Why does Rob design to -301 dB, how can that be verified, and how does small-signal accuracy relate to depth?

The test Watts means is a 6 kHz sine wave at -301 dB fed through a digital module in simulation, with the output checked by FFT for amplitude and, later, phase Head-Fi, Feb 2016Head-Fi, Jul 2021Head-Fi, Apr 2022. His stated reason is listening: he reports that errors in small signals, however small, damage the perception of depth Head-Fi, Mar 2016Head-Fi, Feb 2018Head-Fi, Apr 2022. Statements below are dated and tied to the product he was discussing.

2015: DAVE and the 350 dB noise shapers

In October 2015 he wrote that the brain is extremely sensitive to small-signal distortion, "in the sense there is no limit to how good small signal integrity needs to be" Head-Fi, Oct 2015. Later that month, for DAVE, he wrote "Dave's noise shapers are accurate to -350 dB and this was the performance required by depth perception", adding that the brain may be sensitive to even smaller levels but that 350 dB was the best he could do with current FPGAs Head-Fi, Oct 2015.

On 1 December 2015 he gave the history. "Before the Dave project, my target for noise shapers was better than 200 dB distortion and noise performance." Over a 90 day period he kept improving the noise shapers and heard depth improve each day, ending with a 17th order design at 350 dB, and reached the conclusion "there was no limit to how good the noise shaper needs to be in order to resolve depth perception" Head-Fi, Dec 2015. He separated two mechanisms in noise shapers, noise floor modulation and fundamental linearity (how accurately small signals are reproduced), and said of the second "Now this only affects depth perception, it does not do anything else." Head-Fi, Dec 2015. He also hedged in the same post: "Perhaps its down to something else, and the noise shaper number is merely a proxy for something else going on in the analogue domain." He then reported that raising DAVE's internal digital noise shapers from 220 dB to 350 dB improved depth, which he took as suggesting the brain really is sensitive to no error in small signals Head-Fi, Dec 2015.

2016: the -301 dB test becomes his standard

On 25 February 2016 he described running a Verilog simulation of DAVE's noise shaper with a -301 dB sine at 6 kHz: "If it can resolve a signal at -301 dB, then we can safely say that small signals are accurately encoded, at least in the digital domain." He added that -301 dB is better than 50 bits accuracy Head-Fi, Feb 2016. On 6 March he called it "way better than 50 bits, and actually more like 64 bit accuracy" Head-Fi, Mar 2016. On 31 March he wrote "Today, when I design I now formally test for this", and showed a 24 bit WTA output reproducing the tone at -301.030 dB Head-Fi, Mar 2016. In May he called it "my standard test for depth capability", showing a simulation of DAVE's 20 pulse array elements (with ideal analog performance) reproducing the tone to within 0.001 dB, and said better than 350 dB had audibly deeper depth than 330 dB, though a smaller change Head-Fi, May 2016.

In September 2016 he clarified how to read the number. It is the noise shaper's digital-domain performance, and "in reality the DAC actual analogue outputs will be very much worse than this". The point is not the noise level but that "a noise shaper becomes blind to tiny signals", so small signals are attenuated and eventually lost Head-Fi, Sep 2016. A day later he called -301 dB "my tests now for all modules", wrote "The honest answer is I don't know for sure" whether the brain needs -301 dB itself or whether a system that resolves -301 dB simply resolves -120 dB signals more accurately, and said the first idea struck him as absurd Head-Fi, Sep 2016. In October, posting an FFT of data from DAVE's noise shaper, he wrote "Absolutely this performance is measurable"; he said he could see why claiming the brain needs this accuracy looks absurd, but "I stand by my claims, based upon repeated listening tests" Head-Fi, Oct 2016.

2017 to 2019: applied to every module, and timing complicates it

In 2017 and 2018 he said all modules in DAVE and the M scaler pass the test, that all his digital modules inside the FPGA (writing in the Hugo 2 thread) must reproduce -301 dB accurately, and that each filter and truncation stage in Hugo 2 and Qutest must pass a -301 dB sine with perfect amplitude reproduction to protect depth Head-Fi, Jun 2017Head-Fi, Sep 2017Head-Fi, Feb 2018. In April 2018 he called -300.99 dB his digital-domain benchmark and said he had run the test dozens of times with different modules and depth always correlated with 350 dB digital-domain performance, but also that DAVE "will not show -350 dB in real life, as analog noise will swamp this performance", with analog noise at -128 dB Head-Fi, Apr 2018. For TT2's volume module in October 2018 he said it is not bit perfect but passes the -301 dB test and adds no distortion or noise within the audio band to -350 dB accuracy, adding "All my code has to pass this test now" Head-Fi, Oct 2018.

The M scaler (at that time the filter in the Blu Mk2) complicated the picture. In June 2017 he wrote that the M scaler passes the test, yet in its video mode, with THD and noise identical, 2/3 million taps against the full million gave a big difference: the sound-stage opened up with the full set. "And I still do not fully understand why this is the case." Head-Fi, Jun 2017. A transcript of a Hifistatement clip of a slide talk at Chord's Pump House, published in October 2017 (recording date not established), has him saying depth had always been about small signal integrity and that the tap-length effect was puzzling Hifistatement 3:43. In March 2019 (a date the archive estimates from the post ID) he described a "signal perfect" digital path as having no amplitude change with signal and "no phase shifts with amplitude from -301dB to 0dB" Head-Fi, Mar 2019; this is the earliest statement of the phase requirement found in this archive. In December 2019 he said the M scaler's 11th order truncation noise shaper holds "a -301 dB signal is accurate to +/-0.001dB in amplitude and +/- 0.001 deg in phase" Head-Fi, Dec 2019.

2021 to 2022: phase, Mojo 2 and the skeptics

In July 2021 he gave the pass criterion and procedure. He takes an FFT of a module with a 0 dBFS 6 kHz input, records amplitude and phase, repeats with the tone attenuated to -301.03 dBFS, and passes it only if it is accurate to "+/-0.001dB and +/-0.001 deg of phase" Head-Fi, Jul 2021. He said the approach "is very radical, and to some would be considered excessive; but after many listening tests, it is the only way to accurately reproduce soundstage depth" Head-Fi, Jul 2021. He added that he has no evidence that a constant phase shift hurts depth, only phase that varies with amplitude or time Head-Fi, Jul 2021. The same month he posted a DAVE analog-output plot showing a -186 dB signal resolved, noting a consistent +0.6 dB amplitude error across his DACs that he suspected came from the test instrument's own ADC Head-Fi, Jul 2021. He also said "The puzzle is why we need -301dB with zero phase and amplitude errors" Head-Fi, Jul 2021.

For Mojo 2 (January 2022) he wrote that the original Mojo's noise shaper "did have a phase error at -301dB, and eliminating this gave much better depth perception" Head-Fi, Jan 2022. In April 2022 he described the listening test behind that: of several internal delay settings on the original Mojo noise shaper, one sounded best for depth, and simulation then showed the worst setting had "a 2uS error, the two OK ones was 100nS, and the sweet spot setting the error was only 10nS" Head-Fi, Apr 2022. The Mojo 2 DSP core was designed to pass the test, using 104 bit fixed point with noise shaping on all internal nodes, after a 104 bit design without noise shaping failed the phase check Head-Fi, Jan 2022Head-Fi, Feb 2022MFG Audio Reviews 36:12. He said conventional 64 bit DSP has significant errors for small signals and is inadequate for transparent EQ Head-Fi, Jan 2022Head-Fi, Feb 2022. In a post that does not name the product, he said a four-element noise shaper reproduces -301 dB but its -320 dB noise floor at 6 kHz stops him proving the 0.001 dB and 0.001 degree figures; he gave it as 250 dB against DAVE's 350 dB Head-Fi, Feb 2022.

In April 2022 posters challenged him, and he answered directly. "Actually I agree; the idea that we need accuracy at -301dB is plainly nuts, and makes no objective sense", but he follows the evidence of what he estimates are hundreds of listening tests Head-Fi, Apr 2022. He said "I am not saying that a -301dB signal is in any way audible - I am just saying that the distortion performance at that level is audible", and that how it becomes audible "I do not understand" Head-Fi, Apr 2022. He described the setup as an 80 bit sine source at 768 kHz, noise shaped into the module under test, run in Verilog simulation, then FFT Head-Fi, Apr 2022Head-Fi, Apr 2022. On verification he wrote "I have not published my results in say the AES" and "My listening tests would be considered anecdotal and not scientific evidence; but my job is to close the gap from live to recorded sound, and the tests I do are extremely carefully done and objective…", and said he would run a single blind test with disinterested parties when a result defies explanation Head-Fi, Apr 2022. The next day he wrote "I always treat my listening tests as being tentative and subject to re-evaluation, no matter how careful you approach things" Head-Fi, Apr 2022. He also said he had done "a huge number of listening tests (some blind)" Head-Fi, Apr 2022.

2023 to 2026: restated in posts, talks and interviews

In March 2023 he said the phase finding dated from "5 years ago", after the M scaler work, that the higher-order noise shapers from Hugo 2 to DAVE have no phase errors at -301 dB anyway, and that the phase shift at -301 dB "only influences the perception of soundstage depth" Head-Fi, Mar 2023. In September 2023 he said Mojo 2's UHD DSP EQ was designed to pass the amplitude and phase test, and that failing 0.001 dB or 0.001 degree at -301 dB has subjective effects, "notably the perception of soundstage depth and fine details" Head-Fi, Sep 2023. Transcripts of 2023 talks repeat the 0.001 dB and 0.001 degree figures and the story of listening to DAVE noise shapers from 200 dB up to 350 dB The Headphone Show 43:19Amplify Audio 5:34Amplify Audio 6:28. In 2024 he said of 330 dB against 350 dB: "if I do this as a blind listening test, which I have done, you can still perceive these changes" MFG Audio Reviews 45:45. In a 2024 Quartet interview he said DSD cannot reproduce -301 dB HIFICLUB 39:59.

In a podcast recorded in October 2025 (published March 2026) he said "a minus 301 dB is never going to be audible, but a minus 301 dB error is perceivable" ecoustics 49:13. In the same interview he said that when someone listens without knowing which is which, "the blind listener will come back with the same result that I was hearing"; he also recalled that at the time of DAVE he had suspected the noise shaper was a proxy for something analog, and said purely digital truncation noise shapers show the same need for better than 350 dB ecoustics 39:09ecoustics 40:09. Asked there whether the error can be measured, the transcript has him answer "you can't actually measure the errors" before describing his -301 dB test suite for every digital module ecoustics 41:24. He dated the phase discovery differently from 2023, counting from that recording: "three or 4 years ago I discovered that actually the phase shift of that signal compared to naught dB was also important" ecoustics 41:49.

In a HiFi Buys interview published in October 2026 (recording date not stated; its transcript places it before May 2026) he again said that under blind conditions other listeners, not knowing what they were hearing, reported the same improvement in depth HiFi Buys 1:22:59. He traced the phase work back to a depth change he heard with the M Scaler and Blu 2 in 2017, followed by a quick listening test with a switchable small-signal delay (he does not name the product in this passage) HiFi Buys 1:24:04HiFi Buys 1:28:26; the transcript gives the figures as the best setting "accurate within A couple of nanoseconds" and the others "off by 10, 20, 30 nanoseconds" HiFi Buys 1:29:40, which differs from the 2022 Mojo figures above. He said "there's virtually no limit to how accurate it needs to be" HiFi Buys 1:30:14. In a Soundnews Quartet interview, recorded in autumn 2026 and published in October 2026, he said its equalizer passes the -301 dB amplitude and phase test article, Oct 2026.

How he links small-signal accuracy to depth

His stated mechanism is that depth is carried by small reverberant and echo cues. In 2015 he wrote "Depth perception is indeed mostly down to the reverberant signal to direct sound signal ratio" Head-Fi, Dec 2015. In 2016: "small echo cues tells the brain that a sound is further away", so attenuating them degrades perceived depth Head-Fi, Sep 2016. In the HiFi Buys interview (published October 2026, recording date not stated) he described reverberant tails as "small in amplitude, chaotic in timing", needing to be reproduced perfectly for the brain to make sense of them HiFi Buys 1:38:00. For the phase finding he offered, in the same interview, a hypothesis that the brain uses the timing difference between direct and reflected sound, saying "this is not something in textbooks, this is just me thinking about things" HiFi Buys 1:25:41. On why the brain is this sensitive he offers only guesses: "It's likely that correlation functions play a part in this" Head-Fi, Apr 2022. In the ecoustics podcast (recorded October 2025, published March 2026) he called it "absolutely bizarre, makes no sense" ecoustics 42:36.

His description of what else small-signal errors affect varies by post. In December 2015 he said fundamental linearity affects only depth Head-Fi, Dec 2015, while a post that October said small signal linearity is useful for detail resolution as well as depth Head-Fi, Oct 2015. In posts from 2018, 2021 and 2022 he wrote depth and detail together Head-Fi, Feb 2018Head-Fi, Jul 2021Head-Fi, Jan 2022, and a 2023 talk transcript has small signal nonlinearity "very important for depth and detail resolution" The Headphone Show 40:09. For phase specifically, he said in March 2023 that it affects only depth Head-Fi, Mar 2023, and in September 2023 named depth and fine details Head-Fi, Sep 2023. These are differences in wording across posts, and this archive does not show him saying he revised the claim.

On analog parts he says the same kind of small-signal error occurs, for example at metal to metal contacts, but "it's not possible to directly put a number onto these issues, unlike in the digital domain" Head-Fi, Apr 2022Head-Fi, Oct 2015.

What he has not said

He does not claim a -301 dB signal is itself audible, does not claim the mechanism is understood, and does not claim the figure can be measured on a DAC's analog outputs Head-Fi, Apr 2022Head-Fi, Apr 2022. He says his results are unpublished and his listening tests would count as anecdotal Head-Fi, Apr 2022. He reports that some tests were blind and, in 2026, that blind listeners heard the same depth changes, but this archive contains no published or independent test data Head-Fi, Apr 2022HiFi Buys 1:22:59. One transcribed passage renders the level as "minus 201 dB" where context shows 301 MFG Audio Reviews 33:04. He gives the bit-depth equivalent as more than 50 bits in 2016 Head-Fi, Feb 2016, about 64 bit in a 2016 post Head-Fi, Mar 2016, and about 60 bit in an October 2017 talk, published in December 2017 RMAF 49:13.

Quotes

“Today, when I design I now formally test for this by ensuring that it will perfectly reproduce a -301 dB signal which ensures its much better than 50 bits accuracy.”2016-03-31 Head-Fi, Mar 2016

“Now small signal accuracy is very important for depth perception, as small echo cues tells the brain that a sound is further away.”2016-09-13 Head-Fi, Sep 2016

“I am not saying that a -301dB signal is in any way audible - I am just saying that the distortion performance at that level is audible.”2022-04-13 Head-Fi, Apr 2022

“I always treat my listening tests as being tentative and subject to re-evaluation, no matter how careful you approach things.”2022-04-14 Head-Fi, Apr 2022

“a minus 301 dB is never going to be audible, but a minus 301 dB error is perceivable.”2025-10-28 ecoustics 49:13

Dated positions

Caveats and open points

• Everything here is Watts's own account; this archive contains no published or independent measurement or blind-test data supporting or refuting the -301 dB claim. His own reports of blind tests are statements, not data.
• He says the -301 dB figures are digital-domain simulation results and cannot be measured on analog outputs Head-Fi, Sep 2016Head-Fi, Apr 2022.
• The delay-test figures differ between a 2022 post on the original Mojo noise shaper (2 us, 100 ns, 10 ns) and an interview transcript published October 2026 that does not name the product (a couple of ns against 10 to 30 ns).
• The date he gives for the phase discovery differs: a 2023 post (5 years earlier, after the M scaler), a podcast recorded in October 2025 and published in March 2026 (3 or 4 years earlier) and an interview published October 2026 (the M Scaler with Blu 2 in 2017). The earliest phase-requirement post found is dated March 2019, an estimate from the post ID.
• One post about a four-element noise shaper does not name the product.

Topics: Small-signal accuracy and resolution, Measurements, test equipment and simulation, Depth and soundstage