Why do digital cables sound different?

Hi, I've been away for a while, but have been watching the pot bubble on this topic. Let's talk about jitter. Jitter is not a harmonic distortion. It is a clock timing error that introduces an effect called phase noise either when a signal is sampled (at the A/D) or the reconstruction of a signal (at the D/A), or both. Think of it this way: a sine wave goes through 360 degrees of phase over a single cycle. Suppose we were to sample a sine wave whose frequency was exactly 11.025 kHz. This means that with a 44.1 kHz sample rate we would take exactly four samples of the sine wave every cycle. The digital samples would each represent an advance in the sine wave's phase by 45 degrees (1/4 of a cycle). The DAC clock is also supposed to run at 44.1 kHz; think of this as a "strobe" that occurs every 22.676 nanoseconds (millionths of a second) that tells the DAC when to create an analog voltage corresponding to the digital word currently in the DAC's input register. In the case of our sine wave, this creates a stairstep approximation to the sinewave, four steps per cycle. Shannon's theorem says that by applying a perfect low pass filter to the stairsteps, we can recover the original sinewave (let's set aside quantization error for the moment... that's a different issue). Jitter means that these strobes don't come exactly when scheduled, but a little early or late, in random fashion. We still have a stairstep approximation to the sine wave, and the levels of the stair step are right, but the "risers" between steps are a little early or late -- they aren't exatly 22.676 microseconds apart. When this stairtep is lowpass filtered, you get something that looks like a sine wave, but if you look very close at segments of the sine wave, you will discover that they don't correspond to a sinewave of at exactly 11.025 kHz but sometimes to a sinewave at a tiny bit higher frequency, and sometimes to a sinewave at tiny bit lower frequency. Frequency is a measure of how fast phase changes. When the stairstep risers which corresponds to 45 degrees of phase of the sinewave in our example, comes a little early, we get an analog signal that looks like a bit of a sine wave at slightly above 11.025 kHz. Conversely, if the stairstep riser is a bit late, it's as if our sine wave took a bit longer to go through 1/4 of a cycle, as if it has a frequency slightly less than 11.025 kHz. You can think of this as a sort of unwanted frequency modulation, introducing a broadband noise in the audio. If the jitter is uncorrelated with the signal, most of the energy is centered around the true tone frequency, falling off with at lower and higher frequencies. If the jitter is correlated with the signal, peaks in the noise spectrum can occur at discrete frequencies. Of the two effects, I'd bet the latter is more noticeable and objectionable. Where does jitter come from? It can come if one tries to construct the DAC clock from the SPDIF signal itself. The data rate of the SPDIF signal is 2.8224 Mb/sec = 64 bits x 44,100 samples/sec (the extra bits are used for header info). The waveforms used to represent ones and zeroes are designed so that there is always a transition from high to low or low to high from bit to bit, with a "zero" having a constant level and a "one" having within it a transition from high to low or low to high (depending on whether the previous symbol ended with a "high" or a "low"). Writing down an analysis of this situation requires advanced mathematics, so suffice it to say that if one does a spectrum analysis of this signal (comprising a sequence of square pulses), there will be a very strong peak at 5.6448 MHz (=128 x 44.1 kHz). A phase locked loop can be used to lock onto this spectrum peak in attempt to recover a 5.6448 MHz clock signal, and if we square up the sine wave and use a simple 128:1 countdown divider would produce a 44.1 kHz clock. Simple, but the devil is in the details. The problem is that the bit stream is not a steady pattern of ones and zeroes; instead it's an unpredictable mix of ones and zeros. So if we look closely at the spectrum of the SPDIF waveform we don't find a perfect tone at 5.6448 MHz, but a very high peak that falls off rapidly with frequency. It has the spectrum of a jittered sine wave! This means the clock recovered from the SPDIF data stream is jittered. The jitter is there due to the fundamental randomness of the data stream, not because of imperfections in transmitting the data from transport to DAC, or cable mismatch, or dropped bits or anything else. In other words, even if you assume PERFECT data, PERFECT cable, PERFECT transport, and PERFECT DAC, you still get jitter IF you recover the clock from the SPIF data stream. (You won't do better using IMPERFECT components, by the way). The way out of the problem is not to recover the DAC clock from the data stream. Use other means. For example, instead of direct clock recovery, use indirect clock recovery. That is, stuff the data into a FIFO buffer, and reclock it out at 44.1 kHz, USING YOUR OWN VERY STABLE (low-jitter) CLOCK -- not one derived from the SPIF bitstream. Watch the buffer, and if it's starting to fill up, bump up the DAC clock rate a bit and start emptying the buffer faster. If the FIFO buffer is emptying out, back off the clock rate a bit. If the transport is doing it's job right, data will be coming in at constant rate, and ideally, that rate is exactly 44,100 samples per seconds (per channel). In reality, it may be a bit off the ideal and wander around a bit (this partly explains why different transports can "sound different" -- these errors make the pitch may be a bit off, or wander around a tiny bit). Note that recovering the DAC clock from the SPDIF data stream allows the DAC clock to follow these errors in the transport data clock rate -- an advantage of direct clock recovery. But use a big enough buffer so that the changes to DAC clock rate don't have to happen very often or be very big, and even these errors are overcome. Thus indirect clock recovery avoids jitter, and overcomes transport-induced data rate errors (instead of just repeating them). That's exactly what a small Discman-type portable CD player with skip-free circuitry does. Shock and vibration halt data coming from the transport, so for audio to continue, there must be a large enough backlog built up in the FIFO to carry on until the mechanical servos can move the optical pickup back to proper place. Better audio DACs, such as the Levinson 360S use this FIFO buffering and reclocking idea to avoid jitter, as well. In principle, a DAC that uses this kind of indirect clock recovery will be impervious to the electrical nuances of different digital cables meeting SPDIF interface specifications. And that's as it should be.

Geez... sorry for the brain fart in my posting above. 1/4 of a cycle is 90 degrees of phase, not 45. Try visualizing a sine wave that's sampled 8 times per cycle and rebuilt using 8 stair steps. Now suppose that some of the stairsteps risers come a teeny bit early or a teeny bit late and you'll get the picture.

Nice explaination 1439bhr! You seem to be the first poster who really seems to know completely what they are talking about (I include myself in the uninformed). Very well put and easily understandable. I did catch the 1/4 cycle but I knew what you meant. Great Job!

1439bhr, I got a question I am sure you can answer. Does the low pass filter on the output of the DAC also handle any aliasing that may be present? Also, how much phase noise is acceptable in the system before there is any degredation and does phase noise closer to the carrier or farther away from the carrier seem to have the most effect. Thanks in advance for your response.

Using a FIFO and reclocking is not the end all and is not so simple. When the Gensis Digital Lens came out, Bob Harley assumed that all transports would sound exactly the same. He found that he was wrong. Rather than reclock, the best solution, given the current CD methodolgy is to have a custom data transfer mechanism like Lvinson and Spectral. I believe that the SPDIF interface is inadequate for high quality playback. I did some testing about 7-8 years ago to prove that there was no difference in transports or digital cables and published that dat on the net. At the time I had only worked with proprietary digital record and playback protocols and was not that familiar with the CD playback mechanism. My tests proved just the opposite of what I thought. Not only that but subjectively the tests seemed to show that jitter was not the most important of the digital flaws, both read errors from discs and signal loss of high frequencies seemed to be more of a problem. While discman buffering is universal and basically required for a device that bounces around, everyone I've ever owned always said to turn off the buffering when not needed because the sound was not as good as the direct signal. I still believe that the fewer components in between the transport and the DAC the better. Buffering of CD data has all sorts of other issues that need to be handled like skipping forward / back etc that make it impractical since you always have to handle the case when the buffer is empty. All the sysytems I have designerd, and most commercial systems with proprietary protocols in general send raw data to the DAC and the DAC interface has the only clock and jitter is at an absolute minimum. Jitter is a fact of life in any digital medium. The use of the clock has been there since digital technologies in the 60s. I always get a kick out of manufacturers who claim jitter reduction devices that produce 0 (zero) jitter. It's physically impossible to accurately measure jitter anyway. We can improve the accuracy, but there is always some small error in the measurement. This error will decrease as technology improves. By the way jitter errors have a much more detrimental effect than just causing pitch errors. Lack of perfect integrity of the audio signal effects soundstage and imaging and if jitter is so bad that the dac syncs incorrectly on the signal, severe static can be produced. See my previous postings.