![]() That's pretty ugly as some frequencies got shifted so that they alias and thus have a positive frequency shift. This creates negative frequencies (green) that are mirror images of the positive frequencies. The resulting signal is complex, but we want a real signal, which we get by throwing away the imaginary part. Modulation here is by a complex exponential (the signal is multiplied by the complex exponential). The frequency shift $-\frac$ is an example. Here the range of possible frequencies in the signal are drawn as two arrows each spanning half the circumference of the z-plane unit circle: I would call it single-sideband frequency shifting. I have a bunch of images from 15 years ago to explain a way to do frequency shifting so that it has the best chance of sounding good. ![]() ![]() They may be referring to patent US3800088 by Harald Bode.
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