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Constant Q Filter

Let's look at the frequency response of a filter with a centre frequency of 1 kHz, a Q of 4 and a two different amounts of boost or cut. If we plot these responses on the same graph, they look like Figure 6.11.

Figure 6.11: The frequency responses of a peak/dip filter with a centre frequency of 1 kHz, and a Q of 4. The Blue curve shows the filter with a gain of 12 dB, the black curve, a gain of -12 dB.
\includegraphics[width=2.75in]{06electroacoustics/graphics/1k_Q4_cutboost}

Notice that, although these two curves have ``matching'' parameters, they do not have the same shape. This is because the bandwidth (and therefore the Q) of a filter is measured using its 3 dB down point - not the point that's 3 dB away from the peak or dip in the curve. Since the measurement is not symmetrical, the curves are not symmetrical. This is true of any filter where the Q is kept constant and gain is modified. If you compare a boost of any amount with a cut of the same amount, you'll always get two different curves. This is what is known as a constant Q filter because the Q is kept as a constant. The result is called an asymmetrical filter (or non-symmetrical filter) because a matching boost and cut are not mirror images of each other.

There are advantages and disadvantages to this type of filter. The primary advantage is that you can have a very selective cut if you're trying to eliminate a single frequency, simply by increasing the Q. The primary disadvantage is that you cannot undo what you have done. This last statement is explained in the following section.

Figure 6.12: The frequency responses of various constant Q filters, all with a centre frequency of 1 kHz, gains of either 12 dB or -12 dB (depending on whether it's a boost or a cut) and various Q's. Black Q = 1. Green Q = 2. Blue Q = 4. Red Q = 8.
\includegraphics[width=2.75in]{06electroacoustics/graphics/constant_Q}


next up previous contents index
Next: Reciprocal Peak/Dip Filter Up: Equalizers Previous: Filter symmetry   Contents   Index
Geoff Martin 2006-10-15

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