Click here to purchase the entire book in PDF format. Digital Gear in the PCM World As we've seen in previous chapters, digital gear has relatively easily defined extremes for the audio signal. The noise floor is set by the level of the dither, typically with a level of one half of an LSB. The signal to noise ratio of the digital system is dependent on the number of bits that are used for the signal - increasing by 6.02 dB per bit used. Since the level of the dither is typically half a bit in amplitude, we subtract 3 dB from our signal to noise ratio calculated from the number of bits. For example, if we are recording a sine wave that is using 12 of the 16 bits on a CD and we make the usual assumptions about the dither level, then the signal to noise ratio for that particular sine wave is: (12 bits * 6 dB per bit) - 3 dB = 69 dB Therefore, in the above example, we can say that the noise floor is 69 dB below the signal level. The more bits we use for the signal (and therefore the higher its peak level) the greater the signal to noise ratio and therefore the better the technical quality of the recording. (Do not confuse the signal to noise ratio with the dynamic range of the system. The former is the ratio between the signal and the noise floor. The latter is the ratio between the maximum possible signal and the noise floor - as we'll see, this raises the question of how to define the maximum possible level...) We also know from previous chapters that digital systems have a very unforgiving maximum level. If you have a 16 bit system, then the peak level of the signal can only go to the maximum level of the system defined by those 16 bits. There is some debate regarding what you can get away with when you hit that wall - some people say that 2 consecutive samples at the maximum level constitutes a clipped signal. Others are more lenient and accept one or two more consecutively clipped samples. Ignoring this debate, we can all agree that, once the peak of a sine wave has reached the maximum allowable level in a digital system, any increase in level results in a very rapid increase in distortion. If the system is perfectly aligned, then the sine wave starts to approach a square wave very quickly (ignoring a very small asymmetry caused by the fact that there is one extra LSB for the negative-going portion of the wave than there is for the positive side in a PCM system). See Figure 10.2 to see a sample input and output waveform. The ``consecutively clipped samples'' that we're talking about is a measurement of how long the flattened part of the waveform stays flat. If we were to draw a graph of this behaviour, we would result in the plot shown in Figure 10.3. Notice that we're looking at the Signal to THD+N ratio vs. the level of the signal. Figure 10.3: A plot of a measurement of the signal to THD+N (caused by noise and distortion byproducts) ratio vs. the signal level in a typical digital converter with a dither level of one half an LSB measured with a 997 Hz sine tone. The curves are 8-bit (yellow), 12-bit (green), 16-bit (blue) and 24-bit (red). The resolution on the input level is 1 dB. The positive slope on the left is the result of the increase in the signal level over the static noise floor. The nasty drop on the right is caused by the sudden increase in distortion when you try to make the sine tone go beyond 0 dB FS. The interesting thing about this graph is that it's essentially a graph of the peak signal level vs. audio quality (at least technically speaking... we're not talking about the quality of your mix or the ability of your performers...). We can consider that the X-axis is the peak signal level in dB FS and the Y-axis is a measurement of the quality of the signal. Consequently, we can see that the closer we can get the peak of the signal to 0 dB FS the better the quality, but if we try to increase the level beyond that, we get very bad very quickly. Therefore, the general moral of the story here is that you should set your levels so that the highest peak in the signal for the recording will hit as close to 0 dB FS as you can get without going over it. In fact, there are some problems with this - you may actually wind up with a signal that's greater than 0 dB FS by recording a signal that's less than 0 dB FS in some situations... but we'll look at that later... this is still the introduction.