Architecture
The input signal is fed into a Hilbert Transform, an all-pass network that outputs two signals (the “real” and the “imaginary” signal) which are mutually phase shifted by 90°. This pair of signals represents kind of a “complex” version of the input signal (without negative frequencies).The signal pair is then modulated by a complex sinusoid (a cosine and a sine, i.e. again a signal pair mutually phase shifted by 90°) resulting in a frequency shifted version of the input. The amount of shifting may be controlled by am optional LFO.Finally, the effect signal can be mixed with the original input or one of the outputs of the Hilbert Transform (the “real” or the “imaginary” signal).Note that shifting the signal spectrum “below” zero Hertz will result in negativefrequencies that are clearly audible, meaning that at some point frequencies you're shifting “down” will reappear as frequencies that are rising “up”! This is not a bug of the Frequency Shifter but a fact of Digital Signal Processing mathematics. For more information see for example “The Scientist and Engineer's Guide to Digital Signal Processing” by Steven W. Smith, Ph.D. (a free PDF version of this great book is available at www.dspguide.com).