Sampling theory and ideal reconstruction

Reconstruction filters and timing

Answers on this topic

• Isn't pre-ringing bad? Why doesn't Chord offer minimum-phase, apodizing or NOS filters, and are NOS DACs really bit perfect?
• Why does tap length matter, and why a million taps?

Everything he said on this topic (153)

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

• 2014-04-17Watts explains that bandlimited samples are perfectly reconstructed by an infinite-tap filter, including transients starting mid-sample, and timing precision falls off as taps are reduced. Head-Fi, Apr 2014
• 2014-05-22Watts explains FIR taps and WTA coefficients, says perfect reconstruction needs infinite taps, and that Hugo's 26,368 taps run on 16 parallel DSP cores at 208 MHz. Head-Fi, May 2014
• 2014-07-03Watts explains that an infinite-tap filter perfectly reconstructs bandlimited signals while finite taps cause transient timing errors, hundreds of uS for one tap, so he lengthened taps by listening. Head-Fi, Jul 2014
• 2014-07-03Watts says a sin(x)/x impulse response reconstructs missing points perfectly, but an 8 times oversampling filter needs nearly a million taps for 16-bit accuracy. Head-Fi, Jul 2014
• 2015-03-01Watts says short filters cause transient timing errors of tens of microseconds; Hugo uses 26,000 taps, 164,000 still beats 100,000, and about a million taps would give 16-bit accuracy. Head-Fi, Mar 2015
• 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
• 2015-06-27Answering what '12 bits accurate against the ideal' means, Watts says the WTA impulse response matches the sinc to 12 bits, and he has not yet hit the audible limit. Head-Fi, Jun 2015
• 2015-12-11Watts rejects 'more than one way to skin a cat': transparency to live music requires very long tap-length sinc filters, and other designers fail to address timing and NFM. Head-Fi, Dec 2015
• 2016-01-09Watts says sound quality depends on the interpolation filter, infinite processing would perfectly recover the analog signal, and Mojo has 500 times conventional chips' processing power and 44 DSP cores. What Hi-Fi? 4:16
• 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
• 2016-03-30Watts says perfect reconstruction needs an infinite-tap, infinitely oversampling sinc filter; he does not know how many taps suffice, and Davina will let him test 768k to 48k and back. Head-Fi, Mar 2016
• 2016-03-31Watts poses a paradox: an ideal infinite sinc filter rings infinitely yet reconstructs a bandlimited signal unchanged, and says the industry's push to minimize ringing gets filters wrong. Head-Fi, Mar 2016
• 2016-04-10Watts says an ideal sinc filter's infinite ringing reconstructs bandlimited signals perfectly, and that pre-ringing worries come from testing with non-bandlimited impulses. Head-Fi, Apr 2016
• 2016-04-20Watts says his ADC runs at 104.25 MHz so analog anti-alias filtering is easy, but he does not know how much decimation rejection suffices (-140 dB is not). Head-Fi, Apr 2016
• 2016-05-17Watts says an ideal sinc reconstruction filter adds no ringing, but theory says nothing on how an ADC should bandlimit; Davina will test aliasing rejection beyond 140 dB. Head-Fi, May 2016
• 2016-07-24Watts says keeping digital data unchanged or minimizing ringing are wrong goals; a DAC's purpose is to reproduce the analog waveform at the A-to-D converter. Hifistatement 0
• 2016-07-24Watts says a DAC must recover the missing timing information between samples, changing the data to what an infinite oversampling ADC would give, with complexity digital and analog simple. Hifistatement 43
• 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
• 2017-02-13Watts defends his Mojo timing illustration as a simplification, targets non-linear timing uncertainty rather than ringing, says doubling taps halves the error, and notes WTA accommodates half-band decimation. Head-Fi, Feb 2017
• 2017-04-27Watts says image upscaling like RAISR does not carry over to audio, where only transient timing must be recovered with longer filters, and plans Davina tests of 1M-tap losses. Head-Fi, Apr 2017
• 2017-08-13Watts says Davina will test how many taps are enough and whether ADC bandwidth limiting matters, noting sinc reconstruction is required and his IIR decimation filter gives 300 dB rejection. Head-Fi, Aug 2017
• 2017-08-21Watts says only a sinc reconstructs correctly, short filters sound soft and warm, and he will post blind Davina files comparing FIR and IIR decimation filters with 300 dB attenuation. Head-Fi, Aug 2017
• 2017-08-21Watts says only a sinc filter perfectly reconstructs sampled data, but bandwidth limiting before sampling can use any filter, provided there is no output at or above FS/2. Head-Fi, Aug 2017
• 2017-08-26Watts says audible timing errors are non-linear, not fixed delays; the M scaler's 1,015,808 taps match ideal sinc to 16 bits, Hugo 2 about 13; doubling taps adds a bit. Head-Fi, Aug 2017
• 2017-10-13Watts says a DAC should reproduce the analog signal inside the ADC, not bit-perfect data, and introduces an illustration of a sampled 20 kHz sine burst. miceblue425 11:08
• 2017-10-13Watts says Whittaker-Shannon theory proves an infinite-tap FIR filter perfectly reconstructs a bandwidth-limited signal, regardless of the sampling interval. miceblue425 12:46
• 2017-10-13Watts repeats that a bandwidth-limited signal and a Whittaker-Shannon sinc filter give perfect reconstruction, recovering the missing pulse. miceblue425 13:31
• 2017-10-13Watts says a sinc impulse response decays to zero only over infinite time, so a perfect filter needs infinite delay and processing, and that this theory is fact. miceblue425 13:48
• 2017-10-13Watts poses a paradox: a sinc filter perfectly reconstructs a signal, yet an impulse fed into it comes out looking nothing like the impulse. miceblue425 16:17
• 2017-10-13Watts says a Dirac impulse is an illegal, non-bandwidth-limited signal: useful for showing a filter's coefficients, never for judging its sound, since bandlimited signals have zero output at FS/2. miceblue425 17:25
• 2017-10-13Watts says a Dirac has the same level at 22.05 kHz as at DC, and the audio business is wrong to judge filter sound quality from Dirac responses. miceblue425 18:10
• 2017-10-13Watts explains that each sample's impulse response carries pre-ringing that sums with the others to rebuild the waveform where the data is zero, with no stray pre-ringing for bandlimited signals. miceblue425 18:49
• 2017-10-13Watts recalls reading hearing physiology as a student and learning sampling theory, and realizing that LC filters, with no FIR filters available, could not recover transient timing. miceblue425 26:21
• 2017-10-18Watts says inadequate bandwidth limiting harms sound via aliasing; Davina's first decimation filter has 260 dB rejection, and non-decimating FIR and IIR versions will let listeners hear bandwidth limiting. Head-Fi, Oct 2017
• 2017-10-18Watts says with bandwidth-limited signals longer filters ring less, pre-ringing is needed for transients, half-band brickwall filters alias badly, and slow roll-off beats them but loses to proper brickwalls. Head-Fi, Oct 2017
• 2017-10-20Watts says a DAC must calculate the missing information between samples, and that a Whittaker-Shannon sinc filter running from infinite past to infinite future perfectly reconstructs a bandlimited signal. Hifistatement 0
• 2017-10-20Watts says filter tests use an illegal impulse with output at FS/2; a bandlimited impulse gives no extra ringing in his filters, and a sinc filter returns it exactly. Hifistatement 1:58
• 2017-10-20Watts says the paradox of a filter that rings infinitely yet recovers everything perfectly arises only because the test signal is not bandwidth limited when it should be. Hifistatement 2:51
• 2017-11-15Watts says the M scaler's WTA coefficients match an ideal sinc to 16 bits, needing about 1 million taps and the right algorithm, which PC up-samplers lack. Head-Fi, Nov 2017
• 2017-12-02Watts says sampling theory only requires bandwidth limiting, which may use a non-pre-ringing IIR filter; his pre-ringing remark concerned DAC interpolation filters, and coefficient calculation matters beyond tap length. Head-Fi, Dec 2017
• 2017-12-02Watts says WTA optimizations improved every recording consistently, so the rule is to get as close to an ideal sinc as possible even for recordings with aliasing or ringing. Head-Fi, Dec 2017
• 2017-12-26Watts says he aims to recover the original bandwidth-limited analog signal with as little change as possible, because that gives the best sound and the best measurements. Audiophile Style, Dec 2017
• 2017-12-26Watts says the only exact reconstruction is an infinite sinc interpolation filter: linear phase and a brick wall rather than slow roll-off, with infinite pre-ringing. Audiophile Style, Dec 2017
• 2017-12-26Watts says an ideal filter rings forever yet reconstructs perfectly because a Dirac impulse is not bandwidth limited, so it is an illegal signal under sampling theory. Audiophile Style, Dec 2017
• 2017-12-26Watts says a bandwidth-limited impulse through an ideal sinc filter is reconstructed perfectly, with no added pre- or post-ringing. Audiophile Style, Dec 2017
• 2018-01-16Watts says a sinc only perfectly reproduces signals with zero output at FS/2, but modern ADC half-band filters leave -6dB, causing unrepairable aliasing; Davina will reach -240dB. Head-Fi, Jan 2018
• 2018-02-23Watts says a DAC is meant to reproduce the analog signal that was in the A to D converter before sampling, not to reproduce the digital data. MajorHiFi 9
• 2018-02-23Watts says time-domain debates about pre-ringing and NOS designs get it wrong: NOS appeals because it reproduces the data, but a DAC should reproduce the original analog signal. MajorHiFi 2:37
• 2018-02-23Watts says he thinks in terms of recovering the original bandlimited analog signal rather than data, that the transcript's garbled subject does this poorly, and that the brain is very sensitive to non-linear timing errors. MajorHiFi 3:26
• 2018-02-23Watts says transients shape perceived imagery, timbre and pitch, that the interpolation filter recovers timing, and that theory allows perfect recovery of a bandlimited signal at any sample rate. MajorHiFi 7:07
• 2018-02-23Watts explains that perfect recovery needs a sinc function filter whose ringing extends to infinity in both directions, requiring infinite time and processing power. MajorHiFi 7:51
• 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
• 2018-03-03Watts 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
• 2018-03-17Watts says ideal reconstruction needs an infinite-tap sinc; DAVE's WTA matches ideal to 13.9 bits and the M scaler to 16.6 bits, an unexpectedly large audible step. Head-Fi, Mar 2018
• 2018-05-04Watts says his DSD filters reconstruct the analog signal, but DSD's lost timing information cannot be repaired; Hugo 2's improved DSD filter softened his stance though he prefers Redbook. Head-Fi, May 2018
• 2018-06-09Watts says image removal alone is not enough: filters with near-identical frequency response sound different, closer to sinc sounds better, and 0.5 million to 1 million taps is clearly audible. Head-Fi, Jun 2018
• 2018-07-19Watts says modern ADCs' -6dB at FS/2 causes unrepairable aliasing, yet all recordings benefit from an M scaler; Davina will decimate without aliasing, and he will release randomly named files. Head-Fi, Jul 2018
• 2018-07-21Watts says the interpolation filter recovers the waveform, but conventional DACs calculate it poorly, so transients shift constantly between too early and too late, confusing the brain. c w 9:12
• 2018-07-21Watts says a filter allowing no pre-ringing loses the original pulse, an error of about 100 microseconds, while a sinc function filter perfectly reconstructs the bandlimited transient. c w 10:54
• 2018-07-21Watts says a sinc function (Whittaker-Shannon) interpolation filter reconstructs the original exactly, whether sampled at 22 microseconds or 2 picoseconds, and calls the theory absolute. c w 11:42
• 2018-07-21Watts says a sinc filter pre-rings and post-rings forever, needing infinite processing and delay, so one workaround is to shorten the sinc function. c w 12:28
• 2018-07-21Watts says the coefficients match sinc to the 16-bit level, guaranteeing reconstruction of the bandlimited signal to 16-bit accuracy for CD, then begins describing FIR problems on Dave. c w 19:24
• 2018-08-31Watts says the original is the unsampled analog signal; the M scaler's million taps match ideal sinc to better than 16 bits, recovering transient timing regular filters get wrong. Head-Fi, Aug 2018
• 2018-09-01Watts explains that 16-bit accuracy refers to the ideal sinc, errors arise only with transients, NOS is crude sample-and-hold, and delta-sigma ADCs suffer half-band decimation aliasing. Head-Fi, Sep 2018
• 2018-09-02Watts says the M scaler matches a perfect sinc to 99.98%, the worst case for any signal; a 1kHz sine would be 99.9999996% accurate, transients giving larger errors. Head-Fi, Sep 2018
• 2018-09-19Watts calls the claim that filter ringing is reverb pseudoscience: a sinc interpolation filter reconstructs a bandlimited impulse perfectly, with no ringing at all. Head-Fi, Sep 2018
• 2018-09-26Watts says he designed IIR and FIR Davina decimation filters with over 250 dB rejection to test bandlimiting; he expects pre-ringing at 22.05 kHz to prove a red herring. Head-Fi, Sep 2018
• 2018-11-07Watts says PCM can in theory recover the bandlimited signal perfectly given enough processing, hence the M scaler, while DSD is format limited and falls in a lower league. Head-Fi, Nov 2018
• 2018-12-13Watts says a sinc function filter with infinite processing perfectly reconstructs the 20 kHz tone burst, including an initial pulse absent from the digital data, as basic sampling theory proves. Pursuit Perfect System 6:04
• 2018-12-13Watts claims a tenfold reconstruction gain without more taps, says half the WTA coefficients are identical to an ideal sinc function, and says sinc-like filters sound more natural. Pursuit Perfect System 8:20
• 2018-12-13Watts says he felt digital would never sound good until a million taps were possible, and begins explaining why with a sinc response decaying to zero. Pursuit Perfect System 12:33
• 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
• 2019-03-29Watts says TT2 filters are interpolation tweaks not EQ, argues NOS DACs are not truly bit perfect, explains transient timing errors, and warns IIR EQ and dithered volume are not transparent. Head-Fi, Mar 2019
• 2019-04-09Watts says ringing is inaudible because 22.05 kHz is inaudible and bandlimited signals carry no energy there, calling the industry's Dirac-impulse view a misunderstanding of sampling theory. Head-Fi, Apr 2019
• 2019-04-19Watts defines tap length, explains the WTA window leaves just over half the coefficients exactly sinc, guaranteeing reconstruction better than 16 bits, and notes a typo in Keith Howard's article. Head-Fi, Apr 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
• 2019-12-19Watts says the filter reconstructs what happens between samples without changing the originals, and that theory shows a sinc function perfectly reconstructs a bandwidth-limited signal. Passion for Sound 1:09
• 2019-12-19Watts says a sinc function needs infinite processing, and that transients matter because the brain uses them, e.g. interaural delay sensed by a chain of neurons to locate instruments. Passion for Sound 1:50
• 2019-12-19Watts says he was also studying Shannon sampling theory then, which showed that reconstructing the original sampled signal requires a sinc function. Passion for Sound 7:15
• 2019-12-19Watts says the industry is wrong because sampling theory requires a bandwidth-limited signal: content may reach 22.04 kHz but must be zero at 22.05 kHz. Passion for Sound 15:14
• 2019-12-19Watts says an impulse is not bandwidth limited; a bandwidth-limited impulse through a sinc function does not ring, but through MQA or minimum phase filters it rings excessively. Passion for Sound 15:30
• 2019-12-19Watts agrees: the filter creates no new information but preserves the original recording's information, and a sinc function of appropriate length reconstructs it to the needed accuracy. Passion for Sound 21:30
• 2020-01-02Watts says MQA uses a short minimum-phase type filter that looks only into the past; calling pre-ringing bad misreads sampling theory, since sinc pre-ringing is essential for perfect reconstruction. Passion for Sound 18:00
• 2020-01-02Watts says pre-ringing looks unnatural, but sinc ringing occurs at 22.05 kHz, which is inaudible, and a properly bandlimited signal would not ring at all. Passion for Sound 19:20
• 2020-01-02Watts says an impulse is an illegal signal that reveals coefficients, not behavior on music; with bandlimited signals WTA rings less than minimum-phase MQA-type filters, which add ringing. Passion for Sound 19:48
• 2020-11-14Watts says an infinite-tap sinc guarantees correct intermediate values for bandlimited signals, and WTA is far more accurate per tap, with doubling taps doubling accuracy; improvement has not yet converged. Head-Fi, Nov 2020
• 2021-05-23Watts quotes PGGB's FAQ on apodizing and says its windowing function turns sinc into something that should not be called sinc; true offline sinc needs no window. Head-Fi, May 2021
• 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
• 2022-03-19Watts says the cure is to remove both noise floor modulation and timing errors, and that an ideal sinc filter recovers the transient's starting point because it pre-rings and post-rings. MFG Audio Reviews 19:39
• 2022-03-19Watts says a sinc filter perfectly reproduces a bandlimited signal but needs infinite processing from the start to the end of the universe, so the theory is clear but impractical. MFG Audio Reviews 20:23
• 2022-04-26Watts says at 44.1 kHz samples are 22 microseconds apart, the interpolation filter must reconstruct transient timing between them, and perfect reconstruction needs infinite taps. Audio Force 9:59
• 2022-05-03Watts says a brick-wall filter would reconstruct transients perfectly, the WTA filter approximates it via thousands of listening tests, and its optimum is recording-independent because timing error is structural. Head-Fi, May 2022
• 2022-05-09Watts says decimation filters need only adequate aliasing rejection and FIR pre-ringing was inaudible, but DAC interpolation needs a sinc, so he offers one WTA1 filter, no options. Head-Fi, May 2022
• 2022-05-10Watts says decimation needs only removal of everything above the new Nyquist, so IIR works, but interpolation creates new samples and only a sinc reconstructs them perfectly. Head-Fi, May 2022
• 2022-05-13Watts agrees conventional ADCs soften sound through limited HF accuracy and aliasing, says minimum-phase, MQA, apodizing and NOS filters soften it far more, and defends sampling theory. Head-Fi, May 2022
• 2022-06-22Watts says a NOS filter is the crudest oversampling filter, real filters degrade transient timing, and PWM in Class D has amplitude-dependent timing plus filter phase intermodulation. Head-Fi, Jun 2022
• 2022-07-15Watts says removing pre-ringing harms transient reconstruction, impulses are illegal non-bandlimited signals, and his test filtering 20-22.05 kHz ADC aliasing after WTA1 gave little or no benefit. Head-Fi, Jul 2022
• 2022-08-19Watts says the upsampling filter is an FIR filter based on a sinc function, which rings to infinity in past and future, so its ends must be chopped off. AVstore 16:15
• 2023-02-04Watts says the brain detects the smallest errors, then introduces transient reconstruction as most important: digital audio is sampled, with about 22 microseconds between samples. Dusty Audio 35:26
• 2023-02-04Watts says sampling theory proves the waveform between samples can be perfectly reconstructed, but only with a sinc function needing infinite processing. Dusty Audio 38:24
• 2023-02-04Watts says perfect reconstruction uses the infinite past and future; in the 1980s, knowing sampling theory and psychoacoustics, he identified timing reconstruction between samples as digital's fundamental problem. Dusty Audio 39:08
• 2023-02-05Watts says sample-and-hold is a first-order digital filter and oversampling; converting sampled data to a continuous waveform is infinite oversampling, so even a NOS DAC oversamples. Soundnews 14:48
• 2023-03-26Watts recalls studying sampling theory and, on his own, psychoacoustics in the 1980s, learning that transient timing is perceptually vital for pitch, timbre and soundstage. Eric's Hi-Fi 41
• 2023-03-26Watts says most perceptual cues come from transient timing, which needs a sinc filter whose coefficients only converge on zero, so the filter must keep doubling for accuracy. Eric's Hi-Fi 1:26
• 2023-05-04Watts says inter-sample overloads are very unlikely with music, and his -2.73dB overload margin covers Gibbs overshoot and suits his SPDIF de-emphasis filter. Head-Fi, May 2023
• 2023-08-22Watts disputes PGGB's pure-sinc claims, says coefficients must be windowed, and suggests listening for bass pitch, separation, focus and timbre variation. Head-Fi, Aug 2023
• 2023-11-01Watts says sampling theory means shorter latency always degrades transient reconstruction, so low-latency gaming audio is a problem; studio latency also needs attention. Head-Fi, Nov 2023
• 2023-11-20Watts says square waves contain no transients, so a perfect DAC reproduces a bandwidth-limited square wave with Gibbs phenomena and no reconstruction timing error. Head-Fi, Nov 2023
• 2023-12-02Watts says a bandwidth-limited square wave must show ringing, and a DAC that reproduces one without ringing fails in the time domain. Head-Fi, Dec 2023
• 2023-12-02Watts says his DACs reproduce square waves with correct ringing and Gibbs overshoot, without clipping thanks to filter headroom, and a DAC without ringing is not bandlimiting. Head-Fi, Dec 2023
• 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
• 2024-04-08Watts rebuts a claim that more taps make transients collide, saying longer sinc filters make transients independent, and each tap doubling improved sound. Head-Fi, Apr 2024
• 2024-05-16Watts says every DAC converts samples to a continuous waveform to recover transient timing, and an infinite sinc filter with infinite processing would reconstruct it perfectly. ConvinceMeAudio 6:22
• 2024-07-12Watts says sampling theory is the heart of digital audio. HIFICLUB 8:08
• 2024-07-12Watts says Shannon's sampling theory is 100 percent correct, but its proof needs a sinc function that decays over an infinite period of time. HIFICLUB 8:13
• 2024-07-12Watts says any interpolation filter that is not a sinc loses transient timing, his 1980s realization that digital would always be flawed. HIFICLUB 9:04
• 2024-07-12Watts says digital needs complexity, ideally infinite taps; a NOS filter is a first-order hold, the crudest interpolation filter, liked mistakenly because it sounds soft and warm. HIFICLUB 28:56
• 2025-03-25Watts argues comparing DAC output with original sampled data is pointless since an ideal DAC reconstructs the original signal, and says his son Daniel is building the pro ADC project. Head-Fi, Mar 2025
• 2025-03-26Watts explains causal versus symmetric acausal filters, says interpolation pre-ringing at 22kHz is not an issue but EQ should be causal, and lists his CanJam schedule. Head-Fi, Mar 2025
• 2025-03-27Watts says the real issue is full sinc coefficients rather than reversibility, since only full sinc reconstructs perfectly, and that reconstruction up to 104MHz is more complex than discussed. Head-Fi, Mar 2025
• 2025-05-12Watts says digital audio's problem is transient timing: pitch, soundstage, timbre and note starts and stops come from transients, and the DAC must recover the waveform between CD samples. Audiophile Junkie 3:35
• 2025-05-12Watts says a simple interpolation filter gives a transient error of around 100 microseconds, as do NOS, IR, minimum phase and MQA filters; an infinite sinc filter reconstructs perfectly. Audiophile Junkie 5:21
• 2025-05-12Watts says sampling theory shows perfect reconstruction of transient timing needs infinite taps with sinc coefficients, defines taps, and says such a filter pre-rings and post-rings indefinitely. Audiophile Junkie 6:08
• 2025-05-12Watts says pre-ringing is essential to recover transient timing, that more pre-ringing means more accurate reconstruction, and that a bandlimited impulse is perfectly reproduced by a sinc filter. Audiophile Junkie 7:18
• 2025-05-12Watts says that despite infinite pre- and post-ringing, the original impulse ends up perfectly reconstructed. needs context Audiophile Junkie 8:02
• 2025-05-12Watts says finding the best-sounding FIR filter took him over 40 years; theory requires all coefficients to be sinc, but using only sinc in an interpolation filter causes a problem. Audiophile Junkie 8:14
• 2026-03-17Watts says a DAC must rebuild a continuous waveform with accurate transient timing, which improves timbre, separation, location and pitch, but the filters needed enormous processing impossible in the 1980s. ecoustics 2:18
• 2026-03-17Watts agrees and says the aim is to reconstruct the original analog waveform, not a digital waveform. ecoustics 6:01
• 2026-03-17Watts says reconstruction must fill in everything between samples to match the original analog from the microphone into the ADC, within 16-bit accuracy. ecoustics 6:10
• 2026-03-17Watts says leaving the data unfiltered gives a distorted signal with stepped edges unlike a 20 kHz sine; in 1980 he calculated 16-bit reconstruction needed well over half a million FIR taps. ecoustics 10:35
• 2026-03-17Watts says only sinc coefficients reconstruct perfectly, a million-tap sinc filter guarantees better than 16-bit reconstruction, and the Hugo M Scaler achieved that. ecoustics 13:56
• 2026-03-17Watts says a regular interpolation filter distorts a CD's information content, while his aim is to preserve it fully; the key information is transient timing embedded in the samples. ecoustics 15:16
• 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
• 2026-10-02Watts says much of an instrument's timbre lies in its transients, and introduces sampling theory, proved using a sinc function. HiFi Buys 19:16
• 2026-10-02Watts says a sinc function, sine x over x, is infinitely long and infinitely oversampled, and such a filter perfectly reproduces a bandwidth-limited signal. HiFi Buys 20:00
• 2026-10-02Watts says digital audio needs an infinitely long sinc function, and anything short of it degrades transient timing, which he saw clearly in 1981. HiFi Buys 20:21
• 2026-10-02Watts concludes that digital audio is fundamentally flawed. HiFi Buys 21:05
• 2026-10-02Watts says his view in the 1980s was that digital was fundamentally flawed, given 1980s technology. HiFi Buys 21:09
• 2026-10-02Watts says it does if an infinite sinc function is used. needs context HiFi Buys 1:33:36
• 2026-10-02Watts says a sinc function is infinitely steep, cutting off at 22.05 kHz. HiFi Buys 1:50:08
• 2026-10-02Watts says more taps approach the ideal infinitely sharp sinc; claims that its ringing is wrong misunderstand sampling theory, which requires zero energy at FS/2. HiFi Buys 1:50:29
• 2026-10-02Watts says an impulse has full energy at half FS, so it is an illegal signal for testing, though useful because it shows the filter's coefficients exactly. HiFi Buys 1:51:31
• 2026-10-02Watts compares it to the paradox of a ball that never reaches a wall by halving the distance. needs context HiFi Buys 1:54:21
• 2026-10-02Watts says music must be band-limited to be reconstructed properly, and an illegal Dirac impulse is valuable because it shows exactly what a single-stage filter does. HiFi Buys 1:54:34
• 2026-10-02Watts says theorists who call ringing unnatural are not reading the maths correctly: the signal must be band-limited and a Dirac impulse is not. HiFi Buys 1:55:48
• 2026-10-02Watts says an ideal sinc filter would pre- and post-ring forever and look awful, yet would reproduce the original signal perfectly as long as it is band-limited. HiFi Buys 1:56:34
• 2026-10-02Watts says if the signal is not band-limited, everything falls apart. needs context HiFi Buys 1:56:55
• 2026-10-14Watts defines pre-ringing as ringing before an impulse and post-ringing after, saying the best interpolation filter, a sinc function, has infinite amounts of both. Part-Time Audiophile 24:20
• 2026-10-14Watts says people object to pre-ringing as a response to the future, yet sampling theory is proven with a sinc function that perfectly reconstructs the signal. Part-Time Audiophile 25:08
• 2026-10-14Watts says sampling theory reconstructs bandwidth-limited signals, needing exactly zero output at 24 kHz for 48 kHz sampling, whereas an ideal impulse has equal energy at all frequencies. Part-Time Audiophile 25:57
• 2026-10-14Watts says a bandwidth-limited impulse would not be a sharp spike, and gestures its shape. Part-Time Audiophile 26:47
• 2026-10-14Watts says a bandwidth-limited impulse through a sinc filter shows no pre- or post-ringing, while 'audiophile' reduced-ringing filters actually ring; sinc matters for transient timing reconstruction. Part-Time Audiophile 27:12
• 2026-10-14Watts says transient timing modulates with past and future signal and the filter structure, while an infinitely long sinc filter would leave no timing uncertainty. Part-Time Audiophile 28:11