ for negative ones. The design of these pairs is beyond the scope of this discussion (see, for instance, [Reg93]) but Pd does provide an abstraction, hilbert~, to do this. Example H09.ssb.modulation.pd, shown in Figure 8.31, demonstrates how to use the hilbert~ abstraction to do signal sideband modulation. The Hilbert transform dates to the analog era [Str95, pp.129-132].

The two outputs of hilbert~, considered as the real and imaginary parts of a complex-valued signal, are multiplied by a complex sinusoid (at right in the figure), and the real part is output. The components of the resulting signal are those of the input shifted by a (positive or negative) frequency specified in the number box.