Ringing in the Ears.
This set of pages is a version of an article that was orginally published
in the November 2004 issue of Hi Fi News magazine.
During the last few years a controversy has arisen over the behaviour of the processes employed in CD players to reconstruct analogue musical waveforms from digital data. This has centred upon a disagreement about the audibility of a side-effect of using some forms of digital filtering. On one side, some people have felt that the details of any ‘problem’ were such that it wouldn’t actually change the sound in any audible way. Yet others have insisted that the traditional types of filters do alter the sound, and they point to noticeable changes in the filtered waveform as being the reason.
To attempt to resolve the situation I decided to examine the effects of filtering upon a simple example of the kind of waveform we might be expected to process. In particular, I decided to try comparing the results of applying filtered and unfiltered waveforms to some models of human hearing. The aim being to see if the filter effects might be audible or not.
Figure 1 shows the example waveform I chose. It consists of a waveform that switches on at a specific time. Before this starting time, the input level is zero. After this time the wave is a combination of three sinewave components whose relative frequencies are in the ratio 1:3:7. Hence I’ve called this waveform “Burst137”. We can now see the effect of passing this signal through a typical ‘time symmetric’ digital filter of the kind often employed in units like CD players. For the sake of our tests I’ve assumed that the chosen filter is designed to remove any components above ten times the fundamental frequency of our test waveform.
The advantage of time symmetric filters is that they should ensure that the relative phases of frequency components within the intended passband should not be altered by passage through the filter. Hence, ideally, the only effect such a low-pass filter should have is to strip away any high frequency components above the chosen cut-off frequency. The reason filters of this type have become the standard for around 20 years is that – if we accept the traditional argument – they leave all the audible features of the sound unchanged but suppress any unwanted ultrasonic distortions. Unfortunately, they have an Achilles heel...
When we apply our symmetric filter to the burst137 test waveform the results are as shown in Figure 2. This represents the input waveform as a broken blue line and the filtered output as a continuous red line.
We only explicitly included three frequency components in our burst137 waveform. Since these were at 1, 3, and 7 cycles per unit time, and our chosen filter is designed not to alter any components below 10 cycles, we might expect the output to look identical to the input. Yet when we look at Figure 2 we can see this is obviously not the case. The red waveform differs from the input in two quite obvious ways.
- It seems to be delayed by about half a time unit.
- The waveform has a small wiggle during this period while the start of the burst seems to be finding its way through the filter on its way to the output.
This ‘pre-wiggle’ is what tends to be referred to as Pre-Ringing. This is the feature which has attracted attention as a result of claims that it produces an audible change in the waveform. It arises as a consequence of the way that time symmetric filters operate. Along with the delay before the wanted part of the waveform emerges from the filter, the pre ringing is a consequence of how these filters work. In the absence of any pre ringing the short delay would not matter much, and the music would just sound as if we’d pressed the ‘play’ button of the CD player a fraction of a second later than we actually did! However the pre ringing is more worrying as it is a feature that seems to have been added to the music.