Look through the specifications of any piece of equipment, and the terms bandwidth or frequency response will crop up somewhere. But the implications of these figures are not always obvious, as our research reveals.

TO GRAB THE bull by the horns from the word go, what, exactly, do we mean by the terms "frequency" and "bandwidth"? Well, we're concerned here with audio frequencies, ie. the range of sound pitches that can be perceived by the human ear.

To hark back to schoolday science lessons, you'll probably be familiar with the concept of sound waves as being rapid but minute changes in air pressure. Once converted to electricity by means of a microphone, these sound waves are transformed into fluctuations in electrical current. Figure 1 shows these fluctuations in the form of the familiar sine wave produced by a pure tone.

Before delving further, we need to define the audio frequency range, but that isn't quite so straightforward, as no two people respond to sound in exactly the same way.

For a young person who has never been to a Motorhead gig, the audio spectrum might extend from around 40Hz (40 vibrations per second), to over 20kHz (20,000 vibrations per second). 40Hz is heard, and felt, as a very low bass note, whereas 20kHz is so high as to be inaudible to most people.

As people get older or become subjected to extended periods of very loud noise (or several Motorhead gigs), their ability to hear high-pitched sounds becomes impaired, and the top limit for a typical adult may well be around 15kHz. In old age this can fall to just a few kHz, but the appreciation of bass frequencies does not, as far as I'm aware, change a great deal as the pension-book beckons.

It follows, then, that for most of us to appreciate recorded music without sensing a loss at the treble end, our sound system needs to be capable of reproducing frequencies from 40Hz to over 16kHz, and preferably to 20kHz. Many purists swear that even the harmonics they can't hear have an effect on how the music is perceived overall, so it isn't uncommon to find music systems capable of reproducing frequencies up to 22kHz or beyond.

Constraints

MOST DEVICES IN an audio signal chain have a frequency response, even a length of wire - though unless you're using long lengths of coax with high-impedance signals, this particular area shouldn't give cause for concern. But electronic instruments, loudspeakers, amplifiers, signal processors and mixing consoles all have frequency response characteristics which can compromise the performance of the entire system. And the response characteristics of several units connected in series will be cumulative, so what may have started out as a slight bass loss on each unit may end up as quite a serious one for the whole system. So before looking at numbers, let's look at how frequency response is defined and measured.

The first step here is to replace the microphone by a signal generator: a device capable of producing pure sine wave tones of a fixed level at any frequency from, say, 20Hz to 30kHz. Now, if this were fed into a piece of equipment such as an amplifier, and if that amplifier was perfect, then the output waveform would remain at the same level regardless of the frequency of the input. In other words, if the amplifier was set with a gain of ten, the output would always be exactly ten times the level of the input.

But in practice, amplifiers rarely behave as well as this. At the low-frequency end, the way in which most circuits are designed tends to reduce sensitivity as the frequency falls. You might still have a gain of ten at 50Hz, but drop the input frequency to 30Hz and you might find that the gain is only five. Drop the frequency further still, and you may encounter virtually no output at all. For the sake of standardisation, we say that the gain has fallen by half, or 3dB. The frequency response limit has been reached.

The same goes for the high-frequency end: the amplifier may give a so-called flat response up to 18kHz, but fall by 3dB at 20kHz. The frequency response for this amplifier would then be said to extend from 30Hz to 20kHz.

Time for a word of warning. Manufacturers have a tendency to bend the rules a bit in this area by claiming a response of X Hz to Y kHz, plus or minus 3dB, which gives them a total of 6dB leeway; so these figures appear better to the uninitiated. If a graph is provided with the equipment you're looking at, take a look at it and you'll be able to locate the 3dB points yourself. A picture is worth a thousand words, so eyes down to Figure 2, which shows a typical response curve with the 3dB points marked on.

Just to complicate matters, anything that handles signal voltages rather than power is specified between the -6dB points, because this again corresponds to half gain. You'll just have to take my word for it that 3dB is a ratio of 2:1 for power but that 6dB is a ratio of 2:1 for voltage.

To ease the confusion, only amplifiers and speakers are power output devices and therefore subject to the 3dB rule. Mixers and processors are voltage-out devices and conform to the 6dB rule.

Technically speaking, 'bandwidth" is the number of Hz or kHz between the lower 3dB (or 6dB) point and the upper one, but seeing as a relatively small change in the lower point can radically affect bass performance without giving a significantly different bandwidth, this specification can be misleading, to say the least. Marketers of none-too-wonderful small speakers use the term to hide their lousy bass end by glibly stating that the bandwidth is something impressive like 20kHz, not mentioning that this could mean 200Hz to 2.2kHz, or even 300Hz to 2.3kHz.

In reality, getting a good bottom-end response from a piece of electronic equipment is not tremendously difficult these days; it's the top end you need to scrutinise. Not so speakers, however, as these perverse mechanical devices not only lose efficiency at both ends of the spectrum, but also tend to have humps and dips in the response curves, too. And the same is true of microphones, which is not surprising, as these are also electro-mechanical. These deviations from a straight line are what give different types of speakers and microphones their characteristic sounds.

Cause and Effect

IT'S CLEAR FROM what we've covered so far that your mixer, amplifier and monitors must operate over the full audio range if what you're going to hear is a true and accurate representation of the music being fed into the system, and while amplifiers and mixers seldom present a problem in this area, loudspeakers certainly do.

The most common compromise you'll have to make is in the monitoring area, especially in a home studio where space and cost are often factors working against you. Unless you can find the room for a large, full-range monitor, you'll probably have to settle for something with a bottom end response in the order of 50Hz: just about acceptable for serious home and demo recording.

For really serious work, though, monitors that reach down to 40Hz or even lower are necessary. Remember, too, that the response curve of your speakers may have pronounced humps and dips which will colour the sound, so always aim for something with the flattest possible response as this will provide a more honest, neutral sound.

In general, electronic circuitry doesn't suffer from unwanted bumps and dips to anywhere near the same extent as speakers. And such irregularities are usually deliberately incorporated in the creation of equalisers, for example.

Outboard

SO, IF WE need 'a response stretching from 40Hz to 20kHz for faithful music reproduction, why is there still serious outboard gear available with an upper response limit of 10 or 12kHz? Well, whether this is acceptable or not depends on the type of effect or processor in question.

If the whole signal has to pass through the processor, then there's no question that the signal path requires a full audio bandwidth. Processors that fall into this bracket include gates, compressors limiters, equalisers (in their flat position), amplifiers, and DI boxes. The other category includes effects which are obtained by adding a processed version of the sound to an unprocessed version. Echo, for example, is the original dry sound with repeats added. Reverb exhibits the same characteristics, and both chorus and flanging are produced by adding dry and delayed signals together, with a bit of pitch modulation thrown in for good measure. This addition may be carried out in the effects unit itself, where the balance control sets the ratio of dry and effected signal, or it may be done in the mixer.

Whichever method is used, the dry signal patch needs to cover the full audio bandwidth. If the addition of dry and effected signals is done in the mixer, there's no difficulty. But if you mix the signals in the effects unit, what then? Well, if you read the specification for a digital delay or a reverb, you'll probably find that there are two sets of frequency response figures, one for the dry signal path and one for the effected signal. The dry path will almost certainly offer a full bandwidth, but the effect channel, due to the constraints of sampling and memory space, may well be much lower - which is where the 10-12kHz we spoke of earlier comes in. In the case of echo created by a DDL the repeats will lack the brightness of the original sound.

If you've ever listened to one of the analogue delay pedals popular with guitarists, you'll have no doubt noticed that the sound is much duller than the signal fed into it, and that isn't surprising - these units have an upper limit of between 3kHz and 4kHz, which is little better than a telephone.

If you move up to budget digital units offering 7kHz or 8kHz, you'll find a dramatic improvement, though the fine detail in the sound will still be a little blurred if you do a direct comparison with the input. However, once things are up to 10kHz and above, you'd be hard pushed to detect the difference between the input and output signals, especially in a complete mix. In isolation you could still tell the difference, especially if the input signal contains a lot of harmonics. Of course, if the signal you're processing is an electric guitar or some other "middley" sound source, the apparent difference will be negligible.

Likewise with reverb; the effect sound doesn't need to have the same bandwidth as the direct sound.

Natural reverb has a restricted bandwidth due to the fact that sound has to travel a certain distance in order to reflect enough times to produce reverberation - and as it travels, the viscosity of the air absorbs much of its high-frequency energy.

The outcome of this is that a large hall may produce reverb containing little above 4-5kHz. But natural or not, bright reverb has become a popular effect: if it can be done, it will be done. Even here, 10-12kHz is still generally more than enough. Usually, filters on programmable reverbs are needed in order to curtail the brightness before you get an acceptable sound.

Summary

MODERN ELECTRONICS HAVE progressed to the point where amplifiers and mixing consoles, even budget ones, tend to have perfectly adequate frequency responses, and the same should be true of gates and compressors. But digital delay circuitry tends to have a restricted bandwidth, especially at the budget end of the market, because to fit long delay times and good bandwidth into a machine costs memory, and memory costs money.

Yet for all but the most quality-conscious applications, 10kHz is an acceptable bandwidth for delay and chorus/flanging - though more (say 16kHz) is needed for sampling sounds and then triggering them later as sound sources in their own right. For reverb, anything over 10kHz should be perfectly satisfactory, and the subjective brightness takes us into the area of software design rather than absolute bandwidth.

As you should have gathered by now, one area in which you must exercise care is the choice of microphones and speakers. These have obvious compromises at both ends of the audio spectrum, so it's no good picking a mic with a lower limit of 100Hz if you want to record a punchy bass drum. The top end of dynamic mics (particularly cheap ones) may be very limited, so take a long, hard look at the spec before buying. A high-frequency roll-off at 8kHz isn't going to give you those sparkling vocals, no matter what you do afterwards.