Click here to purchase the entire book in PDF format. Q Let's say that you want to build a bandpass filter with a bandwidth of one octave. This isn't difficult if you know the centre frequency and if it's never going to change. For example, if the centre frequency was 440 Hz, and the bandwidth was one octave wide, then the cutoff frequencies would be 311 Hz and 622 Hz (we won't worry too much at the moment about how I arrived at these particular numbers). What happens if we leave the bandwidth the same at 311 Hz, but change the centre frequency to 880 Hz? The result is that the bandwidth is now no longer an octave wide - it's one half of an octave. So, we have to link the bandwidth with the centre frequency so that we can describe it in terms of a fixed musical interval (for you engineers, a musical interval is a measure of the distance between two notes). This is done using what is known as the quality or Q of the filter, calculated using the equation: $$Q = \frac{f_{centre}}{\textrm{BW}}$$ (7.6) Now, instead of talking about the bandwidth of the filter, we can use the Q which gives us an idea of the width of the filter in musical terms. This is because, as we increase the centre frequency, we have to increase the bandwidth proportionately to maintain the same Q. Notice however, that if we maintain a centre frequency, the smaller the bandwidth gets, the bigger the Q becomes, so if you're used to talking in terms of musical intervals, you have to think backwards. The bigger the Q, the smaller the interval. Remember that you can have a very high Q, and therefore a very narrow bandwidth for a bandpass filter. All of the definitions still hold, however. The cutoff frequencies are still the points where we're 3 dB lower than the maximum value and the bandwidth is still the distance in Hertz between these two points and so on...