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Reproduced from Studio Sound, July 1990 Why do equalisers sound different? Michael Gerzon claims to have no
definitive answers to this question but does offer interesting conjectures
and food for thought Every equaliser has its own sound, and for some time it has been suspected
that this is not simply a matter of their amplitude responses. It has been
believed that the ears are insensitive to the phase response of equalisers
but now some people are starting to claim that, really, amplitude response is
quite unimportant and most of the subjective effect of equalisers is due to
their phase response. Certainly, phase response is relevant, as
noted by Phil Newell in his series on monitor loudspeakers1. He
notes, correctly, that adjusting the polarity of speaker units to maximise flatness of frequency response can
often give a much more coloured result than the other polarity, which can
give a sharp dip in the amplitude response but a much smoother phase
response. However, this does not prove (and neither did Newell claim) that phase
response is much more important than amplitude response, only that both are
important and must be carefully related to one
another for the best sound. Let’s look at what determines the subjective
sound of an equaliser. Unlike others, I do not claim to give definite answers. My aim, rather, is to
make some tentative conjectures, report some rules-of-thumb that have often
been used with some success and to raise some questions so people can give
some intelligent thought to the problem and maybe eventually find some
answers. We will rapidly enter the treacherous areas
of hi-fl subjectivism, however, unlike the woolly-minded approach of many in
the hi-fl press, I believe that ultimately one needs no magic pseudo-science to explain the mysteries. The problem with most ‘objectivists’ who
demand measurable reasons for subjective differences, is that they are very
narrow-minded about what kind of measurements they will consider. They often
demand that measurements can easily be done on conventional audio test setups.
We shall see that it is highly unlikely that some of the most audibly
important aspects of equaliser response can be measured either in the
amplitude or the phase response but that we shall probably have to look
elsewhere. Now this is very near
heresy. It is a standard mathematical result in the mathematical theory of
linear filters that the behaviour of any such filter is completely determined
if one knows its amplitude and phase response. This is no longer true if the
filter has nonlinear distortion – and many subjective differences between
equalisers are believed to be due to nonlinear distortion effects. However, I
claim that even if one has a perfectly linear filter and measures both its
amplitude and its phase response, one will still not, from these measurements
alone, be able to predict its sound. I am a mathematician, and
I do believe the theoretical mathematical result that the filter response is
completely specified by its amplitude and phase response. The key words in
the above are ‘if one… measures its
amplitude and phase response’. The point is that real-world measurements are
never exact, and what we shall see is that incredibly small changes in
amplitude and phase response, supposedly quite ‘negligible’ according to
objectivist ideas, can actually have large audible effects. This is not to
say that these effects cannot be measured, only that measurements of
amplitude and phase responses are not the way to do the measurement. If I prove to be right in
my claims, we shall have to stop thinking of filters purely in terms of their
amplitude and phase responses but will have to find other new ways of looking
at them. The evidence In the late 1950s, H D Harwood at the BBC
made a discovery whose importance is still not fully recognised. In investigating
the performance of loudspeakers, he discovered that low-level delayed
resonances severely coloured the reproduced sound even if these resonances
were 40dB below the main speaker response. At first sight there’s nothing
very world-shaking about that. But consider what the effect of such a delayed
resonance is on the amplitude and phase response; 40dB down means a signal
whose amplitude is only 1% of the main signal. This means that the amplitude
response must vary only between 99% and 101% of flat, ie within ±0.1
dB. The effect on phase response must similarly be within 1/100
rad, ie within ±0.6o. In
other words even in the late 1950s Harwood showed that variations in phase
response of around only 1o and in amplitude response of ±0.1dB produced
audible colouration. I am not claiming that
all possible variations of phase and amplitude responses of this magnitude
will produce colourations, only that specific variations produced by delayed
resonances. With the improvements in
audio technology since that date, it would probably now be safer to tighten
up these figures by a factor 10 – in other words to suspect delayed
resonances 60dB down of colouration, even though they would cause amplitude
variations of only ±0.01dB and phase variations of ±0.06o. It should not have been a
surprise in the mid 1970s when it was discovered that turntables had a
‘sound’, since measurements had long revealed bumps in their amplitude
responses associated with delayed resonances in their mechanical system of a
magnitude already identified by Harwood as being subjectively important in
loudspeakers. However, until that time, most audio engineers had ignored the
tiny bumps and kinks in their measurements of record frequency response as
being too small to be audible, despite the prior evidence of Harwood’s work. In the mid 1980s, a
second piece of evidence – that the ears could easily pick out tiny
deviations in amplitude and phase response – emerged, in connection with
digital filters. In an early attempt at digital noise suppression, Roger
Lagadec, then at Studer, investigated a multiband digital noise gate that
split the audio signal into 512 bands, noise-gated the bands separately and
then put them back together again. Although this was very effective in
reducing noise, it was discovered that there was a disturbing audible
colouration, even if the noise-gating action was switched off. It was
discovered that this colouration was due to the amplitude response of the
filtered bands added together again not being quite flat – there was a ±0.1dB
ripple in the frequency response. It was found that to remove the upsetting
audible colouration required this ripple to be reduced to around ±0.001dB. In
this case, all the digital filters had linear phase responses – so only the amplitude
response could be blamed for the colouration. So, from a variety of
directions, we have been finding that tiny ripples in the amplitude and phase
responses can have important subjective audible effects, causing obvious or
even gross colourations. And yet, one can also produce large deviations in
amplitude or phase response that cause almost no colouration, as we shall
see. It becomes evident that simply looking at the magnitude of deviations
from flatness of either amplitude or phase responses tells us very little
about the subjective result. The ears are responding to something else
entirely. But what? Rules of thumb Frankly, we don’t yet know for sure how the
ears I determine the degree of colouration of an equaliser. Over the years,
however, many indirect clues have been found as to what is happening. If we
cannot yet say who committed the murder and how, at least we can list some of
the suspects and their possible motives. One of the oldest
suspects, whose guilt is believed in by many audio designers, hi-fi buffs and
even professionally respected recording engineers, is known, in the best
tradition of spy novels, by a single code letter: Q. The rule of thumb used
by many designers is simple: it will sound coloured if the filter has a Q
much larger than 0.5. I am indebted to Tom Holmes, formerly of Philips Hi-Fi
Labs, many years ago for pointing out that Q smaller than about 0.6 appears
to sound uncoloured, and larger than 0.6 appears to sound coloured. Q is shorthand for
‘quality factor’. In recording work, Q is encountered mainly as a number on
parametric equalisers – with high Q corresponding to sharp peaks or dips and
low Q to broad peaks or dips. However, the concept of Q applies to all
filters, even to all-pass filters, which have a flat amplitude response but a
nonlinear phase response. It is not intended here to give the mathematical
theory of Q – if you are familiar with the theory of filter design you’ll
already know – however, an understanding of the meaning of Q can be given.
Although conventional theoretical accounts of Q look at the frequency
behaviour of an equaliser (ie its amplitude and phase response as a
function of frequency) it is actually easier to explain the idea in terms of
the time response of a filter. All filters smear out in
time any sharp momentary impulse fed into them and it is a commonplace of
filter theory that the behaviour of a linear filter is determined entirely by
its impulse response, ie its output waveform when fed with a sharp
impulse. All analogue filters (as well as those digital filters that use
digital feedback in their realisation – known technically as ‘recursive’ filters) not only
affect the initial shape of the impulse waveform but also affect the way the
impulse response eventually dies away to nothing. It is the nature of this
decaying part of the impulse that has to do with Q. A low Q filter invariably has
the final part of the decay of its impulse response die away smoothly without
any oscillation or change of signal polarity. If, however, the Q exceeds 0.5,
then the final part of the decay oscillates about zero (Fig 1). It appears that the ears are sensitive to such oscillations in
the decay part of the impulse response, even at very low levels. Such
oscillations are often termed resonances, the frequency of the resonance
being the frequency of this final decaying oscillation.
Now Q can be thought of
as a measurement of how rapidly the amplitude dies away per cycle of
oscillation. The bigger the Q, the smaller the decay (in dB) per cycle, and
the more cycles are gone through before a given degree of decay (in dB)
occurs. The effects of this
oscillatory decay are audible even if the early part of the impulse response
of a high-Q filter is such that it has an absolutely flat 1 amplitude
response. It is perfectly possible to design such high-Q ‘all-pass’ filters (Fig 2 gives a typical circuit) and
generally they sound much more coloured than low-Q all-pass filters, even if
the latter are designed to cause many hundreds of degrees of phase shift.
It is significant that,
in order to achieve a flat frequency response with a rapid crossover between
speaker units, most multiway speakers are actually designed to have an
all-pass response and if a high Q all-pass is chosen in order to make
crossover rates more rapid, such speakers are likely to sound coloured2. The magic audibility
threshold Q=0.6, rather than the strict no-resonance figure Q=0.5, suggests
that the ears will actually tolerate some oscillation in the decay but the amount
involved is surprisingly small. For a Q of 0.6, successive cycles of the
oscillation are attenuated by about 80dB compared to the previous cycle. This
means that, for a Q of 0.6, alternate polarity swings are about 40dB below
the previous swing of opposite polarity. The Q=0.6 threshold was
theoretically suggested on quite different grounds derived from the behaviour
of conventional 12dB/octave lowpass filters. The ‘maximally flat’ such
filter, ie the one with the flattest amplitude response in the pass
band, is known as a Butterworth filter and has a Q of 0.71. In much audio
work requiring an uncoloured sound, preference has been for use of a lowpass
filter with a maximally flat phase response, which is termed a Bessel filter,
which has a Q of 0.58. Bessel filters have a slower high frequency roll-off
but their ‘smoothest possible’ phase response has been found to give a
subjectively superior sound. The empirical threshold Q of 0.6 for low
colouration is very close to the Q of the Bessel filter having maximally flat
phase response. Anecdotal evidence of the
importance of Q arises from experiments conducted by Philips in the early
‘70s with the then-new Dolby A noise reduction system. Dolby A is a multiband system using Butterworth filters to separate the
frequency bands. It was noted by many engineers that Dolby A gave some subjective colouration, so Philips’ engineers tried
replacing the Butterworth filters with Bessel filters. They indeed found that
such ‘Bessel Dolby A’ had a much lower audible colouration
than standard ‘Butterworth Dolby A’. The
only problem was that it was incompatible with the already-standard
Butterworth Dolby A system, so it proved to be
impractical to introduce the Bessel version into studio use. Now Dolby A is a reciprocal system, ie one
whose decoding nominally exactly undoes its encoding, so that any audible
effect of the filters was evident only in the small residual decoding errors
due to imperfections in the tape path. Yet, despite the small magnitude of
these errors, the difference between the Butterworth (Q=0.71) and Bessel
(Q=0.58) systems was still easily audible. It is notable that later noise
reduction systems introduced by Dolby Labs tended to avoid high Q filters in
the critical mid-frequency bands of the audio range. Work in connection with
surround-sound encoding and decoding systems at Philips in the mid 1970s
confirming the finding that Q must not exceed 0.6 to avoid audible
colouration could be extended from lowpass filters to allpass filters, ie
the effect was not amplitude response. Not that easy OK, so Q is the reason
for the ‘sound’ of equalisers? Low Q is uncoloured, high Q over 0.6 is
coloured? If only life were that simple. This rule of thumb does seem to work
reasonably well over quite a wide range of analogue filter designs but it is
far from infallible. The demonstration that Q
is not the crucial factor behind audible colouration comes from the highly
coloured digital filter discovered by Lagadec and others at Studer in the mid
‘80s. The coloured filter had a flat phase response and the amplitude
response consisted of 512 ripples of ±0.1dB uniformly spaced across the whole
audio band (ie at about every 50Hz). This gives an impulse response as
shown in Fig 3, ie the main impulse is surrounded by just two smaller
impulses each about 46dB down, one preceding the main impulse by 20ms and one
following it by the same amount.
Now this filter has no
decay whatsoever, ie its Q equals 0. It only has a single discrete
pre-response at low level and a single low-level post-response. Yet its
colouration is highly audible. Detailed investigations showed that the main
cause of the subjective colouration was the pre-response of the filter (ie
the part before the main impulse) and that the pre-response had to be held
below –80dB to avoid becoming
obviously audible. Minus 80dB is merely one part in 100 million of the total
signal energy and in the past, many ‘objectivists’ would have howled with
derision at the thought that such tiny residues of error could possibly be of
any audible importance. Much of what we now know about audible colouration by
filters and equalisers is consistent with the conjecture (informed guess!)
that what matters is not amplitude or phase response, but the low-level behaviour of the impulse
response well away from the main transient. This is certainly not to say that
amplitude or phase response, or the high-level behaviour of the impulse
response, are unimportant or have no effect but that their main effect is
often a relatively benign change of tonal quality, to which the ear can
easily adapt, rather than obvious colouration that remains obvious even after
time for adaptation is allowed. The conjecture just made
is probably not wholly true, eg a 12dB/octave treble boost will sound
pretty ghastly despite having a good decay behaviour but for moderate and
relatively smooth changes in amplitude and phase response, this hypothesis is
at least a reasonable starting point for explaining why some filters sound
more coloured than others. Transient
effects Although we have conjectured that, on the
basis of available evidence, low-level effects well away from the main
impulse may be largely responsible for colouration, we have not yet specified
precisely what kind of low-level effects are important. After all, we have
already noted that a smooth non-oscillatory decay is generally relatively
harmless. At this point we enter
the realms of conjecture and hypothesis in a big way. The following ideas are
suggested as useful to equipment designers and others in getting good results
or avoiding bad ones. These ideas are not pure guesswork – they are
constrained by a lot of existing psychoacoustic knowledge and know-how – but
neither are they gospel truth. No doubt, with time and experience, these
ideas will be refined and exceptions identified. Everything that is known
about the way the ears perceive transients suggests that, all other things
being equal, a pre-response (ie before the main impulse) in a filter
will have more audible effect than a similar mirror-image post-response after
the main impulse. This is not just consistent with Lagadec’s findings on his
digital filter, but is also consistent with the Haas Effect, whereby
transient sounds tend to be preferentially localised by the transient
arriving at the ear first, with later transients (up to about 40ms later,
when separate echoes are heard) playing a reduced role. This is also
consistent with the physiological effect of forward inhibition or temporal
masking, whereby the perception of stimuli tends to suppress or reduce the
sensitivity to the perception of stimuli following immediately afterwards. This is not to say that,
in some circumstances, later stimuli cannot also alter the perception of
those immediately preceding them. Such backwards inhibition effects are well
documented in the experimental psychology literature but generally,
conventional forward inhibition is a stronger effect. From another point of
view, it is not implausible that the ears notice pre-responses much more strongly
than post-responses, since pre-responses (ie effects before the cause)
are rare in nature. This is not to say that they can’t happen. The classic
example is sound being picked up from a distant performer by a microphone on
a stand on a non-rigid floor. Sound travels much faster through solids than
through air, so sounds travelling through the floor and up the microphone
stand to the microphone arrive before the main sound arriving through the
air. Generally, only bass frequencies
arrive via the floor transmission routes but the characteristic bass
pre-response is audible and, once recognised, can be heard as a
characteristic colouration. So one perhaps unexpected
moral of our discussion is the need to take precautions to minimise the
transmission of sounds to the microphone via the floor (or ceiling or walls,
etc). This can be done by suspending microphones in a shock mount or via
appropriate cables, by decoupling microphone stands from the floor by
suitable compliant damped floor coverings and by using microphone types
(notably some omnis) that are relatively insensitive to vibrations
transmitted to their bodies. The particular
undesirability of pre-responses is especially relevant to digital filters and
equalisers. Although it is not absolutely impossible to design analogue
filters that have pre-responses, it is jolly hard. The filters have to be
non-minimum-phase, and to have substantial pre-responses must be very
complicated. Such complication is much easier to achieve in the digital
domain, where memory (and hence pre delay) is cheap and plentiful. The classic example of
pre-responses in digital filters is something many people (including a
previous editor of this magazine) had claimed is always desirable – namely filters having a linear phase response. A
filter with a linear phase response suffers from no phase shift at all (other
than an overall constant time delay, which we can ignore). This seemed like
Nirvana compared with the awful phase shifts suffered by the analogue
minimum-phase brickwall filters widely used with non-oversampling A/D and D/A
converters. A little thought,
however, shows that linear-phase filters might not always be as desirable as
they might seem. Linear-phase filters have an impulse response that is
time-symmetric: their pre-response is the mirror-image of their post-response
(Fig 4). The reason for this is that they have, by definition, no phase
shifts and so behave in exactly the same way whether one looks into the
future time direction or the past time direction.
But, being unnatural and
of greater audible effect than post-responses, such pre-responses could well
have substantial audible side-effects that would be heard as audible
colouration – as Lagadec found with
his filter. Note that I am not
claiming that extended pre-responses automatically give a coloured sound,
only that the risk of such colouration is higher than for similar
post-responses. It is ultimately a question of trying out a given filter
response empirically and listening for colouration. To take an extreme
example, I would expect that a time-reversed high.Q filter (one whose impulse
response is the time-reverse of that of a high-Q filter) to be highly
objectionable and a phase-linearised version of a minimum-phase high-Q filter
to be only a little less objectionable, due to such filters having extended
‘pre-ringing’ in their impulse response. In particular, one would expect
digital phase-linear graphic and parametric equalisers to have worse audible
colouration than a well-designed analogue or minimum-phase digital equaliser
designed more conventionally. Experience of phase-linear digital equaliser
products tends to bear out this increased audibility of colouration. On
the other hand, a well-designed pre-response with no sudden
sharp changes in level (even at very low levels) or oscillations, and
with smooth gradual increase, is expected to be much less objectionable
subjectively, as is a pre-response whose ripples and oscillations lie well
outside the audible frequency range. I would expect, for example,
carefully-designed phase-linear highpass filters for cutting out low
frequency rumble noises or for bass speaker equalisation to sound
considerably better than current minimum phase highpass filters. The latter’s
severe phase distortion produces very audible tonal and dynamic colouration
even when present in small amounts and of low Q. The key words in the above
are ‘carefully designed’, avoiding a badly shaped pre-response. In general, it would be
expected that digital filters somewhere between the minimum-phase behaviour
of analogue filter designs (ie with the minimum phase shift consistent
with the actual amplitude response and with no pre-response) and linear phase
might sound better than either. Designing a carefully-tailored pre-response
to minimise audible colouration is, as yet, uncharted territory but once they
get their teeth into it, I would expect designers of digital equalisers to
start coming up with some subjectively interesting products. I suspect that, as in other
areas of audio, there will be no unique ‘best’ phase response for a given
frequency response but, rather, different choices of trade-offs among
different subjective virtues and defects. We can look forward to countless
future arguments about which of many competing approaches is really best. Post-responses So much for the terra incognita of digital filters with pre-responses.
Conventional analogue filters with only a post-response can still have
substantial audible colouration effects, as was recognised by Harwood in the
1950s. How can we find out what kind of post-responses sound ‘nice’ and what
do not? Although Q can be a useful guide, it does not tell us everything we
need to know. It is possible to design filters with a high Q that don’t sound
too bad, and equally possible to design low-Q filters that are pretty awful
or even downright unlistenable. As everywhere else in
audio, there is probably no single magic number that guarantees the goodness
or badness of a particular filter response. The key to all this probably lies
in learning to understand and analyse filters in a large number of ways, ie
not placing all one’s eggs in one basket. Traditional frequency
responses do tell quite a lot, although they certainly don’t tell whether or
not an equaliser is guaranteed to sound good. The presence of a broad band of
emphasis over a range of frequencies will often give a general indication of
the balance of the sound, although not its subjective quality or frequencies
of audible colouration. However, areas of raised response, eg peaks,
tend to ‘stick out’ as audible colouration, although narrowband dips can
often be virtually inaudible. In general, frequency
responses give one little information about the audible ‘smearing’ of
transients and phase responses (or the closely related measurement of group
delay) may not be that much more helpful. Sudden peaks or dips in the phase
response or group delay can be a symptom of audible transient smearing or
colouration but on its own, phase or group delay response contains too little
information to allow the resulting sound to be reliably predicted. We have
seen that it is also necessary to look at the impulse or time response of
filters and that very tiny discontinuities or oscillations in the time
response can be audible – especially if they are spaced from the main impulse
response by a few milliseconds (before or after). Thus it seems advisable to
examine the tails of the impulse response ‘under a magnifying glass’ if
looking for possible symptoms of colouration. It might even be useful to look
at the impulse response processed by being fed through a compressor with a
very fast time constant, in order to bring up low level artefacts to make
them visible. Neither the response in
the frequency nor the time domains alone are adequate. The eye (used to
assess measured data) is no good at picking out the frequencies at which
trouble is occurring from examination of the impulse response. Simultaneous time/frequency
analysis For this reason, over the years attempts have
been made to analyse sounds and linear system characteristics simultaneously
in both frequency and time, plotting the result as a graph over the two
variables time and frequency. The most familiar example of this is the speech
spectrogram, which plots the level of sounds at each frequency as a function
of time. All such attempts are
compromises. After all, a frequency response analyses the response to
sinewaves, and a sinewave (by definition) lasts forever. Any attempt to
resolve behaviour in time reduces the ability to resolve frequency and vice-versa. If one blurs one’s
resolution in time to a minimum time interval delta t, and one’s resolution
in frequency to a minimum frequency range delta f, then a famous mathematical
result (first used in Quantum Theory) known as the uncertainty principle
asserts that one has to have delta
t . delta f greater than or equal to 0.5 (This is the first and last mathematical
formula in this article!), where delta t is the minimum time resolution in ms
and delta f is the minimum frequency resolution in kHz. So if one has a time
resolution of 5ms, then the frequency resolution can be no better than 100Hz – no good for examining details of the bass response. Actually, as noted by
Dennis Gabor (best known for his invention of holography, but who also worked
in audio) back in 1946, the ears actually analyse the frequency content of
sounds in time faster than suggested by the uncertainty principle by a factor
of about 7. The seeming logical contradiction with the fundamental theoretical
limit of time/frequency resolution is avoided by the ear’s use of a priori or previously assumed knowledge
of the nature of typical sounds but at the expense of getting the analysis
‘wrong’ when sounds not of the assumed form occur. No one has yet succeeded
in devising a method of simultaneous time/frequency analysis that beats the
uncertainty principle limits on resolution using a priori information similar to the ear.
Existing methods of analysis do not resolve enough detail in the two domains
simultaneously to predict reliably how a filter will sound. Nevertheless, several of
the existing methods of time/frequency analysis do reveal some of the things
that cause colouration: for example, both the techniques of Time Delay Spectrometry (TDS) invented
by Richard Heyser, and earlier techniques of measuring frequency response
after cutting off a first part of the impulse response reveal low-level
delayed resonances. With these techniques, the initial frequency response may
measure flat but the frequency responses associated with later times display
a visible decaying resonant peak. However, while these methods have enough
resolution to measure the grosser faults of loudspeakers, they still tend to
mask the more subtle faults associated with many equalisers and also systems
such as turntables. There is an urgent need
to refine existing methods of simultaneous time/frequency analysis to
maximise the amount of fine low-level detail that can be seen. In
computer-based analysis packages, this means carefully devising the filtering
and ‘windowing’ used to minimise all discontinuity, resonance and aliasing
artefacts, and using very high quality graphics to display the results on a
very fine time/frequency grid. Otherwise the eye will not be able to resolve
the required detail. Even when this is done,
analysis using several different trade-offs of time and frequency resolution
will probably be needed, so details that occur predominantly in the time
domain and in the frequency domain can both be examined. Wigner distribution A mathematically beautiful and elegant
method of simultaneous time/frequency analysis was published by Eugene Wigner
in 1932 (his application was to Quantum Statistical Mechanics, although its
original application was apparently in another unspecified field). Despite
its mathematical elegance, this Wigner Distribution has a lot of unwanted
‘high frequency clutter’ obscuring the wanted detail from the eye – for example, if two frequency components are
present, the Wigner distribution also displays a spurious beat-frequency
component at the average of the two frequencies. Despite its use in recent
audio literature, where the Wigner distribution response of a number of
filters and loudspeakers has been published, and despite the fact that in
principle it contains all the information needed to understand a filter
response, the large amount of clutter present makes it impossible for the eye
to make out relevant details. Nevertheless, the Wigner
distribution may well form the basis of future improved methods of
time/frequency analysis beating the uncertainty principle limit. This is
because it can be shown mathematically (the methods of proof are buried deep
in the Quantum Theory literature) that the normal methods of time/frequency
analysis can be obtained from the Wigner distribution simply by
blurring it with a suitable smoothing filter. (Technical note: this
2-dimensional smoothing filter has a response that is also a Wigner
distribution.) Such blurring removes the unwanted clutter, at the expense of also
blurring the wanted information. However, by using less drastic blurring than
used to obtain conventional time/frequency analysis, much of the clutter can
be removed without losing so much detail. So, by time/frequency
analysis using a carefully-smoothed version of the Wigner distribution, in
future we may have the tools to see what filters and equalisers are doing in
the time and frequency domains with more detail than was previously possible.
Designers of the software packages for audio analysers need both to master
the relevant mathematical tools and to design the required smoothing filters
in the software to avoid the kind of discontinuity or oscillation behaviour
we are looking for in the hardware audio filters and equalisers we want to
analyse. In other words, the design of analyser software requires the same
kind of skills required to design good audio equalisers. The
future What an optimistic subheading! Actually, the
future understanding of equalisers is still uncertain. What we do now know is
that many low-level effects often ignored in the past are very important
subjectively and that traditional methods of measurement and analysis are not
yet refined enough to reveal their effects. One priority is to refine our
methods of measurement and analysis to maximise the visibility of low level
effects. This means as much skill
is required in the development of test equipment as has traditionally been
applied to audio equipment. Nothing can be taken for granted. In particular, the
filtering and ‘windowing’ on spectral analysis equipment needs to be much
better behaved than has been the case until now. Much more attention is also
required to the quality of the display of visual information, which should
avoid the kind of steps, kinks and coarse grids of current displays, since
one is actually looking for such discontinuities in an equaliser response as
symptoms of its audible quality. Meanwhile, the design of
equalisers will remain an art, although I hope the questions raised here will
help to inform the art and concentrate attention on potentially important
factors – particularly in the
design of digital equalisers. One topic not covered is
the role of circuit nonlinearities in the sound of analogue equalisers, or of
‘rounding error’ and requantisation effects in the design of digital
equalisers. These are also important but would require several articles to
themselves. In the above, I have assumed that the equalisers have been
designed carefully enough to minimise such nonlinear effects but, sadly, this
is often not the case in commercial products – particularly for digital
equalisers. A
gloomy ending One area of pessimism concerns the viability
of using equalisers to compensate for defects in other equipment
(microphones, loudspeakers and even multiple stages of bass roll-off in audio
electronics). The problem here is that even very tiny residual errors in the
frequency and phase responses may turn out to be almost as audible (or in
some cases even more so) than the original unequalised errors. Equalisation
may improve the tonal accuracy in such cases but it can (and often does)
increase the audible colouration. If this is right, we may
be unable, ever, to ‘fix it in the mix’ properly, and this re-emphasises the
importance of using the best and least-coloured sounding audio equipment at
every stage of the audio recording chain. The best equaliser is no equaliser!
Anything else may add useful creative pizzazz – and it is worth understanding
what such creative equalisers are doing – but there are limitations to how
far an equaliser can actually ‘equalise’ an already-coloured signal. References 1) Philip Newell, ‘Monitor Systems Part One: A Look
at the Overlooked’, Studio Sound, pages
46-53, August 1989 2) Philip Newell,
‘Monitor Systems Part Five: Crossovers’, Studio Sound, pages 60-67 (December 1989) and pages 48-53 (January
1990) [KH note: The Roger Lagadec and Dennis
Gabor articles mentioned in the text but not referenced are R Lagadec and T G Stockham,
‘Dispersive Models for A-to-D and D-to-A Conversion Systems’, Preprint 2097,
75th Audio Engineering Society Convention, 1984 D Gabor, ‘Theory of
Communication’, Journal of the Institution of Electrical Engineers, 93, III,
p429, November 1946 For reasons I can’t explain,
Gerzon’s description of the impulse response of the Lagadec coloured digital
filter doesn’t correspond exactly with that described in the Lagadec and
Stockham paper, which says, “In the case of the model above, which related
well to a realistic (but, in retrospect, ill-designed) filter bank, the
amplitude of the pre- and post-echoes is approximately 0.025, or, in other words,
32dB below the main pulse. The distance between echoes and main pulse is 2048
sampling intervals, or 40 milliseconds (0.04 seconds), and a pre-echo at
–32dB preceding the ‘main’ signal by 40 milliseconds is of course quite
perceptible, even with untrained listeners.”] This article can be downloaded as an A4-format Acrobat file here
or as a US Letter-format Acrobat file here The Gerzon Archive www.audiosignal.co.uk |
