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Anyone know if the Bode frequency shifter has been studied somewhere. I just used an audio plug-in called EchoBode from SonicCharge and this is claimed to use a frequency (pitch) shifting algorithm inspired by the Bode frequency shifter.

The pitch shifting quality on this is pretty darn good I think, thus why I'm asking about it.


Here it's claimed to involve a ring modulator and a Hilbert transform.


Frequency shifting is linear and thus produces inharmonicity, but for small (max. 1-2 semitones) the quality is possibly better than with "granular" pitch shifting approaches. The inharmonicity is also not necessarily distortion or "ring-modulated", but may be even musical for some sounds such as percussive instruments.

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They may be referring to patent US3800088 by Harald Bode.

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. I would call it single-sideband frequency shifting. 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:

Fig. 1

T is integer and represents time. The frequency shift $-\frac{\pi}{4}$ is an example. Modulation here is by a complex exponential (the signal is multiplied by the complex exponential).

The resulting signal is complex, but we want a real signal, which we get by throwing away the imaginary part. This creates negative frequencies (green) that are mirror images of the positive frequencies.

Fig. 2

That's pretty ugly as some frequencies got shifted so that they alias and thus have a positive frequency shift. Also the spectrum of what we want got mixed with wrong-way-going frequencies (reversed spectrum). We can fix these problems using the following procedure:

Fig. 3

We filter away negative frequencies with a filter that has a do-nothing real part and a Hilbert transformer as the imaginary part. Then we modulate with a complex exponential and use another positive frequency pass filter to remove anything that might alias. Finally, discarding the imaginary component creates a nice-looking signal.

I excluded details about gain, but it suffices to know that if at the end the gain is wrong, the output needs to be multiplied by some factor $2^N$, $N$ integer.

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