 # Pole of a filter design

Pole This word has a number of mathematical definitions, some of which relate to audio, and particularly the design and implementation of filter s in audio. Capacitors and/or inductors are often integral components of ( analog ) filter design due to the way in which they interact with varying frequencies of periodic energy. For example, it is possible to create a low pass or high pass filter by placing a single capacitor in a circuit, assuming there is some resistance (a load ) elsewhere in the circuit. This is known as an RC circuit (Resistance and Capacitance). In filter design it is understood that a single RC circuit – a circuit with one capacitor and one resistor – is a one “pole” filter. A two pole filter has two RC circuits, and so on. A one pole filter will generally provide a high or low pass roll off in the neighborhood of 6 dB per octave (accompanied by some phase shift). For example, in a high pass filter the voltage of the signal will be cut in half each time the frequency is reduced by an octave, which corresponds to a reduction of 6 dB according to the formula 20log (V1/V2). A two pole filter will have a steeper roll off of 12 dB per octave. The more poles in a filter the steeper the roll off. In a band pass filter more poles equates to a higher Q. If one were to create a resonant filter, as is common in synthesizers (and wireless communication systems (radio, TV, etc.)), more poles would equate to a higher degree of resonance around a more narrow range of frequencies. All of these concepts are clearly related, but applied in different ways. Digital circuits and software can emulate the behavior of poles through certain types of algorithm s; however, software can also be written which will mathematically reduce the amplitude of frequency ranges in a manner quite different from “conventional” filters, which can allow for more control over certain aspects of a complex signal and produce a different sonic characteristic