Dr. AIX's POSTS — 03 July 2015

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Today, I’m going to continue with additional portions of Richard’s (BitPerfect) explanation of DSD vs. PCM with responses by Benchmark’s John Siau. You may want to read Richard’s entire post at BitPerfect click here or yesterday’s post first (click here).

BitPerfect: “In an SDM-ADC, the trade-off between clock precision and reference voltage precision is resolved entirely in favour of the clock, which can be made as accurate as we want. In effect, we increase the sample rate to something many, many times higher than what is actually required, and accept significantly reduced measurement accuracy. The inaccuracy of the instantaneous measurements are taken care of by a combination of averaging due to massive over-sampling and local feedback with the SDM. That will have to do in terms of an explanation, because an SDM is a conceptually complex beast, particularly in its analog form. In any case, the output of the SDM is a digital bitstream which can be 1-bit, but in reality is often 3-5 bits deep. The PCM output data is obtained on-chip by a digital conversion process similar to that which happens within DSD Master.”

John Siau This statement is wrong. The voltage reference precision is always important. Any noise on the voltage reference will be superimposed on the output signal no matter what combination of digitization and encoding methods are used. Likewise, the clock precision is also always important. Again, the clock precision is equally important for all systems. I should qualify this by saying that there were a few poorly designed conversion systems that actually magnified the clock errors (magnified jitter) but I don’t believe that any of these converters are currently on the market.

SDM does not change the importance of the voltage reference or of the clock.

BitPerfect: “As you know, if you are going to encode an analog signal in a PCM format, the price you have to pay is to strictly band-limit the signal to less than one half of the sample rate prior to encoding it. This involves putting the signal through a ‘brick wall’ filter which removes all of the signal above a certain frequency while leaving everything below that frequency unchecked. In a sample-and-hold ADC this is performed using an all-analog filter located within the input stage of the ADC. In the SDM-ADC it is performed in the digital domain during the conversion from the 1-bit (or 3-5 bit) bitstream to the PCM output.”

John Siau The signal needs to be band-limited in either system. DSD requires a 50 kHz low-pass filter (usually implemented in the analog domain). 96 kHz PCM requires a 48 kHz low pass filter, but this can be implemented in the digital domain, the analog domain, or both.

Modern sigma-delta PCM ADCs typically use a 5 MHz analog lowpass filter in front of the ADC, and a fs/2 digital lowpass filter following the ADC. The fs/2 digital filter is usually a steep filter, but it is almost always a linear-phase filter. Linear-phase filters do not distort the phase of the audio. At 96 and 192 kHz sampling rates, the lowpass filter does not need to be a brick wall. Many converters offer a gentler response at higher sample rates. This tends to reduce in-band variations in the amplitude response.

The DSD system needs two analog lowpass filters. A 5 MHz analog lowpass filter at the input to the ADC, and a 50 kHz analog lowpass filter following the D/A converter. The analog lowpass filter in a DSD system must by a fairly steep filter in order to block the ultrasonic noise in the DSD system. This filter is usually implemented in the analog domain and therefore it is not a linear-phase filter. The DSD analog lowpass filter distorts the phase response.

The PCM system delivers a linear phase response, but the DSD system doesn’t. 96 kHz PCM and DSD 64 have very similar bandwidth (just under 50 kHz).

Nevertheless, the differences between PCM 96/24 and DSD 64 should be inaudible. Both systems are capable of delivering high-resolution audio, and both systems exceed the performance of the CD by a significant margin.

BitPerfect: Brick wall filters are nasty things. Let’s look at a loudspeaker crossover filter as an example of a simple low-pass analog filter that generally can’t be avoided in our audio chain. The simplest filter is a single-stage filter with a cut-off slope of 6dB per octave (6dB/8ve). Steeper filters are considered to be progressively more intrusive due to phase disturbances which they introduce, although in practical designs steeper filters are often necessary to get around still greater issues elsewhere. Now compare that to a brick-wall ‘anti-aliasing’ filter. For 16/44.1 audio, this needs to pass all frequencies up to 20kHz, yet attenuate all frequencies above 22.05kHz by at least 96dB. That means a slope of at least 300dB/8ve is required.”

John Siau This is incorrect. The digital filters used in oversampling SDM converters are usually linear-phase filters. They do not introduce any phase distortion!

The lowpass filter is usually centered at 22.05 kHz and the response is usually only 40 to 50 dB down at the Nyquist frequency. This makes the filter about 1/2 as steep as Richard claims. Higher PCM sample rates ease the requirements of the lowpass filter. Richard should be comparing 96 kHz PCM to DSD 64.

The phase response of a 96 kHz PCM system is much more accurate than the phase response of a 64x DSD system with an analog lowpass filter. This is easy to measure and demonstrate and cannot be disputed.

Stay tuned for part 3 tomorrow. And for those readers in the US, have a great fourth of July holiday.

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About Author

Dr. AIX

Mark Waldrep, aka Dr. AIX, has been producing and engineering music for over 40 years. He learned electronics as a teenager from his HAM radio father while learning to play the guitar. Mark received the first doctorate in music composition from UCLA in 1986 for a "binaural" electronic music composition. Other advanced degrees include an MS in computer science, an MFA/MA in music, BM in music and a BA in art. As an engineer and producer, Mark has worked on projects for the Rolling Stones, 311, Tool, KISS, Blink 182, Blues Traveler, Britney Spears, the San Francisco Symphony, The Dover Quartet, Willie Nelson, Paul Williams, The Allman Brothers, Bad Company and many more. Dr. Waldrep has been an innovator when it comes to multimedia and music. He created the first enhanced CDs in the 90s, the first DVD-Videos released in the U.S., the first web-connected DVD, the first DVD-Audio title, the first music Blu-ray disc and the first 3D Music Album. Additionally, he launched the first High Definition Music Download site in 2007 called iTrax.com. A frequency speaker at audio events, author of numerous articles, Dr. Waldrep is currently writing a book on the production and reproduction of high-end music called, "High-End Audio: A Practical Guide to Production and Playback". The book should be completed in the fall of 2013.

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