A quick index of this page (there'll be several different tutorials):
At the heart of the spectral bidules is something called FFT (Fast Fourier Transform). In the simplest of terms, the Fast Fourier Transform is a mathematical formula used for dissecting audio into bands of frequencies - the "frequency domain" (as opposed to the numeric samples that form a wave, called "time domain").
To illustrate this point, take a look at the images below. The first image shows a 440 Hz sine wave in the familiar time domain. The second shows a spectrum analyzed view of the same sound. "Spectrum analyzer?!?" you exclaim, "I thought we were talking about FFT?" :-) You got it... the best way to visualize FFT is to think of the familiar spectrum analyzer, most of which use FFT to calculate their data.

To use the spectral bidules, you need at least two elements:
a) The deconstruction - The FFT bidule is the key to it all, the one that decodes the audio signal from time domain to the spectral domain. The FFT bidule has two outputs: the yellow one is the frequency data (which identifies all the frequencies contained in the audio being analyzed); and the orange one is magnitude data (which identifies the volume of every frequency band in that particular sound).
b) The reconstruction - once the frequencies and frequency volumes (magnitude) have been manipulated, the two need to be combined and translated back into a time domain signal. The most accurate way of doing so is to use the iFFT bidule (inverse FFT) to reverse the FFT process. However, you can also use the Resynthesizer bidule to synthesize a new signal using a bank of oscillators. This alters the sound somewhat, giving different (but more creative) results.
Starting to make more sense now? Proceed to the next tutorial to see one simple use of the spectral bidules that can sometimes produce surprisingly original results.
In this tutorial, you will use FFT bidules to deconstruct two sounds, then multiply the magnitude signals to create a simple vocoder. This is known as spectral convolution.
1 To begin with, you'll need two sound sources. In this case, I'm using Crystal (the VST instrument, set to the Acid Trumpet preset - my fave), and a short voice sample which will be triggered with the Boboche sampler bidule.
2 Right-click the patchbay and select Spectral > FFT to add an FFT bidule to the layout. Repeat to add a second one.
3 Connect both of Crystal's outputs to the inputs on the first FFT bidule, and then connect all 12 (yes, I said ALL 12) of the samplers' outputs to the second FFT's input. Inside the sampler, I've set the vocal loop to play on all 12 notes (i.e., on any MIDI note).

4 To imprint one sound upon the other, you need to cross the magnitudes of both sounds with the frequencies of the first. In this case, we'll use a Magnitude Binary Operator bidule to multiply both magnitudes together. Right-click the layout, and select Spectral > Magnitude > Binary Operator. Double-click the bidule, and select * from the Operator drop-down list. Then rename the bidule to "*". Finally, connect the magnitude outputs from both FFT bidules to each of the inputs on the * bidule.
5 The resulting magnitude will carry the combined shape of both sounds, but isn't all that loud. Add a second Magnitude Binary Operator bidule for multiplication, and connect the first operator's output to the left input of this new one.
6 Now, you need to feed it another magnitude. Right-click the patchbay, and select Spectral > Magnitude > Variable. Connect the variable's output to the remaining input on the second * bidule. Rename the variable to "Output Volume". Open the bidule, and set the minimum value to 0, the maximum to 100, and give it a starting value of 25. Your patchbay should look something like this.

7 Right-click the patchbay and select Spectral > iFFT to add an inverse FFT bidule to the layout. Connect the frequency output from the first FFT bidule to the iFFT bidule, then connect the magnitude output from the second binary operator. Finally, connect the audio output from the iFFT bidule to an input on your mixer bidule.
8 Now, play your MIDI keyboard. The resulting sound will be something similar to a vocoder. Click the image below to hear an example (Ogg file) of the Crystal patch convoluted with the vocal sample.
Note the CPU usage: 43.04%... this is on a PIII 1 GHz processor. FFT operations, even in Bidule, are extremely demanding on the CPU. Please keep this in mind when using spectral bidules in compositions.
TIP Why not save this new FFT convolver as a group so that you can use it again? Click here for the UBUFAQ tutorial on groups, to learn more about Bidule groups.