Chapter 6: Digital

To understand how digital works, we need to understand the process of converting an analogue signal to digital and then, turning the digital signal back to analogue with the hope that we restore the signal back to what it was when we began, which is not a simple task. When you digitize an analogue source, that music, although we hear separate instruments playing, as well as what notes and chords they are playing at different times, by the time it is all coming through a bunch of microphones and through a mixing board, it is now what I would like to call a time-variant voltage. Also, we are often told that second harmonic distortion is benign, and I think some people get the silly idea that a music system can hear the notes individual instruments are playing and then creates a second harmonic on these notes. There is absolutely no truth in that and furthermore there is nothing benign about second order harmonic distortion because if there is a great deal of second harmonic distortion, then there is a great deal of intermodulation distortion (IMD), which literally means one instrument is modulating the output of another instrument. This is what makes music sound muddy.

Since we certainly do not want distortion in a system we must now look at how to digitize this time-variant voltage. This is done simply by sampling which is done at a certain rate and at a certain number of bits. You can think of the bits as stair steps and the bit rate is how often we are looking at each step. In the compact disc (CD) quality system, for the Red Book standard it was decided to sample at 44.1 kilohertz (kHz). The reason for 44.1 kHz is that it was in reference to what was being done with video, not audio. It was also decided that 16-bit depth was about as much as could be handled at the time with converters being what they were. In the very first players, the converters were quite expensive, so much so that 16 bits was considered to be enough. Lastly, this is called the Red Book standard because it is printed in book with a red cover. Today, we have standards with more bit depth and higher sampling rates, which are said to be better. That is up to you to decide.

Now as the voltage increases, the number increases and 16 bits gives you numbers from zero to 64,000, with 32,000 being in the middle and being zero voltage. That means as you cross zero, you are going from 32,000 to 32,001, but you are also flipping the most significant bit, a problem we will deal with a little bit later. Put simply enough, digitizing an audio source has both time and bit possible errors. The timing of the analogue to digital conversion is very important. One thing to keep in mind about all audio going back to the earliest recordings of phonograph records are that the people making the records used studio recording equipment of generally high quality because they had the budget to do so. Although most people may be listening to their product on lower quality equipment, the recording people still tended to make recordings of very high quality and this required a great deal of care. We should expect with digital, that since studios can invest large amounts of money in an analogue to digital converter, the equipment can be very, very good because they only need one converter.

Now we get to the playback problem which is a big one. In the Red Book standard, it was known the CD as Sony and Philips invented it was going to read with quite a few errors and that Reed-Solomon coding is used to correct these errors. It also noted that 50% of the data on the CD is error corrected. This does not mean that everything is recorded twice. Instead, it means that every 16-bit word (2 bytes) has extra ones and zeroes on the end that allow it to be checked. As such, the coding allows for the process of what we now know as error correction. Once the error correcting is done, we have a few problems to deal with in the digital to analogue converter. One of these has been largely discussed as jitter. Now in the converter, there is also a clock running and like any good clock, it should tick off at consistent intervals which is not a simple thing to do. If a sample, which is just a number, in this case a 16-bit word that corresponds to a number from zero to 64,000, if this number is read at the wrong time that is just as bad as reading the wrong numbers. So, in addition to error correction we have jitter correction and over time manufacturers have made equipment with very low jitter and solved that problem.

The next problem is the filtering that must be done to remove the 44 kHz sampling because sampling literally creates a full level. You might think of it as a full level square wave riding along with the audio and we cannot be putting that into our amplifiers or preamplifiers, and certainly not into our tweeters. This must reduce to a very, very low level and that is where the filter comes in. Now early on, the filters were done analogue, and they were very sharp filters and had their audible problems. One of the ways to get around the filtering problem was to over sample, which means to raise the sampling rate to two times, four times, or eight times the frequency where the filtering becomes much easier because this high frequency we are trying to filter out is now much farther away from the audio that we want at 20 kHz. So, it is simpler to make a gradual filter than it is to make a sharp filter. Since gradual filtering is being done digitally, the question becomes is that as good as an analogue filter.

One of the things that is rarely talked about with digital is that as digital signals go to lower levels, the distortion increases rather than decreases. On analogue systems such as tape or vinyl, the opposite occurs. At lower and lower levels, distortion decreases and in higher levels distortion increases. Just to give you some figures, a typical good tape recorder, such as a 1950s Ampex, would have less than 1% distortion at 0 VU. A phonograph record might have a few percent distortion on the playback end of it, but again as the signal gets lower, the distortion gets proportionately lower. Now of course, both tape and phonograph records had a noise limit. On tape, you could typically get a signal to noise ratio of about 70 decibels (dB) and on phonograph records, maybe about 60 dB, but as the signal got softer, the distortion would get lower. With digital, it is just the opposite, and this is because when you drop down to say -60 dB in level, you do not have nearly as many bits to be switching so the steps get larger, and the distortion gets higher. If you look at distortion graphs of CD music, as they go down to lower and lower levels, you will see distortion get higher and higher, and at about -100 dB, you have distortion of several percent.

If you look at stereo file wave forms at the low bit levels, I think at -90 dB is where it is often done, you will see that there are only a few steps left and these steps may not be very pretty. Keep in mind at low levels, CD quality sound is not as good as analogue, and this may be part of what people object to. Certainly, there is a lot more going on in decoding digital with the converters, filters, and output amplifiers. Some people have even suggested that modern converters are designed by people who are young enough, say under 40, that they have never really studied analogue circuits and that in the analogue circuits that they are familiar with, the converters may be one of the larger contributors to the differences in sound we hear. Now quantization error is what mostly occurs at the lower levels where the steps are rather large and we are, of course, approximating an analogue voltage that might be in between the steps. This is where dithering comes in handy, and it has been proven that a little bit of dithering will improve the sound. This is simply because the dithering, which is in a way adding noise to this mostly noiseless system, does not raise the noise level enough that we really hear it. In addition, it allows the converters to step between those lowest bits, but it only makes an improvement at the very, very bottom, and I think that probably more is made of dithering than one really should. I think we all must realize that in digital audio, a lot of bragging rights go to picking up a few decibels of noise here or there or different measurements that may not really matter.

I would like to note something from a technical perspective here. There are many people making modifications to players where they remove the analogue electronics and substitute vacuum tubes or even transformers following the digital to analogue (DAC) chip. One should be very careful about buying these because the people who do this do not tell you how much they have increased the distortion of the player, especially at high levels. The advantage of having a vacuum tube following the DAC chip is mostly imagined and not real. Of course, some people just like to have a vacuum tube because they like to have a vacuum tube. The reason for this is depending on the DAC chip, most of these chips put out a current, not a voltage. Whether they are resistor ladder or another configuration, they expect to be connected to what we call a virtual ground, which literally means we have a chip, and it wants to put out a current into something where the voltage never changes and is zero, that is what is called a virtual ground. This is a perfect application for an operational amplifier (opamp), which has infinite gain and DAC chips were designed to work with opamps. There is no simple vacuum tube circuit that provides a virtual ground. Certainly, the circuits we see where there is one tube per channel cannot come even close to providing a virtual ground and maybe only supplies an input impedance of a few hundred or maybe even 1,000 ohms where we would hope to have an input impedance of zero. This is one of the cases where an input impedance of zero is desired. Of course, in these players, the filtering must be done digitally because to come directly out of the converter to a vacuum tube, there is not enough circuitry there to do any sort of adequate filtering, so the filtering would have to be done digitally.

Now, there is a resurgence of a converter called the 1-bit converter. Sony (and some other companies) was making these in the mid-to-late 1980s in their ES series. The 1-bit converter is different than the standard, more popular converters we call 16-bit parallel converters. These converters take the digital 16-bit word, which is 16 ones and zeroes that correspond to a number from zero to 64,000, and convert them to a voltage. The main problem with 1-bit converters is the most significant bit error (MSB error). This is an error that was designed into the system. I believe that when Sony and Philips designed the system, they knew they were doing something bad, but they wanted to do something very simple and expected that the converters would eventually get good enough to make this MSB error infinitesimal. One should understand the MSB error because it will give you a deeper understanding of digital conversion. What happens is if at 32,000, you have a zero that is followed by 15 ones, then you are at 32,000 counts, which corresponds to zero volts. This is because the way the system was set up is that a zero count is full negative, and a 64,000 count is full positive and in the middle is 32,000. The problem is that in the converter when you are at 32,000, with the next number up being 32,001, you must flip the most significant bit to a one followed by all zeroes. This is a very difficult thing for a converter to do accurately. It means that the value of that bit must be exactly 32,000 to make the switch and that is a very difficult thing to do. You may remember that there were players in the 1990s that had MSB correction with a trim pot on the most significant bit. The question that always came to my mind is how accurately will that stay in trim? Of course, you can adjust it at the factory, but will it drift down the road? How would the user make an adjustment?

As I noted earlier, Sony and some other companies came up with the 1-bit converter, which was successful although it went away after a while, but now it has come back. A 1-bit converter is a very different thing. Instead of converting 16-bit or 24-bit words one at a time, it takes the 16-bit word and strings it out into a bunch of bits and converts them into a pulse width, and that is the other name for it, pulse width modulation (PWM). It turns them into a width of a pulse, which then merely needs to be averaged and it is very easy to average this. Then the trick becomes making sure that the width of each of these pulses is exactly the right width between a zero width and a 64,000 width. This was the problem that they had in the beginning, which they have now gotten better at, and I think that now we will probably see more of these PWM 1-bit converters.

One of the advantages of creating a music file on your computer is that you could rip your CDs on the computer and with good ripping programs, you can correct errors that the CD player could not. Maybe you have experienced having a CD that skips and then when you rip it and make a copy, the skip has gone away. This is because the computer has the time and the computing power to correct the coding using coding correction schemes that the CD player would not have the time or the computing capacity to do. This is also because ripping does not have to be done in real time whereas the CD does have to play in real time. You can in some systems choose a ripping program that has a very high level of error correction and can take a long time to rip the CD because it is sitting there correcting errors and then once it is done, you now have a very accurate file, which you can burn onto another CD, or you can just play it off your computer. Now, of course, there is a lot of controversy out there about what computer plays digital files better and what converter converts them better. I will leave that up to you to decide. It is very hard to measure these things and is certainly going to mostly be left up to the listener’s ear. I believe that the differences are probably not that large, but if you are really into digital, I am so sure your friends, reviewers, and even some manufacturers will make them into very large differences.