The Precision Journal
The Architecture of Temporal Fidelity
Chapter I—Upsampling and Digital Filters
The Paradox of Perfect Specs
On paper, today's best DACs appear nearly perfect. Frequency response is flat within fractions of a decibel, and distortion vanishes into the noise floor at –120dB or below. By conventional metrics, digital audio was effectively solved decades ago.
Yet listeners—especially those familiar with live, unamplified music—continue to report differences in spatial stability, transient precision, harmonic density, and tonal substance between components whose measurements appear indistinguishable. The gap between what we measure and what we hear is not shrinking; it is becoming more conspicuous.
The explanation lies in a limitation embedded in our measurement vocabulary. Most conventional metrics quantify magnitude—how much deviation exists at a given frequency, how much distortion is added, how much noise remains. They say very little about sequence. They do not tell us when energy arrives, how long it lingers, or how precisely its internal relationships are preserved.
This installment examines the first and most consequential point at which that temporal sequence can be altered: the reconstruction stage of digital conversion. Before a signal is converted to analog form, it is interpolated, filtered, and mathematically reshaped. Digital filtering and upsampling are not peripheral implementation details; they are structural decisions. And it is here, at the moment of reconstruction, that time-domain fidelity is either preserved—or compromised.
Music Unfolds in Time
Consider what happens when a violinist draws the bow across a string. The motion does not simply produce a tone; it sets a mechanical system into motion. The string vibrates, establishing a fundamental pitch. That vibration transfers through the bridge into the body of the instrument—the plates and the enclosed air—each responding according to its material and geometry. Energy moves step by step, not all at once. Some elements react immediately; others respond fractions of a moment later as vibration propagates through wood and air. What we hear is the result of this ordered sequence.
The sound is not a single frequency but a coordinated emergence of fundamentals and harmonics, rising, stabilizing, and eventually decaying as energy dissipates into the surrounding space. The spectrum we measure is a description of this event. The event itself is temporal: a progression of energy transfers unfolding across microseconds and milliseconds.
Human hearing is acutely attuned to that progression; it detects subtle disruptions in timing even when comparable irregularities in frequency or phase pass largely unnoticed. We localize sound, perceive distance, and recognize instrumental character through timing relationships—onset cues, harmonic alignment, and decay patterns. When those relationships remain intact, reproduction feels natural. When they are altered, even subtly, the ear detects the difference.
The critical question, then, is how digital systems reconstruct this unfolding sequence. That process begins with upsampling and digital filtering.
Upsampling and Digital Filtering: Necessary Reconstruction
Upsampling and digital filtering are the first stages in the conversion process where time-domain errors are typically introduced. Before the signal ever reaches the analog circuitry, its shape is mathematically reconstructed. The way this reconstruction is handled determines whether the original temporal relationships are preserved—or reshaped.
Before any digital signal can be converted to analog, it must be rebuilt into a smooth, continuous waveform. Digital audio stores sound as a series of individual snapshots taken in rapid succession. On their own, those samples do not form a flowing curve; they mark discrete points in time. Upsampling is the process that enables that curve to be reconstructed. By calculating additional, precisely positioned intermediate samples between the originals, it increases the resolution with which the waveform can be described, allowing its shape to emerge with greater accuracy. Reconstruction filters then remove unwanted high-frequency artifacts created by the sampling process and define the usable bandwidth of the system. Together, these steps create a coherent, high-resolution digital waveform that can be handed off to the converter, where it is finally transformed into a continuous analog signal.
These processes are not optional; without them, accurate conversion is impossible. But they are not neutral either. The mathematical choices that govern interpolation, filter length, phase behavior, and transition-band steepness determine how sharply a transient forms, how harmonics align as they develop, and how long energy persists. In short, reconstruction does not merely rebuild amplitude—it determines how energy is distributed across time.
How Conventional Upsampling and Filtering Reshape the Time Domain
It is within the upsampling and reconstruction filtering stage that time can first be meaningfully altered. The mathematical decisions made during interpolation and image suppression determine how energy is positioned around each event in time.
Every filtering strategy carries temporal consequences. Linear-phase designs may preserve frequency balance while redistributing energy symmetrically around a transient. Minimum-phase approaches eliminate pre-ringing but shift energy later in time. Longer filters narrow transition bands yet extend their influence further into the event. In each case, the objective may be spectral precision; the cost is temporal redistribution.
When that redistribution overlaps with the leading edge of a piano note, the bite of a saxophone reed, or the alignment between a fundamental and its overtones, the ear does not perceive an abstract error. It perceives a change in immediacy, density, and spatial stability. The time domain—the order in which energy rises, aligns, and decays—is the framework through which musical authenticity is judged. Digital filtering and upsampling are therefore the first structural point at which those relationships can be reshaped. Once altered at this stage, they cannot be restored downstream.
Figure A
Figure A (Above) — Linear-Phase Filtering: Symmetrical Temporal Smear
A conceptual illustration of linear-phase upsampling and reconstruction filtering. The preserved signal (blue) shows energy arriving in ordered succession: a clean attack followed by a harmonically aligned decay. The linear-phase result (orange) exhibits symmetrical pre- and post-ringing around the transient. Because the impulse response is symmetrical, energy appears both before and after the event. Although frequency response remains flat and phase relationships are mathematically linear, the transient is redistributed across time, subtly softening attack definition, harmonic integrity, and spatial precision.
Figure B (Below) — Minimum-Phase Filtering: Frequency-Dependent Temporal Smear
A conceptual illustration of minimum-phase upsampling and reconstruction filtering. Pre-ringing is eliminated, but energy is shifted entirely after the transient. The result is frequency-dependent delay: higher-frequency components are displaced differently from lower ones, altering harmonic alignment as the event unfolds. The attack remains visually sharp at onset, yet the internal temporal structure of the harmonic bloom is reorganized. The spectrum may measure similarly, but the timing relationships that define instrument character are no longer identical.
Figure B
Classical Digital Filter Tradeoffs
Modern DAC designers confront an unavoidable reality: reconstruction filtering involves trade-offs. Some manufacturers even provide multiple filter options within a single unit, effectively turning engineering compromises into user preferences.
One common approach—linear-phase finite impulse response (FIR) filtering—achieves extremely flat frequency response and keeps harmonic phase relationships mathematically aligned. The cost is ringing around each transient. A ripple appears both before and after the event, spreading what should be a sharply defined moment across a brief slice of time. The leading edge softens. The end of the note becomes less clearly defined.
Another approach—minimum-phase FIR filtering (including so-called apodizing variants)—removes the ripple that occurs before the transient. Nothing appears ahead of the event, which sounds intuitively correct. But the trade-off shifts. More energy trails behind the transient, and the relative timing between harmonics changes. The frequency response may remain accurate, yet the internal timing of the note is no longer identical.
A third strategy increases filter length and tap count to improve measured performance. In practical terms, this means the algorithm consults a larger window of samples—both before and after the moment being reconstructed—to calculate each output value. While this can sharpen frequency-domain metrics, it also extends the filter’s influence in time. Each reconstructed point becomes dependent on information drawn from adjacent musical moments. The effect is this: the start of a note carries a trace of what came before, and its decay blends slightly into what follows. The temporal boundaries between events soften, and transient precision is incrementally reduced.
All of these designs can measure superbly. Each, however, changes how energy is distributed over time. The measurements converge in the frequency domain; the differences listeners perceive arise in the time domain. Once the event is reshaped at this stage, it cannot be restored later in the signal chain.
The PEtER Spline Filter: A Different Reconstruction Philosophy
In digital audio, high-end audio designers choose among established filtering compromises. CH Precision did not choose among them—it invented a different approach. The PEtER spline filter is a proprietary CH development, created to address time-domain distortion at its origin rather than manage its side effects.
A spline filter reconstructs a waveform by connecting discrete sample points with smooth, mathematically continuous curves rather than forcing them through an idealized brick‑wall template. In CH Precision’s implementation—PEtER, short for Polynomial Equations to Enhance Resolution—this spline-based interpolation defines the reconstruction process itself.
Where conventional filters begin with a frequency-domain target and manage the side effects, PEtER begins with the waveform. Its objective is continuity in time: preserving the natural curvature of the signal as it unfolds between samples. Instead of correcting artifacts after they appear, it minimizes their formation at the source.
On conventional frequency-response plots, CH DACs and their competitors may look similar. In the time domain, they do not behave the same. By preserving temporal structure at the reconstruction stage, PEtER Spline uspsampling enhances rhythmic precision, stabilizes harmonic relationships, and maintains spatial coherence. Instruments occupy defined positions. Silence remains unpolluted. Musical flow remains intact. This preservation of temporal integrity rarely appears in standard measurements, yet it governs how music feels—whether rhythm propels forward, whether overtones integrate naturally, whether the acoustic space holds together. PEtER addresses the time-domain problem at its origin, establishing a coherent temporal foundation before the signal reaches the converter. All CH Precision digital platforms are built upon this principle.
Figure C
Figure C (Above) — Time-Domain Energy Settling: Linear Filter vs. CH Spline Filter
This plot compares the time-domain settling behavior of a classical windowed-sinc linear-phase FIR filter (blue) and the CH Spline Filter (orange) using normalized accumulated energy (NAE), which tracks how quickly impulse energy accumulates around the main transient (t = 0). The linear filter exhibits a distinct oscillatory transition, reflecting symmetric pre- and post-ringing and a broader temporal energy spread. In contrast, the CH Spline Filter shows a smoother, monotonic energy build-up with much tighter time localization and negligible ringing contribution. The result is faster effective settling and dramatically improved temporal coherence, with far less time-domain smearing around the reconstructed transient.
Figure D (Below) — Temporal Behavior: Original Signal vs. Spline-Based Filtering
This conceptual plot compares the original signal (blue) with spline-based upsampling and filtering (orange, dashed). The spline approach preserves precise peak alignment with the source transient while nearly eliminating pre-ringing ahead of the event. Following the main impulse, the spline response settles in line with the original, exhibiting temporally correct extension and decay tail. The result is an accurate temporal construction of energy around the transient, maintaining sequence integrity without post-event ringing and spread.
Figure D
The C1.2: Elevated Temporal Fidelity
In the C1.2 Digital to Analog Controller, CH Precision has evolved its temporal reconstruction strategy by significantly expanding the processing headroom available to the proprietary PEtER spline algorithm. A four-fold increase in computational power, combined with 32-bit fixed-point processing, allows the C1.2 to apply PEtER across a broader range of high-resolution formats — including PCM up to 768 kHz and native DSD512 — while maintaining the stringent continuity and smoothness that define temporally coherent reconstruction.
Unlike conventional upsampling schemes that interpolate via zero insertion and selectable linear- or minimum-phase filters, each introducing some degree of temporal redistribution, PEtER in the C1.2 reconstructs the waveform as a continuous spline curve. This approach preserves the integrity of the original digital samples while substantially reducing pre- and post-ringing artifacts, allowing transients to remain sharp and harmonic relationships to stay aligned as they unfold in time. Crucially, this refined implementation of PEtER forms the temporal foundation for all downstream processing in the C1.2’s digital domain. By addressing continuity at the earliest stage, the C1.2 ensures that timing cues, the very sequence that makes music feel immediate and alive, are established long before the signal reaches the analog output stage.
The C10: Spline Interpolation and Temporal Fidelity
In the C10 Reference DAC, PEtER is implemented as a proprietary spline-based interpolation and upsampling engine that reconstructs the digital waveform before conversion. Operating in 32-bit fixed-point precision, PEtER upsamples incoming PCM data by up to 64×, raising, for example, a 44.1 kHz signal to 2.8224 MHz and a 48 kHz signal to 3.072 MHz. Unlike conventional approaches that introduce zero-filled samples and then suppress images with a choice of linear-phase, minimum-phase, or mixed filter topologies — each with its own trade-offs in pre-/post-ringing and phase behavior — the spline algorithm interpolates the waveform as a continuous curve, preserving the integrity of the original sample values while minimizing the temporal redistribution typical of these other methods.
By establishing smooth continuity between samples—while nearly eliminating pre- and post-ringing—PEtER delivers a high-frequency, temporally coherent digital signal whose onset behavior, harmonic alignment, and decay structure are defined with precision before any analog conversion occurs. In the C10, this disciplined reconstruction establishes the temporal foundation upon which the entire conversion process is built, ensuring that what ultimately reaches the analog domain is not merely accurate in magnitude, but structurally faithful to the original musical event.
Stay Tuned For More
At this point in the signal chain, CH Precision’s PEtER spline filter has delivered a digitally reconstructed waveform whose temporal structure closely mirrors the original event: onset intact, harmonic relationships preserved, decay unencumbered by unnecessary extension. The digital signal is now temporally coherent. The next question is what happens when that signal is converted to analog form.
In the next article, we will turn from filtering to conversion itself. Why does CH Precision employ a deterministic multi-bit R‑2R architecture rather than the more common delta‑sigma approach? The answer is not sentimental; it is temporal. We will examine how conversion topology influences noise shaping, switching behavior, and time-domain determinism—and why CH believes that preserving temporal coherence requires architectural choices made long before the signal reaches the analog stage.