# Frequency shifter

*Not to be confused with a pitch shifter.*

A **frequency shifter** is an effect that shifts all the harmonics in a signal.

When shifting exponentially, each harmonic in the input signal is multiplied or divided by the specified amount.

For example, a 100 Hz sawtooth wave has harmonics at double, triple, etc its frequencies, combining sine waves at 100 Hz, 200 Hz, 300 Hz, and so on.^{[1]}^{[2]} Exponential frequency shifting lets you change this to, say, a 110 Hz sawtooth wave with harmonics at 220 Hz and 330 Hz etc.

*Linear* frequency shifting, on the other hand, is where things get really interesting. Each harmonic has the specified amount *added or subtracted*. As harmonics generally work in an exponential manner, this changes the fractional relationships between all the harmonics, drastically changing the timbre.

Again, the example 100 Hz sawtooth wave has harmonics at 100 Hz, 200 Hz, 300 Hz, etc. This time, if you use the frequency shifter to shift all of these harmonics by 10 Hz, then they'll be 110 Hz, 210 Hz, 310 Hz, etc. But as above, a 110 Hz sawtooth wave would have harmonics at 220 Hz and 330 Hz etc, so this time the signal as a whole is no longer a sawtooth wave, because — from an exponential point of view — the distance between each harmonic has changed. The previously harmonic sound is now inharmonic, suitable for atonal percussion.

If the frequency shifter's voltage controlled, you can automatically sweep around these changes, raising and lowering all the harmonics in order to squeeze them together and spread them out.

A frequency shifter can make various kinds of effects, from subtle flanging through to making harmonic sounds clangy and inharmonic in much the same way ring modulation and frequency modulation can.

The only frequency shifter I'm aware of is the Bode Frequency Shifter by Harald Bode (since cloned in Analogue Systems's RS Integrator, Synth-Werk's 900 Series, and Behringer's 900 Series).

## References

- "System-100 Model 101 manual" Roland, Nov 1976, p. 14
*A Foundation for Electronic Music, second edition*Roland, pp. 17—18

## External links

### Deep dives

- "An Analog-Style Frequency Shifter" Nathan Ho

**Modulation**: FM synthesis | Frequency-shift keying | Frequency shifter

**Synthesis**: Envelope generator | Footing | Frequency shifter | Noise | Oscillator | Periodic waveform | Program (synthesiser) | Pulsewidth modulation | Sub-oscillator