Click here to purchase the entire book in PDF format. Ringing The phase response of a filter is typically strongly related to its Q. The higher the Q (and therefore the smaller the bandwidth) the greater the change in phase around the centre frequency. This can be seen in Figure 6.18 above. Notice that, the higher the Q, the higher the slope of the phase response at the centre frequency of the filter. When the slope of the phase response of a filter gets very steep (in other words, when the Q of the filter is very high) an interesting thing called ringing happens. This is an effect where the filter starts to oscillate at its centre frequency for a length of time after the input signal stops. The higher the Q, the longer the filter will ring, and therefore the more audible the effect will be. In the extreme cases, if the Q of the filter is 0, then there is no ringing (but the bandwidth is infinity and you have a flat frequency response - so it's not a very useful filter...). If the Q of the filter is infinity, then the filter becomes a sine wave generator. Figure 6.20: Ringing caused by minimum phase reciprocal peak/dip filters with centre frequencies of 100 Hz, gains of 24 dB and various Q's. The input signal is white noise, abruptly cut to digital zero as is shown in the top plot. There are at least three things to note: 1) The higher the Q, the longer the filter will ring at the centre frequency after the input signal has stopped. 2) The higher the Q, the more the output signal approaches a sine wave at the centre frequency. 3) Even a filter with a Q as low as 1 rings - although this will likely not be audible due to psychoacoustic masking effects.