### VCF - Voltage Controlled Filter

The mixed oscillators a classical subtractive synthesizer pass a filter. The cut-off frequency can be controlled by a controll voltage. Another parameter of the filter is the resonance (sometimes called Q-factor). The resonance enhances the frequencies near the cut-off frequency. There are different types of filters:

### Low-pass filter (LPF)

As shown in the Figure below, the frequencies above the cut-off frequency are damped.

If the resonance parameter is not zero, then the frequencies near the cut-off frequence are amplified (indicated by the peak in the Figure below) and the frequencies above the cut-off frequencies are damped.

See the low-pass filter induced changes to single VCO waveforms on an oscilloscope:

#### Filtering basic VCO waveforms with a low-pass filter

low-pass-filter + nanoloop:

### High-pass filter (HPF)

Frequencies below the cut-off frequency are made more quiet

### Band-pass filter (BPF)

A frequency band passes the filter.

### Notch filter (NF)

A band of frequencies is cut out of the spectrum.

Low- and highpass filters can be characterized by the edge steepness. Typical values are 12 dB/octave or 24 dB/octave. The edge steepness tells how strong frequencies above the cut-off frequency (in case of the LPF) are damped. The resonance encances the frequencies near the cut-off frequency, this means that in the case of a LPF overtones will be pronounced and in case of a HPF deeper frequencies than the keynote are tuned up.

### Mathematic treatment

Mathematically spoken a filter has a characteristic curve in the frequency space which depends on the parameteres cut-off, resonance, edge steepness and filter-type (LPF, HPF, BPF, NF or in principal any other function curve). The frequency spectrum of the oscillator mix (obtained by fourier-transformation of that signal) has to be multiplied with the caracteristic curve of the filter. After fourier-transformation back into time-space one obtains the filtered signal.

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