In a perfect world there are no clicks, crackle, pops, buzzes or hums, and no hiss - so it's a shame that we live in an imperfect world. Even today, CDs are mastered through analogue stages, and 'vintage' recordings are by definition re-mastered from sources that suffer from such degradations. So audio engineers require technologies that remove noise from recordings.
It would be best to describe what we mean by the term 'broadband' noise, defining it to be an effect that adds (or subtracts) a random amplitude at all times to (or from) all frequencies within the audio spectrum. Thus, we do not include artefacts of limited duration such as clicks or crackles, both of which are removed by quite different methods to those described below.
Next, let's dispel any illusions regarding dual-ended processes that encode during recording and decode upon playback. These limit the accumulation of extra noise added by the limitations of analogue recording tape, but do nothing to remove noise from a signal that already contains it - they simply limit the amount you add when you commit that signal to tape and play it back again. A single-ended process removes noise from your audio prior to committing it to tape, or at the very least, improves the signal to noise ratio without affecting the signal adversely. Which brings us neatly to the volume control... stunningly effective at removing noise, it does nothing to improve the S/N ratio, and has an all-too-noticeable side-effect. No noise, No signal.
Since broadband noise is most intrusive at high frequencies, the first stage in our evolutionary tale is the Low-pass Filter. Less damaging than the volume control, this removes a proportion of the signal above its cut-off frequency. Unfortunately, if, at any given frequency, you reduce the amplitude of the noise by, say, 6dB, you also reduce the desired signal by the same amount. So the low-pass filter will clean your antique '78s (which have little or no high frequency content) but even then, only at a cost.
Dynamic Filters are devices in which the cut-off frequency moves dynamically according to the signal content, thus removing high frequencies when there is no signal present, but leaving them untouched when the noise is being masked by genuine high frequencies. But such devices are limited because they only remove the noise that exists above the cut-off, which is itself an inaccurate representation of the highest frequencies contained in the genuine signal. Secondly, and in common with the simple filter, they have roll-offs of the order -12dB/octave or -6dB/octave, so they allow some high frequencies through. And thirdly, even though the filters are designed to track quickly, they still round off transients and dull the genuine signal.
Now, instead of altering the frequency response of the signal, how about changing the level in some way? Consider: if noise of a relatively constant amplitude is always present then, if the total amplitude drops to the noise level, we can assume that no genuine signal is present. While there are many flaws in this argument, it suggests a device which will eliminate some noise: a Noise Gate. This detects when the signal drops below a 'threshold' set by the user, and then cuts off the signal entirely. There are many enhancements to the idea (added to limit damaging side-effects) but the principle remains the same: if the total signal drops below the threshold, the gate shuts and removes all the noise. Unfortunately, an 'open' gate removes no noise whatsoever.
An Expander is another device with a threshold control, but unlike the gate, this applies a progressive gain reduction, the amount of which is determined by the user. For example, if a signal drops 3dB below the threshold, the Expander may reduce the signal volume by 6dB, 12dB, or any other figure, depending upon the expansion ratio. Unfortunately, the subjective difference between the gate and the expander is small.
A Multi-band Expander separates the audio spectrum into a number of bands, treating each as an individual signal. But multi-band units are still unable to distinguish accurately between genuine signal and noise. They still act upon the inaccurate assumption that, if the total signal level approaches its noise floor, all that is present is noise. Consequently, even the most sophisticated expanders remove genuine signal. Furthermore, the poor band separation filters (typically -6dB/oct or -12dB/oct) severely limit performance. The consequences of these problems are loss of high frequencies, loss of ambience, and degradation of hard transients. Some units feature a combination of dynamic filtering, expansion, and even compression and excitation - effects which have been included in order to obscure some of the side-effects of the noise reduction processes. But these are only partially successful.
All the processes so far described are 'ratio' operations - that is, if (at any given frequency) you remove half the noise, you remove half the signal; if you remove 3/4 of the noise, you remove 3/4 of the signal... and so on. Consider now a signal that has, at a given frequency, 100 units of 'volume' on an arbitrary scale. By measuring the noise content of that signal during an otherwise silent passage, you can determine that there are, say, 20 units of noise present at that frequency. It should be possible to remove this noise by removing 20% of the signal. But what if, a moment later, the total 'volume' of the signal drops to 40 units? An analogue filter, removing 20% of the signal, will remove 8 units. On the other hand, a subtractive filter (which is practical only in the digital domain) will still remove the full 20 units - a reduction of 50%. This is what we want, because the noise at this moment represents 50% of the total signal.
This Spectral Subtraction becomes useful when a DSP is used to split the signal into hundreds of bands. You can then be very precise about how much noise you remove, subtracting a lot at (say) 8kHz, while leaving 8.1kHz virtually untouched. But if this sounds to good to be true, it is. The noise spectrum (the sonic 'fingerprint') can only be measured if there is an otherwise silent passage within the music, and if the fingerprint is not accurate you will hear unpleasant side-effects. But let's assume that you have obtained a perfect fingerprint. You might then expect a good restoration, with few or no side-effects. Yet experience shows that spectral subtraction produces unusably dry and dull results with unacceptable artefacts. This is, in part, because the fingerprint is a snapshot of the random noise, accurate only at the instant at which it is taken. Because the noise is constantly changing, the subtractive algorithm is deriving its result from inappropriate data.
Many companies and independent researchers have investigated enhancements designed to overcome these pitfalls. CEDAR Audio's developments are embodied in a process that updates the noise fingerprint every 1,024 samples, thus tracking variations in the noise content. This also prevents the compression of incoming transients, and distinguishes between true noise and, for example, reverberation in the genuine signal. Other features also help to avoid many of the problems of simple spectral subtraction, and they allow you to remove noise without undue damage to the genuine signal.
But this algorithm still requires a complex user-interface, and it cannot be implemented in a stand-alone box. Removing the requirement for a spectral fingerprint simplifies the interface greatly, but this requires an algorithm capable of autonomous determination of the noise content. Which brings us, finally, to the CEDAR DH-2 and DHX, stand-alone modules that will themselves analyse the noise content of a signal and apply noise reduction with minimal effort on the part of the user.