What do noise shaper order and speed buy, and why does DAVE's 350 dB noise shaper matter?

Short version

Watts's position is that a delta-sigma noise shaper's in-band performance depends on how many integrators it has and how fast it runs, and that this performance decides whether very small signals survive Head-Fi, Sep 2015The Headphone Show 16:07The Headphone Show 16:49. He built DAVE's noise shaper to about 350 dB in the digital domain and reports that improvements from 200 dB upward made recorded depth deeper; from 2016 on he has called the 330 to 350 dB step much smaller than the first one, though in September 2015 he had called a 330 versus 360 dB difference easy to hear Head-Fi, Dec 2015Head-Fi, Sep 2015Head-Fi, Mar 2016Passion for Sound 13:35. He presents this as a listening result he cannot explain, and said so in 2016, 2017, 2023 and 2024 Head-Fi, Sep 2016Head-Fi, Jun 2017Dusty Audio 24:38MFG Audio Reviews 45:45.

Figures from transcripts (the 42 dB, 140 dB, 210 dB, 3 MHz, 6 MHz, 50 MHz and 12th-order figures below, and the ADC figure) come, so check the recording before relying on a number The Headphone Show 17:34Pursuit Perfect System 35:36HiFi Buys 1:24:04.

What he says order and speed buy

In September 2015 he described a noise shaper as a feedback system with n integrators. The number of integrators and their time constants set how much error correction it has, and the time constants are set mainly by the oversampling rate. For a 5th-order ideal system, doubling the oversampling frequency, he said, "converges on a 30 dB improvement in distortion and noise" Head-Fi, Sep 2015. In April 2015 he put it as up to 100 dB lower distortion and noise in the digital domain for a 5th-order noise shaper run at ten times the speed Head-Fi, Apr 2015.

At CanJam NYC in late February 2023 (video published March 2023; show dates unverified) he said the number of integrators is called the order, and that how fast the noise shaper works matters most The Headphone Show 16:07. For a 7th-order design, doubling the speed gives up to a 42 dB improvement in in-band distortion and noise, and the small-signal accuracy improves as well; going from 3 MHz to 104 MHz is, he said, up to 210 dB of improvement The Headphone Show 16:49The Headphone Show 17:34. In the HiFi Buys interview (published October 2026; recording date not stated, and its transcript places it before May 2026) he repeated the 42 dB per doubling for a seventh-order shaper HiFi Buys 1:16:24.

He also named the limits on going faster or higher in order. Going too fast makes the output switches add distortion that damages measurements and sound The Headphone Show 17:34. Adding an integrator means reducing its speed, and past an optimum the extra integrator contributes nothing in the audio band The Headphone Show 19:09. For DAVE he said in 2015 that 350 dB was the best he could do with the available FPGA and flip-flop speed, in 2016 that the limit is "technology limited" given its 20 pulse-array elements, and in 2022 that it is the best he can do currently Head-Fi, Dec 2015Head-Fi, Mar 2016Head-Fi, Apr 2022. In 2016 he said that generally, all things being equal, doubling the element count gives about 3 dB lower noise and 6 dB better signal resolution if the time constants do not change Head-Fi, Apr 2016.

On speed in particular: in 2015 he said he had run his noise shapers at 2048 times the sample rate rather than 256 times since starting his own FPGA designs in 1994, because "Running at a faster rate means that you have more permutations of OP" Head-Fi, Apr 2015. In 2016 he said his noise shapers run at 2048 times, 104 MHz, and in the Passion for Sound interview (part 2 published December 2019; recording date not stated) that merchant noise shapers run at only 3 MHz Hifistatement 6:13Passion for Sound 8:48. In the same HiFi Buys interview he said DAVE's ability to resolve ultra-small levels depends on its noise shaper running at 104 MHz: at 50 MHz "you wouldn't get that number", and at 6 MHz 350 dB is impossible HiFi Buys 1:23:25HiFi Buys 1:24:04.

The figures he gave, by product and date

• Typical chip DACs: about 140 dB, stated in 2015, 2018, 2023 and, in a podcast recorded October 2025, again Head-Fi, Jul 2015Head-Fi, Apr 2018Dusty Audio 21:41ecoustics 35:41. DSD64: 120 dB at best, in 2015 and 2016 Head-Fi, Sep 2015Head-Fi, May 2016.
• Hugo and earlier designs: 200 dB. In the Passion for Sound interview (published December 2019, recording date not stated) he named DAC64 and QBD76 as 200 dB designs, and in a podcast recorded in October 2025 (published March 2026) he said he had used that figure since the 1990s and was stuck there because the FPGA was too small Head-Fi, Nov 2015Passion for Sound 11:25ecoustics 34:57ecoustics 35:41.
• DAVE: 17th order, 46 integrators, 104 MHz, 350 dB (one September 2015 post says 360 dB) Head-Fi, Jul 2015Head-Fi, Nov 2015Head-Fi, Sep 2015. In a February 2016 simulation a -301 dB, 6 kHz sine came out perfect, with a real noise floor at 15 kHz of -380 dB Head-Fi, Feb 2016.
• Mojo: 200 dB in October 2016 Head-Fi, Oct 2016. A February 2022 post gives 250 dB for "The 4e noise shaper" without naming the product; it was posted in the Watts Up thread the day after his Mojo 2 technical presentation there, which suggests Mojo 2, but the post does not say so Head-Fi, Feb 2022Head-Fi, Jan 2022.
• Hugo 2: 260 dB in August 2017 Head-Fi, Aug 2017.
• Hugo TT 2: "300 dB noise shapers running at 104MHz" in October 2018; at a Nintronics open day in November 2018 (talk published December 2018) he described a 12th-order shaper "better than 300 dB" but "not quite as good as Dave" Head-Fi, Oct 2018Pursuit Perfect System 35:36. In May 2018 he said TT 2's improved shaper was about 100 times more effective than Hugo 2's and approaching DAVE's Head-Fi, May 2018.
• Digital-only truncation noise shapers: tested to above 350 dB in Hugo 2 and Qutest (February 2018), and 11th order at 768 kHz, better than 350 dB, in the M Scaler (December 2019) Head-Fi, Feb 2018Head-Fi, Dec 2019.
• Davina, his ADC project: 11th order at 104 MHz, better than 350 dB in 2017, and 400 dB in 2018 Head-Fi, Jun 2017Head-Fi, May 2018. In a podcast recorded in October 2025 (published March 2026) he said "My noise shapers for the ADC just about manages to do 301 dB"; the items do not reconcile this with the earlier figures ecoustics 45:04.

Why he says DAVE's 350 dB matters

The mechanism he gives

Anything below a noise shaper's noise floor is lost, and signals near the floor are attenuated Head-Fi, Dec 2015Hifistatement 2:23. His September 2016 clarification said the 350 dB figure "is only in the digital domain", and that it is not about the noise level (a 24-bit source is a trillion times noisier) but about whether tiny signals keep their amplitude, because small echo cues tell the brain a sound is further away Head-Fi, Sep 2016. He gave numbers for a -120 dB signal the next day: a shaper with a 160 dB limit shifts it by 0.087 dB, a 200 dB shaper by 0.0008 dB, a 300 dB shaper by 0.00000008 dB, and a 340 dB shaper by 0.0000000008 dB Head-Fi, Sep 2016.

The listening tests

His account, repeated from 2015 through interviews published in 2026, is that before DAVE he considered 200 dB sufficient, that Hugo's FPGA was too small to go further, and that DAVE's had about ten times the gate capacity Head-Fi, Nov 2015Head-Fi, Dec 2015Pursuit Perfect System 22:12ecoustics 35:41HiFi Buys 1:17:08. He then raised the performance in steps, 220, 240, 260, onward, and heard deeper depth, over about 90 days, ending at 350 dB HIFICLUBE.NET JVH 6:30Head-Fi, Dec 2015Pursuit Perfect System 24:32Dusty Audio 24:38HiFi Buys 1:22:14. How audible that last step was changed in his telling. In September 2015 he wrote of "how easy it was to hear a 330 dB noise shaper against a 360 dB one - but only in terms of depth perception" Head-Fi, Sep 2015. From March 2016 he called the 330 to 350 dB step small ("I could detect a change going from -330 to -350, but frankly it was small") Head-Fi, Mar 2016, and in the Passion for Sound interview (published December 2019) "very small by comparison to the two hundred to 220 dB, but you could still hear a change" Passion for Sound 13:35. In March 2016 he hedged the step-by-step result: at each improvement it "largely (sometimes it didn't but that's way too complex to talk about) had deeper depth" Head-Fi, Mar 2016. In a podcast recorded in October 2025 he dated the work to summer 2014 or maybe 2015, and in the HiFi Buys interview (published October 2026, recording date not stated) to 2014 ecoustics 37:55HiFi Buys 1:17:08. Compared with Hugo, he said in 2015 that DAVE's depth was around four times deeper on recordings that contain depth, and that this was mostly down to noise shaper performance; close-miked recordings with no reverb still sound flat Head-Fi, Nov 2015. In May 2015 he said the noise shaper is not adding reverb to fake depth, and that it is reproducing the cues the brain uses HIFICLUBE.NET JVH 9:00.

Depth only, or other things too?

In September 2015 he said that while optimizing Hugo's noise shaper, once it reached 200 dB it "no longer got smoother" Head-Fi, Sep 2015. In December 2015 he said a better noise shaper improves both noise floor modulation and small-signal linearity, that his 220 dB design gave better depth "and maybe a bit smoother", and that "better than 200 dB is a good rule of thumb for noise floor modulation, but certainly not for depth" Head-Fi, Dec 2015. In March 2016 he wrote that improving the noise shaper "changed no other aspect of sound quality" Head-Fi, Mar 2016. His 2024 and October 2025 accounts of the 200 to 220 dB comparison say the same, with separation, focus, timbre and bass pitch identical MFG Audio Reviews 45:02ecoustics 36:23ecoustics 37:08. The December 2015 "maybe a bit smoother" is the one account of that step that names anything besides depth, and he did not comment on the difference.

Separately from those comparisons, he has tied small-signal accuracy to detail resolution as well as depth: in 2018 for TT 2, in the Passion for Sound interview (published December 2019), in January 2022 (a module failing the -301 dB test "would degrade depth and detail perception"), in 2023, and for DAVE in the HiFi Buys interview (published October 2026, recording date not stated) Pursuit Perfect System 35:36Passion for Sound 11:25Head-Fi, Jan 2022Dusty Audio 24:38HiFi Buys 1:23:25.

Is the number a proxy for something else?

He raised this himself in his first public accounts of the work. In May 2015 he said he could not tell whether a strange analog effect needed this level or whether it really required 350 dB HIFICLUBE.NET JVH 9:00. In September 2015 he wrote: "My intellectual puzzle is whether this level of small signal accuracy is really needed", or whether the numbers were a proxy for something in the analog parts Head-Fi, Sep 2015. His answer, given in 2015 and 2016, was that he heard the same depth improvement when he upgraded purely digital noise shapers inside DAVE, with no analog consequences; "It doesn't seem to be a proxy" Head-Fi, Dec 2015Hifistatement 5:24. By June 2017 he said he had repeated it about half a dozen times with different pulse-array and truncator noise shapers (56 bits at 768 kHz down to 24) and got the same result, and in an October 2025 podcast he said purely digital truncation noise shapers still show that better than 350 dB is needed for depth Head-Fi, Jun 2017ecoustics 40:09.

He did not claim to understand it. In September 2016 he wrote that "The honest answer is I don't know for sure" whether the brain needs -301 dB signals or whether a system that resolves them simply resolves -120 dB signals better, adding that he suspected the second Head-Fi, Sep 2016. In February 2023 (AV Store, Bucharest) he said "Don't ask me why we need 350 dB performance figures", and offered that it may be about accuracy at -100 dB rather than at -350 dB Dusty Audio 24:38. At that November 2018 open day (talk published December 2018) he put the same idea as a signal at -90 dB being reproduced more accurately, with a vanishingly small amplitude difference (the transcript's figure is garbled, so check the recording) Pursuit Perfect System 25:17. In September 2018 he argued that the brain is thought to use correlation, which can expose signals well below the noise, and that errors become perceptible because they interfere with that process Head-Fi, Sep 2018.

Blind or sighted

In 2014 he said his protocol for small changes such as noise-shaper internals was 30-second repeats, usually not blind, with single-blind tests when he heard something that made no sense Head-Fi, Oct 2014. In June 2017 he wrote that he could not rule out confirmation bias because the tests were not double blind Head-Fi, Jun 2017. In April 2022 he said his observations "should be treated as just my opinion" and that he treats his listening tests as tentative Head-Fi, Apr 2022. He also reports blind results: in a 2018 post he recalled an earlier single-blind test, from his years licensing IP to semiconductor companies, in which a non-audiophile engineer heard a 180 dB against a 200 dB noise shaper and found it easy Head-Fi, Sep 2018. At CanJam RMAF in October 2017 (video published December 2017), right after describing the 330 to 350 dB step, he said that if he does it "under blind conditions with other people, they can easily hear it"; in 2024 and in a podcast recorded in October 2025 (published March 2026) he again said blind listeners perceive the depth changes, without giving which steps were tested or any results data RMAF 22:21MFG Audio Reviews 45:45ecoustics 39:09. In 2016 and 2017 he said he planned a blind test with two Davina recordings at different noise shaper performance, and that he would "eat my proverbial hat" if nobody could hear it Head-Fi, Oct 2016Head-Fi, Jun 2017. No published result of that test appears.

Later developments and limits he put on the claim

• May 2018: for TT 2 he said DAVE remains considerably more transparent even though TT 2's shaper approaches it, because "there is more to depth and transparency than just the noise shapers" Head-Fi, May 2018.
• 2022 to 2023: he said that after the M Scaler work, about five years earlier, he found that timing (phase shift versus amplitude) of small signals also affects depth, tested by detuning Mojo's noise shapers. He said this helped Mojo 2's noise shapers but did not allow an improvement on the shapers from Hugo 2 to DAVE, which already show no phase error at -301 dB Head-Fi, Apr 2022Head-Fi, Mar 2023.
• For truncating to 24 bits he said noise shaping beat dither on depth (2018, for Blu 2's 768 kHz truncators), and in 2024 that the noise shaper built into the Hugo M Scaler gives distortion and noise below 350 dB Head-Fi, Feb 2018Head-Fi, Jun 2024.
• The -301 dB, 6 kHz test came out of this work and, he said in 2016 and 2022, is applied to every digital module Head-Fi, Mar 2016Head-Fi, Apr 2022.

What he has not said

He does not say a real DAVE output reaches 350 dB: he says the opposite, that analog noise (about -128 dB in 2018) swamps it Head-Fi, Sep 2016Head-Fi, Apr 2018. The items describe blind trials but report no data from them. They do not give the order of the original Hugo's, Mojo's or Hugo 2's noise shapers; a 2023 post says only that the Hugo 2 to DAVE shapers have "very high orders of noise shaping" Head-Fi, Mar 2023. A Japanese magazine summary (machine translation) attributes to him a typical noise shaper of about -80 dB, which differs from the 140 dB he gives in his own posts article, Mar 2016Head-Fi, Jul 2015.

Quotes

“its not about noise or noise floor modulation but about how accurate small signals are being preserved in terms of their amplitude.”2016-09-13 Head-Fi, Sep 2016

“increasing the performance of the noise shaper did improve depth. But it changed no other aspect of sound quality.”2016-03-29 Head-Fi, Mar 2016

“And if we went from 3 megahertz to 104 MHz, you're looking at 210 dB's worth of maximum improvement.”2023-02 The Headphone Show 17:34

“The honest answer is I don't know for sure, but it strikes me as being absurd that the brain could (through correlation) need -301 dB signals.”2016-09-14 Head-Fi, Sep 2016

Dated positions

Caveats and open points

• Watts calls 350 dB a digital-domain simulation figure only; he says real analog output is far worse.
• The DAVE figure is given as 350 dB in most items and 360 dB in one September 2015 post.
• In 2023 he defined order as the number of integrators, yet he describes DAVE as 17th order with 46 integrators; the items do not reconcile the two.
• In the 200 versus 220 dB comparisons he says only depth changed (one 2015 account adds 'maybe a bit smoother'), but elsewhere he links small-signal accuracy to detail resolution too.
• The Japanese Weekly ASCII article is a machine translation of a journalist's summary; its typical-shaper figure of -80 dB differs from the 140 dB in his own posts.
• No published result of the planned blind Davina noise-shaper test was found in the archive.
• A 2022 post gives 250 dB for a 4-element shaper without naming the product, and an earlier post gives Mojo as 200 dB; the post's date (1 February 2022) and its thread suggest Mojo 2, but it does not say so, and the items do not reconcile the two figures.
• Davina's ADC noise shaper is given as better than 350 dB (2017) and 400 dB (2018), but an ecoustics podcast transcript (recorded October 2025, published March 2026) says his ADC noise shapers 'just about' manage 301 dB; the items do not reconcile them.
• His account of the top step changed: in September 2015 he called a 330 dB versus 360 dB noise shaper easy to hear (depth only); from March 2016 he called the 330 to 350 dB step small Head-Fi, Sep 2015Head-Fi, Mar 2016.

Topics: Noise shaper design and resolution, Small-signal accuracy and resolution