01 · The problem
A finite range
A large input saturates an ordinary ADC. Widening its range at the same bit depth coarsens every quantization step.
Computational Sensing and Imaging Lab · Imperial College London
Digital audio, reimagined.
Every recorder has a ceiling. Exceed it and loud peaks are cut away; turn the gain down and quiet detail sinks into quantization noise.
USF Audio folds large signals back into range in analog electronics, before they are digitized, then recovers the full waveform with mathematics.
6-bitconverter budget in the hardware experiments
≥ 18 dBmore dynamic range than conventional capture
14real-world recordings made through the prototype
52listeners in a perceptual study
01 · Listen
What happens when sound exceeds the recording range?
Narrow the recording limit, then compare clipping, folding and recovery, and listen to all four signals. Start with a simple wave, then switch to a piano passage.
About this demo. A digital simulation using a newly synthesized phrase of Beethoven’s public-domain melody. Folding is exact wrap-around, and recovery is a simple numerical method applied to the folded samples. Clipped, folded and recovered audio share the same 8-bit budget. Accurate recovery depends on the sound being smooth enough between samples. This is not a recording from the USF Audio prototype or the paper’s recovery algorithm; the hardware experiments, which use a 6-bit converter, follow below. Everything runs in your browser.
Can quantization noise itself carry recognizable music? A companion research note explores this, with equations, audio and reproducible code.
Read the research note02 · See the spectrum
Folding scrambles the spectrum. Recovery restores it.
Spectrograms of the same piano phrase: time runs left to right, pitch rises upward, and darker means louder. Clipping smears energy into extra harmonics. Folding scatters it across the band, yet keeps everything needed to restore the original. Click any spectrogram to hear it.
Recovered · 48.4 dB SNR
Folded measurements
Digital simulation, same model as the lab above: 8 bits, recording limit ±0.50, newly synthesized Für Elise phrase, 0–8 kHz. Headphones recommended; levels are matched across signals.
03 · The idea
Clipping destroys information. Folding re-encodes it.
A conventional converter flattens every peak beyond its range. USF Audio’s analog circuit wraps the signal back into range instead. The result looks unusual, but its structure is what makes recovery possible.
02 · Acquisition
Fold before digitizing
An analog folding circuit maps the large signal into a small voltage interval, which is then sampled and quantized.
03 · Recovery
Reconstruct with mathematics
Algorithms exploit the signal’s structure and the fold pattern to recover the high-dynamic-range waveform.
The technical view
Modulo acquisition
Modulo acquisition
The ideal folding operator and the sampled measurements are
\[\mathscr M_{\lambda}(g)=\bigl((g+\lambda)\bmod 2\lambda\bigr)-\lambda,\qquad y[n]=\mathscr M_\lambda\bigl(g(nT)\bigr).\]
Unlike clipping, this encodes a large signal with bounded measurements. Recovery requires suitable signal and sampling conditions; the recovery algorithm also handles the non-idealities of real hardware.
04 · Hardware
Built into the hardware, not added as an effect.
USF Audio acts before any audio samples exist. A microphone feeds a custom modulo analog-to-digital converter, followed by a numerical recovery pipeline. Circuit, measurements and recovered waveforms were tested together, not just simulated.
Hardware–software co-design
The physical signal is folded in analog electronics, digitized by an ordinary low-bit converter, and reconstructed by algorithms designed for folded measurements.
Conventional and folded acquisition share the same nominal 6-bit budget. The system was evaluated on speech, music, heart sounds, environmental sounds and more.
See the measured results- MicrophoneSound becomes voltage
- Analog foldingBounded representation
- Low-bit ADCDigital measurements
- RecoveryWaveform reconstruction
One-minute explainer
Why folding is different from cutting off peaks
An animation of the central idea: from a limited recording range, through analog folding, to mathematical recovery. The animation explains the mechanism; the paper provides the laboratory validation.
05 · Evidence
What the experiments show.
Two separate questions. Does the converter capture a wider range with finer detail? And can listeners hear the difference when conventional capture is constrained?
≥ 18dB
Dynamic range
Measured improvement over conventional acquisition.
≥ 14dB
SINAD
Signal-to-noise-and-distortion improvement in the reported tests.
≥ 1.5bits
Effective resolution
Improvement in effective number of bits (ENOB).
Controlled hardware tests · 6-bit converter
52 participants · 10 excerpts
What did listeners hear?
In the constrained 6-bit hardware regime, listeners rated USF Audio well above conventional capture. Across the five hardware clips, the participant-level difference is ΔMOS = +0.592.
In a high-precision digital control, 24-bit USF Audio and a 32-bit conventional reference were rated essentially the same (4.16 vs. 4.15; p = 0.749). The advantage appears where conventional capture is range-limited, not as a claim that every recording sounds better.
Mean opinion score1–5 · higher is better
Clipped
1.62
Conventional
3.22
USF Audio
3.81
Table VII of the paper: absolute category rating study, means over participant–clip ratings.
06 · Questions
Questions worth asking.
Plain answers first; open the technical view to go further. Every answer is grounded in the paper and separates demonstrated results from future goals.
Why do loud sounds distort when recorded?
Every conventional recorder accepts a limited input range. Beyond it, the recorded values saturate: different large amplitudes collapse to the same clipped value, so their true heights are lost.
Try the interactive demo and narrow the recording limit.
Technical view
Clipping implements \(C_\lambda(x)=\min\{\lambda,\max\{-\lambda,x\}\}\). Every \(x\geq\lambda\) produces the same output, so the map is not injective, even pointwise.
What does USF Audio do differently?
It changes the measurement itself. An analog circuit folds the incoming voltage into a small range instead of cutting off the peaks, and software reconstructs the larger waveform.
Technical view
Acquisition applies a modulo operator \(\mathscr M_\lambda\), followed by sampling and quantization. Recovery is enabled by the combined hardware–algorithm architecture, not by the modulo map alone.
If the waveform is folded, isn’t information lost?
A single folded sample does not reveal how many times it wrapped. But audio samples are related in time, and those relationships make the missing fold information recoverable. That is why sampling theory and reconstruction algorithms matter.
Technical view
Under ideal folding, \(g(nT)=y[n]+2\lambda k[n]\) for an integer-valued fold sequence \(k[n]\). A suitable signal model and sampling regime allow this structured integer ambiguity to be resolved.
Why not just turn down the microphone gain?
Lower gain avoids clipping, but shrinks faint details relative to the converter’s quantization step and noise. USF Audio aims to accommodate a wide range without proportionally sacrificing small details.
Technical view
At a fixed nominal bit depth \(B\), a wider uniform quantizer range means a larger step size. Folding restricts the analog values reaching the quantizer and shifts the challenge to structured signal recovery.
Has USF Audio been demonstrated in physical hardware?
Yes. The paper reports a microphone front end, a custom modulo ADC and numerical reconstruction working together. Fourteen real-world recordings, including speech, music and biological sounds, were acquired through the hardware.
Can listeners actually hear an improvement?
In the range-limited 6-bit hardware experiment, 52 listeners gave USF Audio an average of 3.81/5 and conventional audio 3.22/5. High-bit recordings already sounded very good in both conditions, with essentially equal scores.
Does USF Audio always sound better than conventional audio?
No. The advantage arises when acquisition is constrained by input range and resolution. In the high-bit comparison, 24-bit USF Audio and the 32-bit reference were perceptually indistinguishable. This is about extending what acquisition can capture, not improving every file.
Is USF Audio a declipping app or an AI enhancer?
No. Declipping starts after a recorder has saturated and guesses what is missing. USF Audio changes what is captured in the first place. Its recovery algorithms work on deliberately folded measurements, not on a clipped recording.
Does USF Audio overturn the Shannon–Nyquist theorem?
No. It changes how amplitude is represented before digitization. Sampling rate, bandwidth and smoothness remain critical to reliable recovery.
Technical view
USF theory studies the invertibility of sampled modulo measurements under bandlimited and other structural assumptions. Sampling rate and bit depth remain design variables; the folding threshold is not a licence for unlimited bandwidth.
Why not simply record at 24 or 32 bits?
High-bit recording can be excellent, and USF Audio does not dispute that. The research asks a different question: what can a converter capture under a fixed bit depth, input range and hardware budget?
Technical view
In a conventional uniform quantizer, resolution and dynamic range are coupled. Bounded modulo acquisition lets reconstruction recover a range larger than the ADC’s instantaneous input interval.
What does quantization noise have to do with music?
Surprisingly, the tiny difference between a waveform and its quantized version can still carry recognizable music. This is not a hardware demo, but it illustrates a larger idea: useful information need not look like the waveform we are used to recording.
Open the Für Elise research note →
Technical view
For ordinary PCM, the quantization noise is \(e_B[n]=x[n]-Q_B(x[n])\). For a uniform, unsaturated quantizer it is a centered modulo representation. In USF Audio, by contrast, folding is a deliberate analog operation performed before digitization.
Is this a real-time commercial recorder? Does it save energy?
Not yet. The implementation is a research prototype that demonstrates capture and reconstruction. Lower-latency recovery, tighter hardware integration and measured power efficiency are future goals; the present study does not establish an energy saving.
Can I reproduce the experiments myself?
Code and data are coming soon. Reproducing the paper’s analog hardware experiments will also require the corresponding hardware and acquisition system.
No questions match. Try another term, or choose “All”.
07 · Go deeper
From hearing the result to understanding the representation.
Behind USF Audio lies a deeper question: must useful digital measurements resemble the original analog signal at all?
Research note 01 · Interactive
Can you hear Beethoven in quantization noise?
The same ten seconds of Für Elise at 2, 4 and 8 bits. Listen to the noise itself, and examine its waveforms, spectra and mathematics.
Open the research noteCode & data
Coming soon
Python source, notebook and audio data for the research note will be released here.
The research note is a digital signal-processing experiment, separate from the paper’s hardware recordings.
Tutorial
USF-Audio for graduate students
Six chapters with live explorers: PCM limits, folding, the bit–sampling law, spectral moments, the USF-ARA algorithm and the hardware evidence.
Start the tutorial → PaperRe-thinking Digital Audio via Unlimited Sensing
Theory, recovery algorithms, hardware validation and a 52-person listening study. R. Guo, Y. Zhu and A. Bhandari.
Read the PDF → Research noteHearing Für Elise in quantization noise
Audio at 2, 4 and 8 bits, with equations and quantitative figures. Code and data coming soon.
Open the note → ArchiveUnlimited Sensing research archive
Foundational work on unlimited sensing and its applications across sensing and imaging.
Visit the archive ↗