Small-signal accuracy and resolution

Noise shaping, accuracy and conversion hardware

Answers on this topic

• What do noise shaper order and speed buy, and why does DAVE's 350 dB noise shaper matter?
• What does Rob mean by depth, and what in a DAC improves or collapses it?
• Why does Rob design to -301 dB, how can that be verified, and how does small-signal accuracy relate to depth?

Everything he said on this topic (197)

One-line summaries in our words, oldest first. Each link opens the original.

• 2014-10-27Watts says RF in Hugo's ground plane causes bright noise floor modulation and zero-crossing currents degrade linearity and depth; the Olimex removes LF currents and matched optical for him. Head-Fi, Oct 2014
• 2014-11-17Watts says low-level resolution is not an issue with the QBD, stresses small-signal accuracy for soundstage depth, and says a 10dB gain change won't help; the post is truncated. Head-Fi, Nov 2014
• 2015-10-01Watts says metal contacts and noise shapers cause the same small-signal distortion that truncates depth, the brain detects levels no instrument measures, and HF distortion alters transient timing. Head-Fi, Oct 2015
• 2015-10-30Watts says Dave's depth, about four times Hugo's, comes from small-signal accuracy of its -350 dB noise shapers; timing gains offset the darkness that reducing noise floor modulation brought. Head-Fi, Oct 2015
• 2015-12-01Watts ties depth to small-signal linearity, distinguishes it from noise floor modulation, and describes raising Dave's noise shapers from 200 to 350 dB with depth improving throughout. Head-Fi, Dec 2015
• 2015-12-11Watts defines musicality as emotional involvement, achieved by reducing errors the brain cannot decode: timing (long taps), small-signal accuracy for depth (2048FS noise shapers), and noise floor modulation. Head-Fi, Dec 2015
• 2016-01-29Watts says Hugo's noise shaping was limited by its four-element pulse array and FPGA; for DAVE each 20 dB improvement from 200 dB deepened the stage, reaching -350 dB. article, Jan 2016
• 2016-01-29Watts describes DAVE's 17th-order noise shaper with 46 integrators, his doubt whether 350 dB was the real cause, and a redesign confirming 350 dB or 48-bit accuracy is needed. article, Jan 2016
• 2016-01-29Watts gives DAVE's noise as -127 dB A-weighted at 2.5 V and distortion 0.000015 percent, and says his converters' distortion falls with signal level, unlike ladder, DSD or chip DACs. article, Jan 2016
• 2016-02-25Watts says he is designing an ADC to match Dave, and shows a Verilog simulation of Dave's noise shaper reproducing a -301 dB sine over a -380 dB floor. Head-Fi, Feb 2016
• 2016-03-01Watts says Dave is source-insensitive through bit-perfect data and immunity to jitter and noise, that depth needs perfect small-signal accuracy (350 dB noise shapers), so no pre-amp sounds better. Head-Fi, Mar 2016
• 2016-03-06Watts says Davina will test whether ADC bandlimiting changes sound once reconstruction is perfect, and whether dither can carry Dave's -301 dB, 64-bit-like small-signal accuracy at 44.1 kHz. Head-Fi, Mar 2016
• 2016-03-07Author says DAVE's enhanced noise shaper reproduces fine signals for spatial recognition; Watts contrasts hearing an organ's distance in church with recordings, saying recovering depth was his concern. article, Mar 2016
• 2016-03-31Watts says DAVE's volume is fully digital because analog controls have small-signal errors that degrade depth, and describes his 350 dB noise shaper and -301 dB test targets. Head-Fi, Mar 2016
• 2016-03-31Watts says DAVE's maximum attenuation is -75 dB with truncation noise near -350 dB, and explains how noise shapers attenuate signals near their resolution, harming depth. Head-Fi, Mar 2016
• 2016-04-02Watts contrasts fixed analog noise with signal-dependent small-signal distortion in R2R, delta-sigma and DSD DACs, and says DAVE's -127 dB dynamic range is set by hiss alone. Head-Fi, Apr 2016
• 2016-04-26Watts says DAVE adds no artificial depth, since flat recordings stay flat, and attributes compressed depth in DACs to small-signal amplitude errors rather than ringing. Head-Fi, Apr 2016
• 2016-04-28Watts calculates that an R2R DAC matching DAVE's -350 dB accuracy would need 0.000000000000003% resistors and 40 fS timing, and argues this cannot be achieved. Head-Fi, Apr 2016
• 2016-05-30Watts recalls using dither with multiple DSD256 noise shapers on the PDM1024 in 1992, says the pulse array made it unnecessary, and notes dither cannot be added to DSD directly. Head-Fi, May 2016
• 2016-05-31Watts gives two reasons adding noise to zero bits can help a DAC, small-signal non-linearity and signal-correlated DSP supply noise, and says DAVE's 350 dB noise shapers justify re-testing it. Head-Fi, May 2016
• 2016-07-24Watts says his noise shaper resolves about a thousand times more than normal DAC noise shapers and 10 thousand times more than DSD's; information below its floor is lost. Hifistatement 1:43
• 2016-07-24Watts says dithered PCM keeps small signals within the noise, but noise shapers cannot be dithered properly and discard them; Hugo's 4E pulse array and gate count limited it. Hifistatement 2:23
• 2016-07-24Watts says the brain detects tiny errors as poorer instrument placement, depth needs perfect accuracy, and he ended with a new 17th-order noise shaper with 46 integrators. Hifistatement 3:54
• 2016-07-24Watts says redesigning DAVE's all-digital noise shapers to 350 dB gave the same results, so the digital path truly needs 350 dB (48-bit) accuracy; it is not a proxy. Hifistatement 5:24
• 2016-07-24Watts says his DACs from Mojo to DAVE show no measurable noise floor modulation or anharmonic distortion, with distortion falling as signal falls, unlike R2R, DSD and silicon DACs. Hifistatement 44
• 2016-09-13Watts clarifies that the -350 dB figure is the noise shaper's exact Verilog-simulated digital performance, mattering for preserving tiny signal amplitudes rather than noise, which he ties to depth. Head-Fi, Sep 2016
• 2016-09-14Watts admits he cannot explain why depth needs 350 dB noise shapers, gives a -120 dB signal's attenuation for 160 to 340 dB shapers, yet still hears the change. Head-Fi, Sep 2016
• 2016-10-16Watts argues musicality comes first and explains why Mojo and DAVE excel on transient timing (NOS errors, tap length, 1M taps), small-signal accuracy and noise floor modulation. Head-Fi, Oct 2016
• 2016-10-18Watts says he has bottomed out depth, needing -350 dB capable paths with no small-signal linearity issues, but expects more timing discoveries with Davina, especially in ADC decimation. Head-Fi, Oct 2016
• 2016-10-20Watts shows an FFT of DAVE's noise shaper output resolving a -301 dB 6 kHz signal, stands by his listening-based claim that depth needs this, and plans Davina tests. Head-Fi, Oct 2016
• 2016-11-10Watts says DAVE's depth comes from preserving small-signal amplitudes, not its -128 dB noise floor; timbre from no noise floor modulation and accurate transient timing; hard USB from non-bit-perfect data. Head-Fi, Nov 2016
• 2017-03-04Watts says his cable work showed oxides cause small-signal non-linearity that harms depth yet is unmeasurable, and DAVE noise-shaper tests show any small-signal error is audible. Head-Fi, Mar 2017
• 2017-06-11Watts says DAVE sounds better via the M scaler not from a WTA fault, citing Verilog simulation and -301 dB tests, and video mode's two-thirds million taps shrinks the soundstage. Head-Fi, Jun 2017
• 2017-09-19Watts explains headphone depth perception, why Hugo 2 crossfeed gives out-of-head sound, and why small-signal accuracy to -301 dB lets the brain use depth cues. Head-Fi, Sep 2017
• 2017-10-13Watts says the M Scaler deepens the soundstage enormously, which puzzles him because filter changes never altered depth before; depth depends on small-signal nonlinearity, which filters can avoid. miceblue425 33:17
• 2017-10-13Watts says DAVE's noise shapers needed 350 dB accuracy to preserve small signals, that 330 versus 350 dB is still audible, and that Davina's noise shapers reach 360 dB. miceblue425 37:35
• 2017-10-13Watts says his girlfriend's blind result, smoother and warmer, matched his, and that the 330 versus 350 dB depth finding seemed too crazy to post. miceblue425 53:52
• 2017-10-13Watts says he could hear 350 versus 330 dB and others he asked could too, then turns to his silicon design career. miceblue425 54:37
• 2017-10-16Watts posts his second seminar on DACs: noise shaper listening tests showing sub-threshold errors affect depth, a 350 dB accuracy need, chip DAC limits, DSD and pulse array analog benefits. Head-Fi, Oct 2017
• 2017-10-16Watts posts seminar measurement slides, saying simulation shows -301 dB signals reproduced, his designs have no measurable noise floor modulation, and jitter FFTs should replace marketing claims. Head-Fi, Oct 2017
• 2017-10-20Watts says the USB video mode, two-thirds of a million taps on the same architecture, collapses the soundstage, though architecture and small-signal work carried over from DAVE also matter. Hifistatement 2:57
• 2017-10-20Watts says small-signal integrity was verified by passing the -301 dB test, so he cannot explain why longer taps change depth, which he has tied to small-signal integrity. Hifistatement 3:43
• 2017-12-05Watts introduces small-signal nonlinearity and depth perception as a fascinating and very bizarre subject. RMAF 17:18
• 2017-12-05Watts says since the 1990s he has found fundamental linearity affects depth perception, and defines the test: set minus 60 dB, play a minus 100 dB signal, measure its amplitude. RMAF 17:37
• 2017-12-05Watts says the signal would measure minus 102 or minus 98, with up to 2 or 3 dB error in the early days, visible as humps in fundamental linearity tests. RMAF 18:22
• 2017-12-05Watts says pulse array eliminated the fundamental linearity problem of his 1990s DSD256 DACs; a minus 120 dB signal now measures within a thousandth of a dB, Mojo to DAVE. RMAF 18:43
• 2017-12-05Watts says any small-signal error is audible, recounting that the first Hugo's code was too big to fit, so he slimmed down the noise shaper, worried about sound quality. RMAF 20:51
• 2017-12-05Watts says depth kept improving with noise shapers at 240, 260, up to 330 to 350 dB, a 0.0000001 dB change at minus 120 dB, easily heard blind. RMAF 22:21
• 2017-12-05Watts says 144 dB distortion would need R2R resistors matched to fifty micro-ohms on 1 kilohm, which will never happen, and mismatch also ruins fundamental linearity. RMAF 33:05
• 2017-12-05Watts says R2R switches change most for small signals, adding glitch energy that degrades small-signal integrity and depth; he calls DSD widely misunderstood, though he loves it. RMAF 33:54
• 2017-12-05Watts says the DSD modulator creates noise floor modulation in the digital domain, with DSD64 at about 110 to 126 dB versus the 350 dB his DACs need. RMAF 36:37
• 2017-12-05Watts says every Verilog module must pass a minus 301 dB signal unchanged, about 60-bit accuracy he considers needed for depth, and DAVE's noise shaper shows minus 300.99 dB. RMAF 49:13
• 2017-12-05Watts shows two 16-bit level signals with identical left and right ringing from the digital filter, calling it perfect 16-bit reproduction, then tries a 32-bit LSB signal. RMAF 52:07
• 2017-12-05Watts says a special method on the Audio Precision measured it within 1 dB, an error he attributes to the analyzer since every product shows it, then invites questions. needs context RMAF 52:57
• 2017-12-25Watts explains DSD's 1-bit problems: lower resolution, modulator instability causing noise floor modulation, and small-transient delays, versus his 5-bit 2048FS pulse array and DAVE's -301 dB noise shaper. Head-Fi, Dec 2017
• 2018-02-07Watts lays out the Hugo 2/Qutest signal path from 16FS WTA1 (49,152 taps) to 104 MHz pulse array, and explains noise-shaped truncation and the -301 dB test for depth. Head-Fi, Feb 2018
• 2018-02-11Watts says passive volume controls add small-signal non-linearity via contacts and joints, conventional R2R and delta-sigma DACs resolve small signals poorly, so he ensures -301 dB resolution. Head-Fi, Feb 2018
• 2018-02-14Watts says Hugo 1 and Mojo have similar depth because they share the same pulse array, noise shapers and truncators, which set small-signal linearity and hence depth. Head-Fi, Feb 2018
• 2018-04-30Watts says the SYS2722 cannot measure Dave (-118dB versus -128dB on an APx555), calls NFM a top-3 SQ indicator, and uses Verilog simulation to verify -350dB and -300.99dB performance. Head-Fi, Apr 2018
• 2018-10-24Watts summarizes TT2's 10-element pulse array: 300 dB noise shapers at 104MHz, jitter insensitivity, no measurable noise floor modulation or non-linearity, and minimal analog filtering. Head-Fi, Oct 2018
• 2018-10-27Watts says 10 versus 20 pulse array elements helps Dave's transparency, and his noise-shaped volume control is not bit perfect but passes a -301 dB test. Head-Fi, Oct 2018
• 2018-12-12Watts explains small-signal amplitude error: a minus 90 dB signal measured against minus 20 dB comes out slightly high or low, and this changes perceived depth and detail resolution. Pursuit Perfect System 11:46
• 2018-12-12Watts says small-signal non-linearity changes depth at ridiculously small levels, any such error is audible as collapsed depth, and contrasts a cathedral organ 100 meters away with hi-fi's six feet. Pursuit Perfect System 12:32
• 2018-12-12Watts says reproduced audio never conveys true distance, a problem he has pursued since the 1980s, and that however small the small-signal errors are, depth is truncated. Pursuit Perfect System 13:15
• 2018-12-12Watts says he wanted the pulse array to keep DSD's single-element benefit over R2R resistor matching, which never gets small-signal accuracy right, while constant switching removes signal-dependent glitch noise. Pursuit Perfect System 17:18
• 2018-12-12Watts says one switching element gives accurate small signals, and the pulse array adds clock cancellation and constant switching rate at far higher resolution than DSD. Pursuit Perfect System 17:57
• 2018-12-12Watts says the change was in depth perception, a surprise because in 2014 he thought 200 dB noise shaper performance, better than 32-bit, was more than anyone could hear. Pursuit Perfect System 22:12
• 2018-12-12Watts says 350 dB is about 64-bit accuracy, reproducing a minus 90 dB signal more accurately by 0.0000 1001 dB, a difference the ear and brain easily hear. Pursuit Perfect System 25:17
• 2018-12-12Watts says replacing the first-order noise shaper truncating the WTA filter's 56-bit output to 24 bits with 350 dB noise shapers also improved depth, showing small-signal accuracy is fundamental. Pursuit Perfect System 26:51
• 2018-12-12Watts says from earlier cable design that purer copper, silver solder and plating purity sounded better, and attributes this to small-signal non-linearity from oxide layers and joints. Pursuit Perfect System 27:40
• 2018-12-12Watts says oxide joints present higher impedance to microvolt signals, mathematically identical to the noise shaper issue, and that 100 meters of poor versus good copper cable measured no different. Pursuit Perfect System 28:35
• 2018-12-27Watts says the M scaler unexpectedly improves reverb and depth perception, normally tied to small-signal accuracy, speculating about its 1.438 s of data versus concert-hall RT60, unconvinced. Head-Fi, Dec 2018
• 2019-05-11Watts says chip DACs suffer substrate noise, NFM and jitter, while his discrete DACs measure -120dB signals to +/-0.001 dB and resolve -186 dB within 1dB. Head-Fi, May 2019
• 2019-12-10Watts says R2R's only benefit is having no noise shaper, which might help small signals, but measured R2R small-signal accuracy is awful and chip delta-sigma DACs do much better. Passion for Sound 14:05
• 2019-12-10Watts says he cares about competitors' technology, not their sound, and that R2R distortion extends to infinite frequencies and stays constant as signal falls until it exceeds the signal, very audibly. Passion for Sound 15:47
• 2019-12-10Watts says delta-sigma distortion has fewer harmonics and falls naturally as the signal level is reduced. Passion for Sound 16:37
• 2019-12-10Watts says chip DACs have a problem in that some distortion always remains as the signal gets smaller. Passion for Sound 16:49
• 2019-12-10Watts says R2R uses 0.01% resistors, about -80 dB; 144 dB would need impossible tolerances, while his noise shapers reach 64-bit accuracy or 350 dB. Passion for Sound 17:48
• 2019-12-16Watts says ten years ago he would have said a 200 dB noise shaper, 32-bit accurate, was enough, since no analog section could reach that accuracy. Passion for Sound 10:56
• 2019-12-16Watts says DAC64 and QBD76 had 200 dB noise shapers while the best chip DACs reach only 140 dB, so they reproduce small signals poorly, degrading depth and detail. Passion for Sound 11:25
• 2019-12-16Watts says after three months he reached a final 330 dB versus 350 dB noise shaper, still heard subtle depth changes, and concludes any depth error is audible. Passion for Sound 13:35
• 2019-12-18Watts says M scaler output is 11th-order noise-shaped to 24 bits at 768k for -301 dB accuracy, ranks Gaussian dither above TPDF, and advises keeping the source bit perfect. Head-Fi, Dec 2019
• 2021-03-29Watts says Linn-style PWM FPGA DACs have amplitude-dependent transient timing errors and a roughly 3MHz noise shaper, unable to reach the 350dB accuracy of his pulse array. Head-Fi, Mar 2021
• 2021-06-04Watts says metal-to-metal interfaces attenuate small signals, his analog noise shaper gives TT2 20GHz and Dave 0.5THz gain bandwidth, and the pulse array creates no noise floor modulation. Head-Fi, Jun 2021
• 2021-06-22Replying that NOS, R2R and ESS DACs have caught up with TT2, Watts says his digital modules exceed 64-bit float, reproduce -301dB, with fixed-point noise-shaped noise below -400dB. Head-Fi, Jun 2021
• 2021-06-22Watts says R2R cannot cancel resistor mismatch, since -301dB accuracy needs 400 dB matching, and NOS and R2R fans are enjoying distortion; rival DACs at shows sound as expected. Head-Fi, Jun 2021
• 2021-07-23Watts says the volume control output is aggressively noise shaped, not truncated or dithered, reproducing -301dB within +/-0.001 dB, and shows the M scaler truncator's -390dB noise floor. Head-Fi, Jul 2021
• 2021-07-24Watts says resolution means resolving small signals, not fixed noise (21.3 bits for Dave); Dave resolves -186dB; and 1M taps' 16.7-bit accuracy now looks insufficient for transients. Head-Fi, Jul 2021
• 2021-07-25Watts says more work is ongoing with news expected next year, and depth needs cues preserved in amplitude and timing; why -301dB accuracy matters remains a mystery. needs context Head-Fi, Jul 2021
• 2021-07-25Watts describes his -301.03dBFS FFT test requiring +/-0.001dB and +/-0.001 degree accuracy, saying phase that varies with amplitude degrades depth while constant phase shift does not. Head-Fi, Jul 2021
• 2021-11-30Watts says correct filter timing errors are amplitude independent but transients intermodulate through non-sinc windows; a WTA simulation matched 0dBFS and -301dB, and coefficient accuracy improved depth. Head-Fi, Nov 2021
• 2022-01-31Watts names three issues separating his DACs from others: small-signal accuracy, important for depth and detail, and noise floor modulation, which other DACs show heavily; he begins defining it. Darko.Audio 6:56
• 2022-01-31Watts says DSP also degrades small-signal accuracy, recalling that during DAVE's development around 2014 he thought 200 dB noise shapers were enough since no one hears -200 dB. Darko.Audio 21:22
• 2022-01-31Watts says depth improved at each noise shaper step, 220 dB, 240 dB, up to DAVE's 350 dB, even 330 to 350; noise shapers shrink his -301 dB test signal. Darko.Audio 22:09
• 2022-01-31Watts says chip DACs use noise shapers of -140 dB and lose anything lower, and DSP EQ is worse because bass EQ multiplies the signal by very small coefficients. Darko.Audio 23:00
• 2022-01-31Watts says the attenuated signal is summed thousands of times so small errors become large; conventional DSPs cannot resolve -301 dB signals, degrading depth and detail. Darko.Audio 23:50
• 2022-01-31Watts says two or three years ago he found amplitude-dependent phase shift is audible as suppressed depth, while investigating why 1 million taps beat DAVE's 164 thousand for depth. Darko.Audio 24:34
• 2022-01-31Watts says DSP filters give small signals a different phase; his formal test compares phase at 0 dB and -301 dB, and 0.002 of a degree audibly suppresses depth. Darko.Audio 25:21
• 2022-01-31Watts says COVID-era listening tests revealed very small audible effects, so the DSP had to reproduce -301 dB perfectly in phase and amplitude, requiring a different core. Darko.Audio 26:13
• 2022-01-31Watts says he built a 104-bit DSP core rather than the usual 64 bits; it passed -301 dB amplitude but failed phase until each node got a noise shaper. Darko.Audio 26:59
• 2022-01-31Watts says the DSP then showed zero phase shift at -301 dB, and it sounded better once the noise shapers were in. Darko.Audio 27:50
• 2022-01-31Watts presents Mojo 2: coupling capacitor removed, new noise shaper, and a UHD DSP EQ he says passes -301dB amplitude, phase and NFM transparency tests that 64-bit DSP fails. Head-Fi, Jan 2022
• 2022-02-01Watts says it reproduces -301dB but its -320dB noise floor at 6kHz prevents proving 0.001dB accuracy; the 4-element noise shaper is 250dB versus DAVE's 350dB. Head-Fi, Feb 2022
• 2022-02-14Watts says 64-bit floating-point EQ creates noise floor modulation and small-signal errors; Mojo 2 uses 104-bit noise-shaped fixed point; his DACs need no warm-up or break-in. Head-Fi, Feb 2022
• 2022-02-22Watts says RF only degrades low-level linearity if signal-correlated, his DACs' RF output is low and uncorrelated, and analog pre-amps add coloration rather than beating Chord's volume control. Head-Fi, Feb 2022
• 2022-03-19Watts explains small signal non-linearity: a -120 dB signal may come out at -121 or -119 dB, an amplitude error that confuses the brain and impairs depth perception. MFG Audio Reviews 9:00
• 2022-03-19Watts says inaccurate small signals are one cause of lost depth, the smallest error collapses depth, and his test is reproducing -301 dB, a figure he hesitated to publish. MFG Audio Reviews 10:36
• 2022-03-19Watts says he expected to be called a liar over -301 dB, but hundreds of listening tests show depth degrades without it, and science explains evidence. MFG Audio Reviews 11:30
• 2022-03-19Watts says conventional EQ adds noise floor modulation and collapses the soundstage as small signals lose amplitude accuracy, and recounts puzzling over why an M Scaler markedly improves depth. MFG Audio Reviews 30:09
• 2022-03-19Watts says the M Scaler's depth gain cannot come from small signal amplitude, set by quantization and noise shaping, so depth must involve timing; he tested a detuned noise shaper. MFG Audio Reviews 30:53
• 2022-03-19Watts says simulation showed no difference between the settings at -90 or -120 dB, but at -301 dB amplitude was perfect while small-signal delay differed. MFG Audio Reviews 32:19
• 2022-03-19Watts says the delays were 2 microseconds, 100 nanoseconds and under 10 nanoseconds, he chose the best unaware, and asks how the brain detects 100 nanoseconds at minus 201 dB. MFG Audio Reviews 33:04
• 2022-03-19Watts says DSP EQ uses biquad filters whose small bass coefficients and truncation errors grow through feedback, so very small signals are lost and phase shifted. MFG Audio Reviews 33:55
• 2022-03-19Watts says 64-bit float sounds brighter, and transparent EQ DSP must reproduce -301 dB perfectly in amplitude and within a thousandth of a degree in phase, without floating point. MFG Audio Reviews 35:31
• 2022-03-19Watts says the digital simulation is the real output, and shows the DSP reproducing -301 dB within thousandths of a dB and thousandths of a degree. MFG Audio Reviews 38:18
• 2022-03-19Watts shows no noise floor modulation (same -177 dB floor with signal on or off), low distortion, and a perfectly reproduced 16-bit small signal with left and right superimposed. MFG Audio Reviews 45:02
• 2022-03-19Watts says DSD cannot reproduce -140 dB, DSD256 and 512 are better but all 1-bit DSD has noise floor modulation, and decent performance would need around DSD 16,000. MFG Audio Reviews 54:40
• 2022-03-26Watts says desktop mode isolates the battery, and that recursive IIR EQ needs 104 bits plus noise shaping while FIR filters need fewer bits to reproduce -301 dB accurately. Head-Fi, Mar 2022
• 2022-04-07Watts says M scaler depth gains led him to test phase shift with amplitude (2uS, 100nS, 10nS errors), so modules must now pass -301 dB in amplitude and phase. Head-Fi, Apr 2022
• 2022-04-08Watts says -301 dB phase measurements are digital-domain only, analog paths suffer small-signal non-linearities, and he recommends multiple 0.6mm solid-core PTFE silver-plated conductors for speaker cables and 0.4mm for interconnects. Head-Fi, Apr 2022
• 2022-04-09Watts says -301 dB is about 600 electrons driving a Stealth, yet many listening tests, some blind, show it matters, as with Dave versus TT2's small difference. Head-Fi, Apr 2022
• 2022-04-12Watts says the brain copes with harmonic distortion (cochlea about 4% THD) but not small signal distortion, noise floor modulation, anharmonic or timing errors, justifying -301dB accuracy. Head-Fi, Apr 2022
• 2022-04-13Watts describes his -301 dB Verilog simulation test with an 80 bit 768 kHz source, explains not publishing, and ties poor reproduced depth to small signal accuracy. Head-Fi, Apr 2022
• 2022-06-12Watts recounts crossfeed giving an out-of-head experience with a Hugo 2 prototype on a flight, never with the original Hugo, linking better small-signal accuracy to more effective crossfeed. Head-Fi, Jun 2022
• 2022-08-31Watts says TT2 had no cost-saving compromises, DAVE proved more transparent than he expected, Chord is engineer-run, and noise floors are about -400 dB (digital) and -350 dB (best noise shapers). Head-Fi, Aug 2022
• 2023-01-19Watts says his point concerned the Hugo M scaler's 24-bit outputs, not DACs, and noise shaper size depends on type and task, though all need -301 dB performance. Head-Fi, Jan 2023
• 2023-02-04Watts names three issues, small-signal accuracy, noise floor modulation and transient reconstruction (the most important), and begins explaining small-signal accuracy with a -100 dB signal. Dusty Audio 18:36
• 2023-02-04Watts says 1990s DACs showed 1 or 2 dB of error at -100 dB; the pulse array eliminated it, and -120 dB measures accurate within a thousandth of a dB. Dusty Audio 19:20
• 2023-02-04Watts says such measurements take three or four hours, that better small-signal accuracy gave better detail and depth, and that reproduced depth collapses compared with a distant cathedral organ. Dusty Audio 20:06
• 2023-02-04Watts says improving small-signal amplitude accuracy improved depth, and developing Dave with a bigger FPGA after Hugo let him try better noise shapers. Dusty Audio 20:50
• 2023-02-04Watts says going from 330 to 350 dB was the first step where depth differences became hard to hear, and that small-signal accuracy is vital to depth and detail. Dusty Audio 24:38
• 2023-03-19Watts says phase shift with amplitude, found after the M scaler work, affects depth; tuning Mojo's noise shaper for minimal -301dB phase error led to Mojo 2's UHD DSP. Head-Fi, Mar 2023
• 2023-03-26Watts says he hears -350 dB errors found in digital simulation that analog test gear cannot measure, and claims no measurable noise floor modulation in any of his DACs. Eric's Hi-Fi 31:00
• 2023-03-28Watts says R2R distortion rises as signal level falls, the opposite of the ear, harming soundstage and detail and sounding harder and brighter; he is not a fan. The Headphone Show 12:57
• 2023-03-28Watts says faster noise shapers also improve small-signal accuracy: tenfold speed gives 140 dB, 3 MHz to 104 MHz up to 210 dB, until output switching distortion rises. The Headphone Show 17:34
• 2023-03-28Watts says reproduced depth falls far short of live, small-signal nonlinearity is crucial, and all his digital parts are tested in simulation with a -301 dB signal. The Headphone Show 42:34
• 2023-03-28Watts says errors of a thousandth of a dB in amplitude or a thousandth of a degree in phase are audible, and recalls DAVE's development starting from 200 dB noise shapers. The Headphone Show 43:19
• 2023-03-28Watts says at 104 MHz the noise shaper digitally reproduces -301 dB with perfect amplitude and phase, has no noise floor modulation, and shows no transient timing errors in simulation. The Headphone Show 47:23
• 2023-04-03Watts says DAVE's transparency and depth come from small-signal accuracy, and that before DAVE he assumed noise shapers needed only 200 dB (32-bit) performance. Amplify Audio 4:53
• 2023-04-03Watts says on DAVE he heard depth improve from 200 to 220 dB noise shapers and up to 350 dB, leading to his rule that modules reproduce -301 dB perfectly. Amplify Audio 5:34
• 2023-04-03Watts says every module must pass a -301 dB test within 0.001 dB amplitude accuracy, and every module that failed a listening test had failed the -301 dB test. Amplify Audio 6:28
• 2023-04-03Watts says before the M Scaler he thought depth depended only on small-signal amplitude; raising WTA tap length had never changed depth before, suggesting timing matters for depth. Amplify Audio 7:04
• 2023-04-03Watts says timing means phase, so he examined the phase shift of a small signal against a large signal. Amplify Audio 7:49
• 2023-04-03Watts says digital filters show a phase shift that changes for very small signals, because the DSP cannot resolve them and the filter stops working as a filter. Amplify Audio 7:59
• 2023-04-03Watts says in listening tests, removing a phase shift error from noise shapers improved depth, and notes EQ introduces a large phase shift. Amplify Audio 8:35
• 2023-04-03Watts says transparent EQ needs -301 dB performance in amplitude and phase; after a couple of years' work, the DSP core in this unit is 104 bits. Amplify Audio 8:57
• 2023-09-24Watts says output level changes are made digitally, not with analog resistors and switches, without changing amplitude or phase (0.001dB, 0.001 deg) for his -301dB test signal. Head-Fi, Sep 2023
• 2023-10-01On the EQ, Watts says he tests with a -301 dB signal, far below audibility, because the brain can perceive it if the quality of that signal is slightly wrong. The Source AV 8:39
• 2023-10-01Watts says that if amplitude and phase of tiny signals are slightly wrong the brain detects it, compressing soundstage depth and hiding detail. The Source AV 9:21
• 2023-10-01Watts says conventional IIR filters stop resolving at about -140 to -150 dB, so very small signals get wrong amplitude and phase shift. The Source AV 9:55
• 2023-10-01Watts says engineers would call designing to -301 dB idiotic; ten years ago he said 200 dB sufficed for a noise shaper, but you know nothing unless you listen. The Source AV 22:41
• 2024-03-20Watts says processor state changes create GHz noise bursts correlated with the signal and worst for small signals; the DAC's analog circuitry demodulates this into audio-band noise corrupting small signals. MFG Audio Reviews 20:22
• 2024-03-20Watts says correlated noise makes small signals slightly bigger or smaller than they should be, which degrades the perception of depth. MFG Audio Reviews 21:06
• 2024-03-20Watts says reproduced audio lacks depth (a cathedral organ 200 feet away does not sound so on headphones), calls depth his biggest challenge, and says tiny small-signal errors degrade it. MFG Audio Reviews 21:17
• 2024-03-20Watts explains small-signal amplitude and phase nonlinearity: a signal reduced from -60 dB to -120 dB may measure -121 or -119 dB and show a different phase shift. MFG Audio Reviews 42:00
• 2024-03-20Watts says amplitude errors and phase shift varying with amplitude strongly affect depth perception, and asks how he knows this. MFG Audio Reviews 42:51
• 2024-03-20Watts says a 200 dB noise shaper loses signals below -200 dB; he thought that ample, a thousand times better than typical 140 dB shapers, but assumptions mislead. MFG Audio Reviews 44:05
• 2024-03-20Watts says even 330 to 350 dB was audible in blind tests, so tiny signals' amplitude and phase must be perfect or depth changes; analog components show similar errors. MFG Audio Reviews 45:45
• 2024-03-20Watts says contacts, solder joints and copper oxide (a diode) make small-signal impedance differ from large-signal impedance, so metal interfaces, crystal boundaries, purity and surface oxides matter. MFG Audio Reviews 46:36
• 2024-07-12Watts says simulation lets him measure digital circuits at minus 350 dB distortion and below, and his DACs' digital circuits must reproduce minus 301 dB perfectly. HIFICLUB 18:45
• 2024-07-12Watts says a slight amplitude or phase error at minus 301 dB is perceived as truncated soundstage depth, and normal engineers call this mad. HIFICLUB 19:36
• 2024-07-12Watts says Quartet taught him that the Hugo M Scaler's better-than-16-bit reconstruction is not enough; much better is needed, with effects too small for measurement equipment. HIFICLUB 20:23
• 2024-07-12Watts says such cables sounded massively different; silver-plated vs standard copper, high-purity solder and gold vs tin phonos are audible because of small-signal errors. HIFICLUB 26:39
• 2024-07-12Watts says cables measure the same but sound different because the brain perceives tiny errors, which is why minus 301 dB accuracy is needed and analog must stay simple. HIFICLUB 27:26
• 2024-07-12Watts names three main issues for ideal conversion: transients (interpolation filters, running at very high rates), small-signal accuracy (minus 301 dB), and a third. HIFICLUB 31:17
• 2024-07-12Watts says all DACs create noise floor modulation; the pulse array was invented to improve small-signal resolution and eliminate measurable noise floor modulation, though some unmeasurable remains. HIFICLUB 34:29
• 2024-07-12Watts says R2R resistors can never be matched, giving large small-signal errors that hurt depth and detail, and switching limits R2R to 768 kHz and poor timing. HIFICLUB 35:53
• 2024-07-12Watts says DSD's distortion falls as signal falls, matching how the ear works, whereas R2R distortion stays fixed and can exceed very small signals. HIFICLUB 37:45
• 2024-07-12Watts says DSD's switching activity varies with signal, causing noise floor modulation, and its 64 times noise shapers reach only 130 dB, so minus 301 dB is impossible. HIFICLUB 39:59
• 2024-07-12Watts says the pulse array avoids noise floor modulation and element distortion because all elements carry the signal with constant switching; its 104 MHz noise shaper reproduces minus 301 dB. HIFICLUB 44:15
• 2025-02-17Watts says 64-bit float on a PC is not accurate enough for IIR work; his -301 dB test needs amplitude within a thousandth of a dB and phase within a thousandth of a degree. audio-2G 17:33
• 2025-02-17Watts says modern DSPs miss that accuracy but his Mojo 2 cores and a similar Quartet core do, so EQ keeps depth intact; he tests with alternating half-dB bands. audio-2G 18:39
• 2026-03-17Watts says DSD sounds artificially soft and loses depth through poor small-signal accuracy, then begins explaining how finely the brain perceives depth, as with a phone moved half an inch. ecoustics 29:55
• 2026-03-17Watts says the biggest depth cue is reverberant-to-direct energy from myriad ever-smaller reflections, so a DAC must reproduce very small signals from many sources very accurately. ecoustics 32:34
• 2026-03-17Watts says reflections' amplitude and timing must be perfect, with no lower limit to errors that damage depth, which he learned developing DAVE in 2014. ecoustics 33:25
• 2026-03-17Watts says the errors cannot be measured; every digital module he develops must reproduce a -301 dB test signal within one thousandth of a dB. ecoustics 41:24
• 2026-03-17Watts agrees it is inaudible and unmeasurable, and says three or four years ago he found the phase of small signals relative to 0 dB also affects depth. ecoustics 41:49
• 2026-03-17Watts says small-signal phase must be within one thousandth of a degree of the 0 dB phase, harder than the amplitude test, and failing it audibly loses depth. ecoustics 42:36
• 2026-03-17Watts says skin effect then changes the impedance, so the issue is small-signal accuracy and timing, the same issue as with noise shapers. ecoustics 53:05
• 2026-10-02Watts says this is a very non-linear distortion, and the principal problem of R2R DACs is that distortion grows relative to the signal as the signal gets smaller. HiFi Buys 38:40
• 2026-10-02Watts says R2R distortion is fixed, reaching thousands of percent at low levels, while delta-sigma distortion vanishes as signals shrink, as the ear's does. HiFi Buys 38:50
• 2026-10-02Watts says the second aspect is small-signal accuracy: the faster a noise shaper runs, the more accurate the amplitude reconstruction. HiFi Buys 1:16:10
• 2026-10-02Watts says doubling the rate of a seventh-order noise shaper gives a 42 dB improvement each time, so 10 times faster gives well over 100 dB, improving small-signal accuracy. HiFi Buys 1:16:24
• 2026-10-02Watts says even the step to 350 dB was perceivable, and at -100 dB the numbers amount to a 0.1001 dB change in amplitude level. HiFi Buys 1:22:14
• 2026-10-02Watts says every module must reproduce a -301 dB signal within a thousandth of a dB or depth suffers; in 2017 he took Blu 2 from 0.5M to 1M taps. HiFi Buys 1:24:04
• 2026-10-02Watts says the brain computes depth from timing and reverberant ratio, suggesting small-signal timing matters for depth, which the WTA filter improves. HiFi Buys 1:27:36
• 2026-10-02Watts says better timing means better phase accuracy, so he quickly added an adjustable small-signal delay with a toggle switch, without simulating first. HiFi Buys 1:28:26
• 2026-10-02Watts says he picked the best-sounding setting, then simulations showed it had much better phase timing accuracy at -301 dB. HiFi Buys 1:29:18
• 2026-10-02Watts says the best setting was accurate within a couple of nanoseconds versus 10 to 30 for others, so nanosecond timing at -301 dB is perceivable as depth. HiFi Buys 1:29:40
• 2026-10-02Watts concludes small-signal accuracy must be perfect, NFM at -350 dB matters, and nanosecond accuracy at -301 dB matters, so transient timing accuracy has no limit. HiFi Buys 1:30:14
• 2026-10-02Watts explains reverberant sound reaches the ears via chaotic, random reflections off walls, ceiling and floor, getting smaller with each reflection. HiFi Buys 1:37:12
• 2026-10-02Watts says a hall's RT60 decay to -60 dB takes a couple of seconds, so small, chaotic reverberant tails must be reproduced perfectly for the brain. HiFi Buys 1:38:00
• 2026-10-02Watts says his early DACs were within a couple of dB at -90 dB, when others fell off a cliff, and better small-signal accuracy gave better depth and detail. HiFi Buys 1:38:42
• 2026-10-02Watts says modern pulse array DACs measure perfectly, a -120 dB signal within a thousandth of a dB, yet ultra-small errors still matter profoundly for depth. HiFi Buys 1:39:33
• 2026-10-14Watts says a delta-sigma ADC is mathematically a DAC with analog integrators, so pulse array benefits apply: lower noise floor modulation, better separation, accuracy to a -301 dB signal. Part-Time Audiophile 54:50
• 2026-10-14Watts says that accuracy gives better detail and depth, the pulse array ADC shows the same benefits as the DACs, but differs because a DAC oversamples a low-rate input. Part-Time Audiophile 55:39
• 2026-10-17Watts says the EQ at extreme settings passes a minus 301 dB test, phase within a thousandth of a degree and level within a thousandth of a dB, so it is transparent. article, Oct 2026