Filter stage architecture and oversampling rates

Reconstruction filters and timing

Answers on this topic

• How are Chord's filter stages split across 16FS, 256FS and 2048FS, and what does each stage do?

Everything he said on this topic (92)

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

• 2014-04-17Watts says Hugo has five filters: two WTA stages (first 26k taps) to 16FS, a linear interpolator to 2048FS, two IIR filters; the new QBD filter just meets timing. Head-Fi, Apr 2014
• 2014-06-02Watts says bit depth does not affect delay but doubling sample rate quarters it, since the first stage always upsamples to 8FS. Head-Fi, Jun 2014
• 2014-06-10Watts corrects that taps belong to the FIR oversampling filter, not the DAC section, and says Hugo's tap length is two orders of magnitude above conventional silicon DACs. Head-Fi, Jun 2014
• 2014-07-03Watts says Hugo digitally filters to 9.6nS resolution, adding 2048 new samples, and that 4uS is only the ear's inter-aural delay resolution. Head-Fi, Jul 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 DAVE's FPGA is 10 times more complex than Hugo's, giving 164,000 taps, an enhanced WTA algorithm, FIR filtering to 256 times, then further filtering to 2048. HIFICLUBE.NET JVH 45
• 2015-05-20Watts calls a 256-times FIR filter a world record, cites 166 parallel DSP cores, and says sampling theory needs an infinite-tap, infinitely oversampling filter for perfect reconstruction. HIFICLUBE.NET JVH 1:17
• 2015-11-10Watts says Dave's key gain is timing: WTA filtering to 256FS reconstructs timing to 88 nS, improving starting and stopping of notes, while depth comes from the noise shapers. Head-Fi, Nov 2015
• 2015-12-18Watts says Dave's HF filter is a 60 kHz cutoff set of 16FS-to-256FS WTA coefficients meant to cut ADC noise in hi-res recordings, and it unexpectedly improves 44.1 kHz too. Head-Fi, Dec 2015
• 2016-01-17Watts says all FIR filters need an overload margin for Gibbs phenomena, which his designs have had for twenty years, tested with 0 dBFS noise and square waves. Head-Fi, 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 a single-stage 16FS WTA first stage sounded much better, by more than 26,000 versus 164,000 taps, and 256FS second-stage filtering improved timing accuracy from microseconds to nanoseconds. article, Jan 2016
• 2016-04-10Watts says a built-in impulse detector switches the WTA filter out when it sees an impulse, which music cannot trigger, and that the windowed coefficients are fixed in the FPGA. Head-Fi, Apr 2016
• 2016-06-02Watts says DAVE sounded too dark and soft late in development until a 256FS WTA stage improved perception of note starts and stops and restored balance. Head-Fi, Jun 2016
• 2016-06-04Watts says WTA1 uses 90% of DAVE's FPGA DSP, so a power amp fed 16FS data could use a bigger WTA2; the DAVE power amp will outpower the Hugo amp. Head-Fi, Jun 2016
• 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 better 2048FS filtering on Hugo also improved timing resolution, so in place of Hugo's 8x-then-16x WTA stages he tried a single 16x WTA stage, which sounded a lot better. Hifistatement 6:51
• 2016-07-24Watts says this mattered more than going from 26 thousand to 164 thousand taps, 16x filtering is accurate only to microseconds, and he added a 16x-to-256x WTA stage. Hifistatement 7:47
• 2016-07-24Watts says the FIR filter now runs at 256 times FS, beyond others' 16 times (he once did 32), using many DSP cores and making a massive change. Hifistatement 8:32
• 2016-08-11Watts says he always uses direct-form FIR filters, folded when fewer multipliers are needed, that FPGAs are SRAM-limited, and that WTA group delay cannot be removed without hurting sound quality. Head-Fi, Aug 2016
• 2016-10-20Watts lists the filter stages: Hugo and Mojo use WTA 16FS, linear interpolation to 2048FS and 260 kHz low-pass filters; DAVE adds a WTA stage to 256FS, nearer ideal sinc. Head-Fi, Oct 2016
• 2016-10-21Watts says adding the 256FS WTA filter turned DAVE from rich, dark and almost soft to sharper and tighter, improving starting and stopping of notes by nearing ideal sinc. Head-Fi, Oct 2016
• 2017-01-09Watts explains Dave's 16FS-to-256FS WTA stage replacing IIR filters, says any timing error is audible, notes Hugo 2 filter settings switch that stage, and contrasts 88 nS with 2.6 uS. Head-Fi, Jan 2017
• 2017-01-23Watts says Hugo 2's 256FS filter matches Dave's, and the HF filter is best off with the M scaler and Dave since stop-band rejection is already 130 to 150 dB. Head-Fi, Jan 2017
• 2017-01-23Watts says the 256FS filter improves starts and stops of notes, Hugo cascaded two WTA stages while Dave uses one, and Dave remains well above Hugo 2. Head-Fi, Jan 2017
• 2017-01-28Watts explains peak error, why 16-bit accuracy needs about 1M taps, why doubling sample rate only halves conventional filters' error, and that taps are not the whole story. Head-Fi, Jan 2017
• 2017-03-19Watts says quoted tap lengths cover only the WTA1 stage, so 49,152 taps apply to the 1FS to 16FS filter whether the 16FS or 256FS output is selected. Head-Fi, Mar 2017
• 2017-03-23Watts says the 49,152 WTA1 taps never change and exclude WTA2, refusing 'effective tap' marketing, and the HF filter matters more above 48 kHz in both filter modes. Head-Fi, Mar 2017
• 2017-03-24Watts says white to green is a small change at 44.1 kHz, more useful at 96 or 192 kHz; dropping WTA2 for linear interpolation (orange or red) is large. Head-Fi, Mar 2017
• 2017-06-15Watts says Hugo 2's HF filter matters little at 44.1 kHz but more at 96 to 768 kHz, and the 256FS WTA stage audibly snaps note starts into focus. Head-Fi, Jun 2017
• 2017-07-25Watts says Hugo's WTA1 ran 1FS to 8FS at 26,368 taps; Hugo 2's goes 1FS to 16FS at 49,152 taps, then WTA2 to 256FS on white/green. Head-Fi, Jul 2017
• 2017-07-25Watts adds that beyond the WTA FIR filtering there are still three filter stages up to 2048FS. Head-Fi, Jul 2017
• 2017-07-26Watts confirms linear interpolation runs 256FS to 2048FS on white/green and 16FS to 2048FS on orange/red; the HF filter changes LPF time constants from 0.7 uS to 2.8 uS. Head-Fi, Jul 2017
• 2017-09-14Watts says the final stage is more than linear interpolation: a three-stage filter at 2048 FS, linear interpolation followed by two IIR low-pass filters. Head-Fi, Sep 2017
• 2017-12-19Watts says removing these sampling images is one reason he digitally filters to 2048FS. Head-Fi, Dec 2017
• 2017-12-26Watts says his WTA filters roll off very fast: 49,152 taps reach -1dB within 75Hz of FS/2, the M Scaler's 1M taps within 4Hz, matching ideal sinc beyond 16-bit accuracy. Audiophile Style, 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
• 2018-03-03Watts says he is building a direct measurement of transient error to prove the WTA approach, and WTA 2 is always needed to further reconstruct the 768 kHz signal. Head-Fi, Mar 2018
• 2018-07-26Watts says Qutest, Hugo 2, TT2 and Dave share the post-scaler process (WTA2 to 256FS, third-order filter to 104 MHz), notes diminishing returns, and previews DX amps' transparency. Head-Fi, Jul 2018
• 2018-07-27Watts doubts vendors' software tap claims such as Audirvana's 500,000 taps, says PCs are noisy and poor at real time, and that filter structure alters sound. Head-Fi, Jul 2018
• 2018-08-04Watts explains TT2's 98,304-tap 16FS WTA1, says WTA2 matches Hugo 2 and Dave, TT2 sounds warmer than Hugo 2, and describes fixing 192kHz crackles in Windows. Head-Fi, Aug 2018
• 2018-08-20Watts speculates why the test filter is poor, and says the 16FS, WTA2 256FS and 2048FS path is identical from Qutest to Dave; noise shaper, pulse array and analog differ. Head-Fi, Aug 2018
• 2018-09-09Watts says the HF filter and WTA2 settings are unaffected by the M scaler, which works from 1FS to 16FS, and explains the vague autumn delivery as distribution time. Head-Fi, Sep 2018
• 2018-10-31Watts explains WTA1's 768 kHz output as a listening-test balance, WTA2's 256FS step shared by all current DACs except Mojo, and a three-stage IIR filter to 9.6 nS. Head-Fi, Oct 2018
• 2019-01-20Watts details WTA1 modes, WTA2 versus the three-stage IIR, the HF filter at about -1dB at 20kHz, and says Stereophile's Qutest frequency response was wrong due to latency. Head-Fi, Jan 2019
• 2019-01-21Watts drives B&W 803D3 from TT2 single-ended via XLR pins 1 and 2, explains the third-order filter to 2048FS, and uses green for his 96k recordings. Head-Fi, Jan 2019
• 2019-01-29Watts says finite filters trade oversampling rate against data, that 4 uS interaural resolution proved insufficient, and that high rates matter for transient timing accuracy, not hearing 768k. Head-Fi, Jan 2019
• 2019-02-09Watts says the HF filter changes the 2048FS filter's time constants rather than switching a path: -3 dB at 150 kHz without it, 37.5 kHz with it. Head-Fi, Feb 2019
• 2019-06-16Watts offers three reasons green sounds warmer on RBCD, favoring the HF filter retuning the 256FS-to-2048FS stage from 160 kHz to 40 kHz, lowering noise floor modulation. Head-Fi, Jun 2019
• 2019-07-22Watts says the M scaler converts 48k to 768k with 16-bit sinc accuracy, each doubling of rate quarters the transient error area, and WTA2 timing gains above 768k remain audible. Head-Fi, Jul 2019
• 2019-07-23Watts says WTA1 changes bass, pitch, timbre and separation while WTA2 affects only note starts and stops, names the RME ADI-2 Pro for test recordings, and describes IIR final stages. Head-Fi, Jul 2019
• 2019-08-04Watts says the HF filter uses the 256FS to 2048FS filter with adjusted time constants, so the original input format makes no difference. Head-Fi, Aug 2019
• 2019-08-05Watts says crossfeed is done at 16FS (705/768k), after WTA1, since all sources end up at that point. Head-Fi, Aug 2019
• 2019-09-14Watts explains the trade-off between output rate and sinc accuracy at fixed taps, says 16FS is optimal for 1M taps, and rejects offline 16FS conversion over file size and metadata. Head-Fi, Sep 2019
• 2020-01-02Watts says the two Qutest filters measure identically yet sound different; WTA1 outputs every 1.3 microseconds and a second WTA stage outputs every 88 nanoseconds. Passion for Sound 3:38
• 2020-01-02Watts says his earlier three-stage IIR filter measured very like the WTA FIR stage, yet the change is audible, so even 88 nanosecond timing resolution matters. Passion for Sound 4:23
• 2020-04-09Watts says the new HF filter is a 4th-order 50kHz digital filter of two bi-quads, tuned for a small 20k boost, and its warmth comes from reduced out-of-band noise. Head-Fi, Apr 2020
• 2020-04-11Watts says the M scaler preserves a recording's HF noise, being flat to FS/2 like an ideal sinc, so the DAC's HF filter, run from 16FS to 2048FS, removes it. Head-Fi, Apr 2020
• 2020-06-25Watts says DAVE used a three-stage filter from 768 kHz up to 104 MHz, and he experimented replacing part of it with a WTA filter outputting every 1.6 microseconds. Part-Time Audiophile 23:30
• 2020-06-25Watts says replacing the conventional IR type filter with a WTA filter running to 88 nanoseconds was immediately audible in the starting and stopping of notes, such as piano attacks. Part-Time Audiophile 24:23
• 2020-11-22Watts says his 0dBFS white noise test shows no out-of-band images from Hugo 2, whose digital filtering extends to 104MHz; noise up to 250kHz comes from the AP's ADC. Head-Fi, Nov 2020
• 2021-09-09Watts says the M Scaler improves tempo, pitch, timbre and separation, while WTA filtering above 16FS has so far only improved clarity, soundstage and starting and stopping of notes. Head-Fi, Sep 2021
• 2022-01-31Watts says Mojo 2 auto-offs after 10 minutes without inputs, stays in desktop mode while powered, trails Hugo 2, uses a digital DC servo, and improved 16FS-to-2048FS filtering. Head-Fi, Jan 2022
• 2022-01-31Watts says the UHD DSP runs at 705/768 kHz on the output of WTA1 or the DSD filter, and there is no WTA2. Head-Fi, Jan 2022
• 2022-03-19Watts says each doubling of sample rate cuts the error area fourfold, 256 times less at 705 kHz, the 16FS sweet spot, and WTA2 is less tap-length sensitive than WTA1. MFG Audio Reviews 52:02
• 2022-07-09Watts explains WTA1 filters to 16FS, WTA2 to 256FS, then a three-stage IIR filter to 104MHz feeding noise shapers and 20 pulse array elements, each stage with different requirements. Head-Fi, Jul 2022
• 2022-08-02Watts confirms orange and red filters bypass WTA2, with the following filters running 16FS to 2048FS, and green/orange removing more HF noise and distortion above 50kHz. Head-Fi, Aug 2022
• 2022-08-19Watts says the DAC's resolving power limits transient reconstruction, and DAVE, Hugo 2 and TT2 add WTA2 filtering to 256FS and another filter from 256FS to 2048FS. AVstore 28:30
• 2022-08-22Watts explains a tap as a sample times a WTA coefficient, summed in an accumulator; the M Scaler uses 63,488 original samples per interpolated sample, going 1FS to 16FS. Head-Fi, Aug 2022
• 2022-09-18Watts says TT2, DAVE and Hugo 2 have a WTA filter from 16FS to 256FS, unlike the 1FS to 16FS WTA, improving speed and the starting and stopping of notes. The Source AV 39:35
• 2023-12-04Watts says Stereophile's Dave response curves are wrong, likely ignoring latency, and that its 384k response reflects the filters from 16FS to 104M and analog filtering. Head-Fi, Dec 2023
• 2023-12-05Watts says 8FS inputs are upsampled to 16FS by the WTA1 filter in the same way as 1FS inputs. Head-Fi, Dec 2023
• 2023-12-05Watts says at 384k Dave's WTA1 is flat to 191.8kHz, with response limited by analog and other digital filters. Head-Fi, Dec 2023
• 2024-01-07Watts says 16FS is the interpolation sweet spot (1.3uS vs 2.6uS timing at 8FS for 48kHz), adding more 200T FPGAs is the economic path, and a battery laptop via optical is hard to beat. Head-Fi, Jan 2024
• 2024-05-10Watts says the sweet point is 16FS and that DAVE takes up 16FS. Reactcore 1:00
• 2024-05-10Watts says a further WTA filter then takes the signal to 256FS. needs context Reactcore 1:09
• 2024-05-10Watts says another filter stage then takes the signal to 2048FS. needs context Reactcore 1:13
• 2025-01-28Watts says WTA1's 98,304 taps are unaffected by filter options, red and orange switch out WTA2, and white and green only adjust the 256FS to 2048FS filter time constants. Head-Fi, Jan 2025
• 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 accuracy requires oversampling to a very high rate, creating 2,048 new samples. ecoustics 8:39
• 2026-03-17Watts says there are 2,048 extra samples between each original sample and the next. ecoustics 8:54
• 2026-03-17Watts says all 2,048 created samples must match the original analog to 16-bit accuracy. ecoustics 9:03
• 2026-03-17Watts says it is complicated, because in the digital domain you want to run as high as possible. needs context ecoustics 9:29
• 2026-03-17Watts says higher rates hit hardware limits: FPGA speed and processing, and discrete flip-flops that lose accuracy above 100 MHz, so about 100 MHz is the sweet spot. ecoustics 9:37
• 2026-03-17Watts says extracting that timing without distortion needs very high oversampling, 2,048 times, and sinc-function interpolation, which he says nobody else does. ecoustics 16:06
• 2026-03-17Watts says DAVE's filter is 164 thousand taps; an M Scaler adds a million taps, converting 48 kHz to 768 kHz (16 times), and DAVE then upsamples to 2048 times. ecoustics 23:40
• 2026-08-30Watts says a single-stage filter trades off two problems like a seesaw; his Blackbird WTA solves each in turn, a new structure cutting the delay to tens of seconds. The Source AV 8:23
• 2026-10-02Watts says all his DACs except Mojo 2 add a WTA stage from 16FS (705/768 kHz) to 256FS (about 12 MHz), then filters up to 104 MHz. HiFi Buys 1:15:13
• 2026-10-02Watts says these stages aim to reconstruct timing resolution down to within 9.6 nanoseconds. HiFi Buys 1:15:58
• 2026-10-14Watts says a perfect 768 kHz filter would improve a chip DAC but not match his FPGA DACs, which filter up to 104 MHz, leaving 9.6 nanoseconds of uncertainty. Part-Time Audiophile 35:47
• 2026-10-14Watts says chip DACs handle the step from 768 kHz up to about 12 MHz poorly, a major focus of his FPGA pulse array DACs. Part-Time Audiophile 36:44
• 2026-10-17Watts says separating the two problems into different filters, each optimized, led to the Blackbird WTA structure. article, Oct 2026