Re-quantization, truncation, dither and word length

Noise shaping, accuracy and conversion hardware

Answers on this topic

• Is Chord's digital volume control transparent, and does it lose resolution at low volume?
• Should audio processing dither or noise-shape, and is 64-bit floating point transparent?

Everything he said on this topic (92)

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

• 2014-09-09Watts says if JRiver's volume control is properly dithered when truncating, there is no distortion or transparency loss to worry about. Head-Fi, Sep 2014
• 2015-01-23Watts says Hugo's 51-bit volume is truncated at 16FS by noise shaping and dither, adding only fixed -180dB noise, and notes its output relay, 75 milliohm impedance and anodizing. Head-Fi, Jan 2015
• 2015-10-03Watts rebuts a Nagra DAC's marketing claims point by point: quantization noise, brickwall filter phase, oversampling as cheating, clocking, and DSD out-of-band noise. Head-Fi, Oct 2015
• 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
• 2016-03-31Watts suggests the files are likely not bit perfect, since one gain-scaling stage loses depth and bad truncation hardens sound; a non-bit-perfect optical link would cause dropouts instead. needs context 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
• 2016-05-30Watts 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 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
• 2016-09-27Watts is unsure about the EQ asked about, explains IIR bi-quads repeatedly truncate tiny bass coefficients, risking low-level distortion, and advises trying it without assuming digital means transparent. Head-Fi, Sep 2016
• 2016-10-20Watts says 768/705.6 kHz 24-bit is best and 32 bits unnecessary, reports noise shaping beat Gaussian and triangular dither on the Blu Mk2 prototype, and Davina will study 44.1/16 losses. Head-Fi, Oct 2016
• 2017-04-07Watts says Hugo 2 truncates its 48-bit crossfeed to 24 bits with noise shaping at 705/768 kHz, which preserves depth better than PC dither, and EQ apps can compromise transparency. Head-Fi, Apr 2017
• 2017-04-08Watts says noise shaping at 44.1 kHz is ineffective above about 4 kHz, unlike at 705/768 kHz; truncating to 44.1 for Davina is unresolved, with Gaussian dither best so far. Head-Fi, Apr 2017
• 2017-07-24Watts says EQ should not affect timing reconstruction, but truncation after DSP matters: noise-shaped truncation at 16FS beats triangular dither, so he applies EQ and volume at 16FS or higher. Head-Fi, Jul 2017
• 2017-10-25Watts says DAVE's data path from input to pulse array is better than 350 dB, so no truncation occurs and large volume changes do not affect detail or depth. Head-Fi, Oct 2017
• 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
• 2017-12-16Watts says DAC64 split WTA and pulse array across FPGAs, and stresses the WTA algorithm, coefficient quantizing and internal truncation as more important than raw tap length. Head-Fi, Dec 2017
• 2018-01-13Watts says it is done digitally with Hugo 2's volume control, whose aggressively noise-shaped truncation gives -400 dB accuracy, and 0dBFS is below the noise shaper's maximum modulation. needs context Head-Fi, Jan 2018
• 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
• 2018-02-09Watts says in Blu 2 truncator tests TPDF dither sounded worst, losing depth, and Gaussian came halfway to noise shaping; he suspects software volume beats analog volume. Head-Fi, Feb 2018
• 2018-02-11Watts says Hugo 2's volume uses aggressive noise shaping at 705/768 kHz to stay below -350dB, preserving depth; software volume degrades depth less than an analog volume control. Head-Fi, Feb 2018
• 2018-02-24Watts says SRC and half-band decimation damage timing, triangular dither degrades depth, so he buys 96k originals; Davina's filters reach about -240 dB and will test bandlimiting and dither. Head-Fi, Feb 2018
• 2018-02-26Watts says he has eliminated decimation aliasing, interpolation needs a closer-to-sinc filter, bandlimiting is likely a red herring, and he worries most about 16-bit reduction harming depth. Head-Fi, Feb 2018
• 2018-06-27Watts says MQA's degradations become obvious with WTA and M scaler; converting the 56-bit WTA output to 24 bits, triangular dither sounded worse than his truncation noise shapers. Head-Fi, Jun 2018
• 2018-12-07Watts says the 4x (48 to 192 kHz) filter uses exactly a quarter of the 16x coefficients, not a decimation, and is volume adjusted with near-Gaussian 24-bit dither. Head-Fi, Dec 2018
• 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
• 2019-01-20Watts says Qutest's output levels are set digitally through one noise-shaped stage at -400 dB accuracy, so audible differences come from ancillary gear; if unsure, use 2 V. Head-Fi, Jan 2019
• 2019-03-03Watts says the Hugo M Scaler adds no dither at full 1M taps, treats 16-bit as 24-bit, and a PC set to 16-bit mode truncates and re-dithers 24-bit sources. Head-Fi, Mar 2019
• 2019-03-25Watts comments on upsampling experiments: stopband beyond -150 dB matters little, output rate should suit tap length, his Davina decimation reaches 250 dB, and truncation needs aggressive noise shaping. Head-Fi, Mar 2019
• 2019-04-22Watts says the filter uses direct, fixed-point convolution with noise-shaped coefficients, explains FFT convolution, and expects sound differences between them; output truncation also matters. needs context Head-Fi, Apr 2019
• 2019-04-25Watts says the M scaler's 56-bit output is reduced to 24 bits by -301 dB noise shapers; triangular dither sounds worse, and non-integer SRC degrades sound. Head-Fi, Apr 2019
• 2019-05-19Watts says DSD-to-PCM is not lossless; his Hugo 2, TT2 and M scaler filters exceed 200dB rejection with -301 dB truncation, against about 60 dB in chips. Head-Fi, May 2019
• 2019-11-25Watts says few DAC designers understand sampling theory or noise floor modulation, warns clip-on ferrites worsen the isolated M scaler, and says floating point creates noise floor modulation. Head-Fi, Nov 2019
• 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
• 2020-01-18Watts says Hugo 2 is Class A into 300 ohms at 5v RMS, AB into lower loads, and explains DSD volume needs another noise shaper because DSD is 1-bit PCM. Head-Fi, Jan 2020
• 2020-02-22Watts says truncating volume changes degrade depth and detail, dither is not transparent, only 705/768 kHz with 11th-order noise shaping works, DSP isn't transparent, and mastered files are best. Head-Fi, Feb 2020
• 2020-03-09Watts says Qutest has no volume control, explains truncation, Gaussian dither and 11th-order noise shaping at 705/768 kHz, and prefers Roon volume over a pre-amp. Head-Fi, Mar 2020
• 2020-07-26Watts says IIR filters used for EQ and DSP run out of bits as signals shrink, so small signals are treated differently from large ones, a major sound quality issue. Head-Fi, Jul 2020
• 2020-07-29Watts proposes testing a 64-bit floating-point PC EQ by setting all bands to -1 dB and raising DAC volume 1 dB; he heard added brightness, worse separation and flatter depth. Head-Fi, Jul 2020
• 2020-07-29Watts says EQ quality depends on implementation; IIR filters worry him most, FIR filters can also harm depth and separation, and FFT convolution depends on accuracy and truncation handling. Head-Fi, Jul 2020
• 2021-06-04Watts says what matters is how many taps are Whittaker-Shannon, about 256M for 24-bit recovery; windowed or apodized sinc fails, and 64-bit float causes 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
• 2021-07-23Watts 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
• 2021-08-19Watts says Opto-DX isolates fully only with batteries on both sides, and calls his volume truncation noise-shapers subjectively lossless but not bit perfect, a claim he is researching. Head-Fi, Aug 2021
• 2021-10-05Watts says to maintain the sample rate, current EQ and 64-bit float are not transparent; in M Scaler tests his 11th-order truncation noise shaper beat rectangular, triangular and pseudo-Gaussian dither. Head-Fi, Oct 2021
• 2021-12-07Watts lists advantages of an FPGA up-sampler over a PC (lower RF noise, clock control, own DSP design) and says 64 bit floating point creates noise floor modulation. Head-Fi, Dec 2021
• 2022-01-07Watts says HRTF works if your own HRTF is modeled with very accurate DSP, 64 bit floating point is inadequate, and HRTF fixes direction but degrades depth. Head-Fi, Jan 2022
• 2022-01-31Watts says EQ cannot be bit perfect, 64-bit floating point on a PC is not good enough for EQ, and proposes a test: all bands +1 dB, volume -1 dB. Darko.Audio 19:43
• 2022-01-31Watts says that test sounds harder, brighter and less deep despite flat response, because floating-point arithmetic creates very low but audible noise floor modulation, making conventional DSP sound bright. Darko.Audio 20:36
• 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 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 FPGAs let him build a custom 104-bit core, and an undisclosed current project runs at 140 bits with coefficients at forty decimal places of accuracy. Darko.Audio 28:41
• 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
• 2022-03-19Watts 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 floating point DSP inherently creates noise floor modulation, about -300 dB for 64-bit, which is audible; he has heard noise floor modulation at -400 dB. MFG Audio Reviews 34:48
• 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 he calculated the DSP needed 104 bits, but tests showed it failed -301 dB in phase though not amplitude, so he added noise shaping. MFG Audio Reviews 36:12
• 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
• 2022-03-26Watts 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
• 2022-03-30Watts says the better output bit depth depends on how the source dithers EQ, suggests trying 24 and 32 bit, and needs no EQ with Stealth on Hugo 2. Head-Fi, Mar 2022
• 2022-04-26Watts says Mojo 2's EQ DSP uses 104 bits and noise-shaped internals, making it far more transparent, and that forum users report EQ changes do not degrade sound. Audio Force 7:49
• 2022-04-29Watts says his DACs never truncate, so no bits are thrown away. Head-Fi, Apr 2022
• 2022-07-06Watts says the Hugo M Scaler's extra noise at 2x and 4x is deliberate Gaussian dither that sounds better, 16x noise is unchanged, and Chord DACs remove its jitter. Head-Fi, Jul 2022
• 2022-07-07Watts cites the Lipshitz dither paper, says triangular dither leaves signal-dependent errors, and reports his tests: rectangular worst, pseudo-Gaussian closest, but noise shaping still better for depth and detail. Head-Fi, Jul 2022
• 2022-07-12Watts says 16/44 gains more from M scaling but 24/192 M scaled is closer to the original; his goal is 24/48 matching 24/192, needing transparent 24-bit re-quantization at 48 kHz. Head-Fi, Jul 2022
• 2023-01-18Watts says the 192k output for Audio Precision measurements uses pseudo-Gaussian dither, noisier than triangular or rectangular dither but sounding closer to the noise-shaped 768k output. Head-Fi, Jan 2023
• 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
• 2023-04-03Watts 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
• 2023-04-03Watts says the DSP runs at 768 kHz, or 705 kHz for 44.1 material, and is noise-shaped, so the EQ is transparent. Amplify Audio 9:29
• 2023-07-29Watts says transparent EQ needs 16FS processing, noise shaping at each node and large fixed-point word lengths, and that Class D's transient timing distortions make it unfit. Head-Fi, Jul 2023
• 2023-07-30Watts says 64-bit floating point creates noise floor modulation, unlike his noise-shaped fixed point in Mojo 2's UHD DSP, and suggests Class H for efficient amplification. Head-Fi, Jul 2023
• 2023-09-14Watts explains why Mojo 2's EQ is loss-less rather than bit perfect, advises against source upsampling, and says an M scaler improves Mojo 2 though algorithm matters more than taps. Head-Fi, Sep 2023
• 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 64-bit floating-point EQ has noise floor modulation around -300 dB that is audible as brightness, and proposes a +1 dB EQ with -1 dB volume test. The Source AV 10:40
• 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 signals below the DSP's 104-bit resolution are remembered by the noise shaper and carried inside the noise, making a true infinite impulse response. The Source AV 12:08
• 2023-11-20Watts says 64-bit floating point creates audible noise floor modulation, and Mojo 2's EQ runs at 16FS with noise-shaped nodes in 104 bits. Head-Fi, Nov 2023
• 2023-11-20Watts says conventional digital EQ is flawed, especially bass EQ where small biquad coefficients are truncated and errors accumulate in IIR feedback. Head-Fi, Nov 2023
• 2024-06-01Watts explains transients and localization, how crossfeed narrows headphone width, and ranks rectangular, triangular and pseudo-Gaussian dither below noise shaping, best for depth. Head-Fi, Jun 2024
• 2024-09-29Watts says his son, a Tonmeister student at Surrey on a recording-studio placement in Belgium, built the tool in weeks, removing the 300 dB limit of Windows 64-bit floating point. The Source AV 8:10
• 2025-02-17Watts says Mojo 2's transparent EQ uses a 104-bit DSP core at 768 kHz with every IIR node aggressively noise shaped, recirculating rather than discarding truncated bits. audio-2G 14:59
• 2025-02-17Watts says transparent EQ needs at least '108 bits, at 104 bits' and aggressive noise shaping, not floating point, which creates audible noise floor modulation heard as unnatural brightness. audio-2G 15:44
• 2025-02-17Watts says his son finds compression and EQ on analog gear sounds more natural, and attributes this to digital processing using 64-bit floating point. audio-2G 17:15
• 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
• 2026-03-17Watts says information below the 16-bit level is encoded by dither or noise shaping, so 16-bit has 96 dB SNR yet an Audio Precision analyzer passes a -130 dB signal. ecoustics 7:02
• 2026-03-17Watts says properly dithered tiny signals pass, that bit depth sets noise and accuracy, and that his DACs create 2,048 new samples because analog is continuous. ecoustics 7:56
• 2026-03-17Watts says he also uses purely digital truncation noise shapers, for example after a digital filter. ecoustics 39:56
• 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 floating point is a major problem and cannot be used. ecoustics 48:33
• 2026-03-17Watts says floating point creates noise floor modulation, which is perceivable however small, using 'perceivable' rather than 'audible' since the brain uses it to make sense of music. ecoustics 48:39
• 2026-10-11Watts says his direct interpolation filter avoids this; 64-bit floating point creates small but audible noise floor modulation, compounded by FFT and IFFT, requiring much higher precision. Distorsiuni Interioare 36:27