Noise shaper design 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?

Everything he said on this topic (176)

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

• 2014-04-16Watts says calling something delta sigma hides a lot, since performance depends on factors such as oversampling rate, with 64FS to 2048FS a huge change. needs context Head-Fi, Apr 2014
• 2014-04-27Watts explains why native DSD inside a DAC is a bad idea, recounting PDM1024 and pulse array history, and details Qute's DSD filter and Hugo's 140 dB decimation filter. Head-Fi, Apr 2014
• 2014-07-26Watts says live acoustic music, not analog tape, is the reference, and that DSD is limited: his noise shaper tests improved up to ten trillion times DSD's resolution. Head-Fi, Jul 2014
• 2014-08-03Watts recounts moving from disliking digital in 1989 to the PDM1 and PDM 1024, then creating the pulse array DAC in 1995 to fix noise shaper resolution and jitter. article, Aug 2014
• 2015-03-11Watts details Hugo's stages: 26,368-tap WTA from 1FS to 8FS, WTA stage two to 16FS with volume, interpolation to 2048FS, and noise shapers at 104.25 MHz tied to the DPLL. Head-Fi, Mar 2015
• 2015-05-20Watts says the noise shaper converts the 24-bit 104 MHz filtered signal to 5 bits feeding the discrete pulse array, so its performance matters greatly. HIFICLUBE.NET JVH 2:41
• 2015-05-20Watts says that tuning Hugo, better noise shaper performance improved perceived depth, limited by Hugo's gates; for DAVE he began listening tests from Hugo's roughly 200 dB. HIFICLUBE.NET JVH 5:32
• 2015-05-20Watts says raising noise shaper performance to 220, 240 and 260 dB each improved depth with no apparent limit, so he redesigned the noise shapers, reaching 350 dB. HIFICLUBE.NET JVH 6:30
• 2015-05-20Watts says the 350 dB is actual digital-domain performance: a 48-bit perfect sine feeds the noise shaper, and an FFT of the summed pulse array elements shows 350 dB in-band. HIFICLUBE.NET JVH 7:13
• 2015-05-20Watts says he finds it very bizarre and cannot accept that the brain requires a 350 dB performance level. HIFICLUBE.NET JVH 8:35
• 2015-05-20Watts says the depth is accurate, not added reverb: dry recordings stay at the speakers. He is unsure whether 350 dB is truly needed or an analog mechanism explains it. HIFICLUBE.NET JVH 9:00
• 2015-07-31Watts says the noise shaper is 5 bits at 104 MHz, 17th order, gives 350dB THD and noise in the digital domain, and resolves audio to 48-bit accuracy. Head-Fi, Jul 2015
• 2015-09-25Watts argues DSD is flawed by its format: limited noise-shaper resolution loses small signals and depth, and level-dependent timing non-linearity softens transients and compresses timbre. Head-Fi, Sep 2015
• 2015-10-22Watts says the update gives more depth and detail from improved internal noise shapers, but most work was non-audio: displays, control, dual data mode and dual programs. needs context 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
• 2015-11-22Watts recounts developing Dave: smoothness from reduced noise floor modulation, Hugo-derived timing gains from 256FS WTA (88nS), and noise shapers raised from 200 to 350 dB for depth. Head-Fi, Nov 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
• 2015-12-01Watts says depth is now about a third deeper and slightly smoother after upgrading internal noise shapers, the only audio change; the rest was control work. needs context 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 says his noise shapers run and filter at 2048 times the sample rate (104 MHz) to keep the digital signal clean, which makes the sound smoother and darker. article, Jan 2016
• 2016-01-29Watts says he had a non-audiophile engineer compare 190 dB and 200 dB noise shapers to convince a company he worked with; the engineer heard the difference easily. 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
• 2016-03-02Watts says 44.1/16 could in principle be near perfect, going from -330 to -350 dB noise shaping changed little, and 1M taps gives 16-bit sinc accuracy but needs costly FPGAs. Head-Fi, Mar 2016
• 2016-03-04Watts explains the pulse array modulator and seven benefits (constant switching, jitter immunity, signal-unrelated currents, 104 MHz noise shaping), why Dave has 20 elements, and Mojo versus Dave THD. 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
• 2016-03-07Watts once thought a 200dB noise shaper, 1,000 times better than high-end DACs, sufficient; developing DAVE he spent 90 days reaching 350dB and found depth improved markedly. article, Mar 2016
• 2016-03-29Watts says AB tests struggle to tell transparency from noise floor modulation, that better noise shapers in DAVE improved depth, and that Verilog simulation can quantify very small errors. Head-Fi, 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
• 2016-05-17Watts explains DSD's and PWM's switching, jitter and amplitude-timing errors, how pulse array balances switching to avoid them, and why DAVE needs 350 dB noise shapers for depth. Head-Fi, May 2016
• 2016-07-24Watts says changing the noise shaper while optimizing Hugo made a large, easily heard difference to depth perception, which audio reproduces badly, citing a cathedral organ 100 meters away. Hifistatement 0
• 2016-07-24Watts says Hugo's noise shaper reached around 200 dB, about a thousand times more resolving power than normal high-end noise shapers, and describes his silicon IP business, stopped weeks earlier. Hifistatement 58
• 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 for DAVE he raised noise shaper performance from Hugo's 200 dB through 220, 240 and 260 dB, depth improving each time, reaching -350 dB over 90 days. Hifistatement 3:05
• 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 the highest-order noise shaper he had seen was 9th order or DSD, and he worried that the 350 dB gains might be a proxy for some analog-domain effect. Hifistatement 4:40
• 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 noise shapers run at 2048 times (104 MHz), digitally filtered to that rate for RF noise and noise floor modulation reasons, making the sound smoother and darker. Hifistatement 6:13
• 2016-07-24Watts says nobody listens to noise shapers but he always has; FPGA size limited him, and to settle a client company's arguments he built 180 dB and 200 dB versions. Hifistatement 9:05
• 2016-07-24Watts says a non-audiophile engineer found the 200 dB noise shaper easily beat the 180 dB one considered perfect, reported this to his company, and the arguments stopped. Hifistatement 9:49
• 2016-07-24Watts says noise shaper design makes a big difference to sound and especially depth, and that WTA and noise-shaping work taught him more in two years than the previous ten. Hifistatement 10:29
• 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
• 2017-06-16Watts admits -350 dB depth sensitivity seems irrational but says repeated noise-shaper tests, including digital-only truncators, confirm it, and plans a blind Davina test with different noise-shaper settings. Head-Fi, Jun 2017
• 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 a non-audiophile engineer compared 180 dB and 200 dB noise shapers: the 180 dB sounded harder and brighter from noise floor modulation; the 200 dB had better depth. miceblue425 55:42
• 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
• 2017-12-05Watts recounts having a chip manufacturer's engineer compare two noise shapers at his house, the first with 180 dB distortion and noise, a hundred times better than standard ASIC chips. RMAF 3:57
• 2017-12-05Watts says the second noise shaper was 200 dB, and the engineer was surprised how easy the difference was to hear; the first had some noise floor modulation. RMAF 4:45
• 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 Hugo's slimmer noise shaper improved only depth, and with DAVE's ten-times-larger FPGA he raised the noise shaper from 200 to 220 dB and depth deepened. RMAF 21:37
• 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 repeated tests confirm it, and putting a 350 dB noise shaper in a purely digital truncator, 56 bits in and 24 out, gave the same deeper depth. RMAF 23:07
• 2017-12-05Watts says the explanation of noise shaping pushing noise out of band made no sense to him and is wrong, so he spent a lot of time understanding noise shapers. RMAF 35:33
• 2017-12-05Watts says a DSD noise shaper is fundamentally unstable away from zero because it would need to output plus two at times, which 1-bit DSD does not allow. RMAF 43:47
• 2017-12-05Watts says clamping makes DSD's noise shaper unstable unless first order, whereas pulse array allows overload so its noise shaper works; the coefficients strongly affect measurements and sound. RMAF 44:33
• 2017-12-05Watts says the pulse array noise shaper is always stable, irrespective of signal conditions. RMAF 45:21
• 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
• 2017-12-25Watts 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
• 2018-01-19Watts says he uses 10 or 20 pulse array elements rather than 8 or 16 for headroom, since a noise shaper must exceed full scale to stay stable. Head-Fi, Jan 2018
• 2018-02-26Watts points to Chord's simplified 10-element pulse array video and says the noise shaper truncator outputs 7 bits, with a 4-bit feedback path at 104MHz. Head-Fi, Feb 2018
• 2018-05-05Watts explains 1-bit DSD noise shapers are signal-dependent and unstable, unlike N-bit designs; Davina's N-bit pulse array ADC has 400 dB noise shaper performance and signal-independent activity. Head-Fi, May 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
• 2018-12-12Watts explains shrinking a design by rewriting code or simplifying it, and says a simpler, smaller noise shaper he tried unexpectedly sounded better in a listening test. Pursuit Perfect System 21:26
• 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 both noise shapers were 200 dB yet differed; he finished Hugo with crossfeed at 98% capacity, then on DAVE's ten times larger FPGA investigated why depth differed. Pursuit Perfect System 22:58
• 2018-12-12Watts says he built a 220 dB noise shaper, verified it in simulation, heard deeper depth on switching against the 200 dB one, then spent three months improving it. Pursuit Perfect System 23:38
• 2018-12-12Watts says 240 dB sounded better than 220, he pushed on through 260 to 300, a new design reached 330 and 350 dB, and depth deepened at each of those. Pursuit Perfect System 24:32
• 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 the pulse array's 350 dB noise shapers are a billion times more accurate for small signals, and keep the analog simple, since each metal-to-metal contact degrades signal amplitude. Pursuit Perfect System 30:12
• 2018-12-12Watts says simpler analog improves depth and detail; the pulse array's 104 MHz rate gives noise shaper resolution and allows an output of one amplifier, two resistors and two capacitors. Pursuit Perfect System 30:58
• 2018-12-12Watts says TT2 has 10 elements and a 12th-order noise shaper beyond 300 dB, better than Hugo 2 but short of DAVE, with one 7 watt amplifier, giving better depth. Pursuit Perfect System 35:36
• 2019-06-21Watts explains how delta-sigma ADC modulators work, why 1-bit DSD modulators lack headroom, cannot be dithered and delay small signals more, and says pulse array and Davina avoid this. Head-Fi, Jun 2019
• 2019-10-06Watts explains 16 pulse array elements encode 5 bits, that 64-clock PWM switching raises truncator resolution to 7 bits as on Mojo, and that raw resolution is no performance indicator. Head-Fi, Oct 2019
• 2019-10-07Watts says noise shaper activity must be signal independent so pulse array jitter noise stays fixed, and that his 2nd-order analog noise shaper amplifier eliminates crossover distortion in Class B. Head-Fi, Oct 2019
• 2019-12-10Watts says the second delta-sigma type is n-bit, typically four or 5 bits, and that 1-bit modulators have huge problems because they very easily go unstable. Passion for Sound 3:35
• 2019-12-10Watts says delta sigma is harder because you must design noise shapers, for example with MATLAB generating coefficients, then implement them in code on an FPGA or DSP. Passion for Sound 9:43
• 2019-12-10Watts says a delta-sigma designer needs DSP or FPGA skills and MATLAB skills, plus an understanding of how to create a noise shaper. Passion for Sound 12:04
• 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 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 eight or ten elements (ten on Qutest) give a 4-bit signal and better small signals, then starts explaining how a noise shaper maps 32 bits to 4. Passion for Sound 6:09
• 2019-12-16Watts explains that truncating 32 bits to 4 leaves a 28-bit error that is fed back, subtracted and integrated through many integrators until it triggers an output switch. Passion for Sound 7:10
• 2019-12-16Watts says each switch change creates a new error fed back, so the noise shaper is a feedback loop whose resolution depends on how fast it runs. Passion for Sound 7:53
• 2019-12-16Watts says merchant noise shapers run at only 3 MHz, giving high-frequency noise and poor in-band performance; his run at 2048 times 44.1 kHz for much better distortion and noise. Passion for Sound 8:48
• 2019-12-16Watts describes Verilog simulation of his noise shaper as exact hardware behavior analyzed by FFT; 1 ms of output once took all day, now 50 ms takes half an hour. Passion for Sound 9:37
• 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 recounts that adding crossfeed to the Hugo One prototype, at 95 percent FPGA use, forced a simpler 200 dB noise shaper, which he expected to sound worse. Passion for Sound 12:06
• 2019-12-16Watts says the simpler Hugo noise shaper sounded better in depth and detail; DAVE's ten-times-larger FPGA let him test this, and a 220 dB noise shaper improved depth. Passion for Sound 12:52
• 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
• 2019-12-16Watts says 200 to 350 dB differences are so tiny he risks being called a lunatic for calling them audible, and does not understand why the brain is so sensitive. Passion for Sound 14:20
• 2019-12-16Watts says he feared objectivists would call him a lunatic for needing better than 200 dB when 140 dB is held sufficient, but consistent listening tests convinced him to publish. Passion for Sound 15:34
• 2020-01-02Watts says this is another reason for a noise shaper running at 9.6 nanoseconds; his outputs can reproduce a 50 MHz sine wave, improving transient reconstruction. Passion for Sound 5:50
• 2020-01-02Watts says resolving 88 nanoseconds requires a noise shaper running at 104 MHz, which only he does; the highest he has seen elsewhere is 12 MHz. Passion for Sound 6:17
• 2020-06-25Watts says distortion interferes with the brain's separation of sounds, sine-wave psychoacoustic tests give crude numbers, and describes an FPGA noise shaper producing distortion at 200 to 400 kHz. Part-Time Audiophile 36:29
• 2020-06-25Watts says fixing the 200 to 400 kHz noise shaper distortion was immediately audible, because very high order harmonics modulate transient timing, which can be perceived. Part-Time Audiophile 37:19
• 2020-11-22Watts says the residual noise is random from the 10e noise shaper, not signal dependent, and describes designing coefficients for uncorrelated noise with maximum resolution. Head-Fi, Nov 2020
• 2020-11-23Watts compares Hugo 2's out-of-band noise with the APx555's 192kHz DAC, explains the 104MHz noise shaper hump, and why gentle analog filtering needs only 4 passive components. Head-Fi, Nov 2020
• 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
• 2021-06-22Replying 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
• 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 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 improved noise shaper gave better soundstage and detail, and bass is tighter; Mojo's power limit forced him to throttle the FPGA. Darko.Audio 37:17
• 2022-01-31Watts says the extra 200 milliwatts funded the digital DC servo, a better WTA filter and noise shaper, and the EQ DSP core; the noise shaper improves depth and detail. Darko.Audio 38:46
• 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
• 2022-03-19Watts says discrete conversion allows single-ended operation, his noise shapers resolve small signals a billion times better than chips, and running at 104 MHz permits minimal analog filtering. MFG Audio Reviews 14:03
• 2022-03-19Watts describes quickly listening to four settings of a detuned noise shaper without simulation: setting three sounded best, two and four degraded depth, and one was flat. MFG Audio Reviews 31:36
• 2022-03-19Watts explains that a noise shaper feeds each error back to correct the next sample rather than discarding it, which requires oversampling, so the DSP runs at 705 kHz. MFG Audio Reviews 36:44
• 2022-03-19Watts says noise shaping cannot work at 44.1 kHz, bass coefficients are tiny, and noise shaping each node separately fixed the 104-bit design's phase failure so it passed. MFG Audio Reviews 37:33
• 2022-04-14Watts explains Verilog module simulation, says improving Dave's noise shapers from 200dB to 350 dB improved depth each step, and treats the -301 dB test as his transparency metric. Head-Fi, Apr 2022
• 2022-06-27Watts says pure DSD and R2R DACs are fundamentally limited, DAVE's noise shaper is not capped at 17th order, the HF filter sits after WTA2, and car batteries are ideal. Head-Fi, Jun 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 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 noise shaper performance is measured by digital simulation; for Hugo he worked to 200 dB (32-bit accuracy), while chip makers generally work to 140 dB. Dusty Audio 21:41
• 2023-02-04Watts says he thought 200 dB good enough in 2015, but Dave allowed better noise shapers with 20 elements, which he tested by listening. Dusty Audio 22:26
• 2023-02-04Watts says a 220 dB noise shaper audibly improved depth over 200 dB, so over three months of Dave development he kept improving it until the sound stopped improving. Dusty Audio 23:10
• 2023-02-04Watts describes raising Dave's noise shaper through 240, 260, 280, 300 and 330 dB with daily coding, simulation and listening tests, eventually reaching 350 dB. Dusty Audio 23:57
• 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
• 2023-02-04Watts says the chip company's engineers disputed his 200 dB noise shaper requirement, costly in gates, for two or three years, until he invited one to his house to listen. Dusty Audio 26:56
• 2023-02-04Watts says he set noise shapers to 180 dB and 200 dB; the engineer was surprised that the 190 to 200 dB difference was so big and easy to hear. Dusty Audio 27:40
• 2023-02-05Watts explains anti-fuse FPGAs needed a new chip for every change; from 1992 he used them for multiple dithered noise shapers summed in the analog domain. Soundnews 17:11
• 2023-02-05Watts says Bitstream's 256 one-bit pulses seemed too few for a 20 kHz waveform, so he modeled noise shapers and paralleled dithered noise shapers in early FPGAs. Soundnews 21:31
• 2023-02-20Watts says Mojo 2's 4-element pulse array runs its noise shaper slower for low distortion, so noise rises around 100k and falls at 400k from analog filtering. Head-Fi, Feb 2023
• 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
• 2023-03-28Watts explains a delta-sigma DAC as a noise shaper plus an analog output stage, reducing 32-bit data to 1 bit for DSD or about 5 bits for multi-bit. The Headphone Show 13:44
• 2023-03-28Watts says plain truncation would give about 40 dB of distortion and noise; a noise shaper feeds back the amplified error at a faster rate, its subtractor being the delta. The Headphone Show 14:35
• 2023-03-28Watts says integrators (the sigma) amplify the error before a quantizer, dither is needed for distortion-free results, and performance depends partly on output bit depth. The Headphone Show 15:23
• 2023-03-28Watts says noise shaper performance depends on order, integrator coefficients and above all speed, and that noise shaper design is complex rather than just maths. The Headphone Show 16:07
• 2023-03-28Watts says noise shapers are nonlinear and need tweaking beyond MATLAB design, and doubling a seventh-order noise shaper's speed gives up to 42 dB less in-band distortion and noise. The Headphone Show 16:49
• 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 each design has an optimum noise shaper speed against analog switching speed, and Head-Fi commenters often miss such conflicting design factors. The Headphone Show 18:23
• 2023-03-28Watts says adding integrators (order) forces each to run slower, so there is an optimum number beyond which extra integrators contribute nothing in the audio band. The Headphone Show 19:09
• 2023-03-28Watts says DSD's 1-bit limit denies the noise shaper the overload it needs, causing internal overloads or instability and hence noise floor modulation. The Headphone Show 20:39
• 2023-03-28Watts says multi-bit delta-sigma DACs let the noise shaper go beyond plus or minus one, keeping it stable and consistent, which eliminates DSD's noise shaper noise floor modulation. The Headphone Show 24:08
• 2023-03-28Watts recounts a company that bought his IP: an engineer in a listening test heard a 180 dB versus 200 dB noise shaper difference he had predicted. The Headphone Show 39:27
• 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 DAVE's noise shapers going from 200 to 220 dB, and later 330 to 350 dB, improved depth; fixed noise is fine but signal-dependent noise creates noise floor modulation. The Headphone Show 44:02
• 2023-03-28Watts says noise changes only half a dB when pulse array elements are fed DC, and pulse array lets the noise shaper run at 104 MHz, reproducing 52 MHz. The Headphone Show 46:38
• 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
• 2023-10-01Watts says Mojo 2 has his own custom 104-bit noise-shaped DSP core running at 705/768 kHz, whose noise shaper keeps impulse-response tails that fall below the noise floor. The Source AV 11:22
• 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 he measures designs digitally down to -400 dB by FFT and listens as errors are removed; while developing DAVE his noise shapers performed at 200 dB. MFG Audio Reviews 43:16
• 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 moving to a 220 dB noise shaper changed only depth, with distant instruments sounding more distant on his depth test tracks, and he kept improving until 350 dB. MFG Audio Reviews 45:02
• 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
• 2024-07-12Watts says the brain perceives errors below audibility thresholds; he had an engineer compare noise shapers at 180 dB and 200 dB distortion and noise at his home. HIFICLUB 23:24
• 2024-08-01Watts says his analog section is one single-ended amplifier doing I to V and output, and his 104 MHz noise shaper, versus 3 MHz delta-sigma, eases filtering. Audiophilesdoteu 3:07
• 2026-03-17Watts explains that a 32-bit signal cannot drive millions of switches, so a noise shaper reduces it to about 4.5 or 5 bits for, in DAVE's case, twenty switches. ecoustics 34:09
• 2026-03-17Watts says noise shaper performance depends on its running rate and number of integrators, and since the 1990s he designed noise shapers to 200 dB performance. ecoustics 34:57
• 2026-03-17Watts says he thought 200 dB, versus 140 dB in chip DACs, was over-specified, but DAVE's larger FPGA finally gave him capacity to try better. ecoustics 35:41
• 2026-03-17Watts says his first improved noise shaper simulated at 220 dB; switching against 200 dB, separation, focus and timbre sounded identical. ecoustics 36:23
• 2026-03-17Watts says bass pitch was also identical but depth was obviously deeper with the 220 dB noise shaper on an organ recording, which made no sense to him. ecoustics 37:08
• 2026-03-17Watts says that for about three months in summer 2014 or 2015 he kept improving and listening, eventually reaching 330 dB to 350 dB. ecoustics 37:55
• 2026-03-17Watts says a subtle depth change was still audible between 330 dB and 350 dB, though the amplitude accuracy difference is minuscule. ecoustics 38:34
• 2026-03-17Watts says blind listeners pick the same depth result, and at the time he suspected an analog proxy effect rather than noise shaper accuracy itself. ecoustics 39:09
• 2026-03-17Watts says purely digital noise shapers, such as 192 bits down to 68 bits, show the same thing in listening tests: better than 350 dB is needed to reproduce depth. ecoustics 40:09
• 2026-03-17Watts says a cello recorded four meters away sounds two meters on DAVE and 2.5 to 3 with Quartet; commercial ADCs noise-shape to 140 dB, his ADC about 301 dB. ecoustics 45:04
• 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 designing DAVE in 2014 with a much bigger FPGA and spare capacity, he believed noise shapers needed 200 dB in-band performance, better than 32-bit accuracy. HiFi Buys 1:17:08
• 2026-10-02Watts says with 16-bit sources limited to 96 dB, needing 200 dB seemed pointless, but that was an assumption. HiFi Buys 1:17:52
• 2026-10-02Watts says he tests assumptions by listening; he added integrators for a 220 dB noise shaper and used a toggle switch because each Xilinx place and route then sounded different. HiFi Buys 1:18:06
• 2026-10-02Watts says moving from 200 to 220 dB left separation, detail and timbre identical but depth clearly better, which he tested with an organ recording heard in a cathedral. HiFi Buys 1:19:47
• 2026-10-02Watts says he would code, simulate, measure digitally and listen; each step from 220 to 240 to 260 dB gave better depth, ending at 330, then 350 dB. HiFi Buys 1:21:26
• 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 DAVE, 11 years old next May, is still the best depth-resolving DAC at any price because its noise shaper runs at 104 MHz. HiFi Buys 1:23:25
• 2026-10-02Watts says he developed the pulse array in 1994 to 1995, using PDM256 (DSD256) chips fed by several randomized noise shapers summed in the analog domain. HiFi Buys 1:41:42
• 2026-10-02Watts says low-distortion flip-flops have not improved in 30 years, so faster ones would add distortion and 104 MHz remains the sweet spot. HiFi Buys 1:44:04
• 2026-10-02Watts says with many elements one can change every 9.6 nanoseconds, and a band-limited system need not reproduce 52 MHz at 0 dBFS. HiFi Buys 1:46:24
• 2026-10-02Watts says he mentions -60 dB because the noise shaper pumping up and down creates noise, an artifact of its functioning. needs context HiFi Buys 1:47:07
• 2026-10-14Watts says delta-sigma noise shapers are enormous feedback loops, and that is how they work. Part-Time Audiophile 1:00:45