Why DSEE?
Lossless audio codecs (FLAC, WAV) can preserve the full 20Hz-22.05kHz spectrum. But real-world digital music sources are far less ideal — MP3/AAC lossy encoding basically flattens everything above 16kHz, and old recordings' microphones and analog tape never captured enough high-frequency overtones. Even modern recordings with sample rates below 96kHz hit the Nyquist wall at 20kHz.
For the final presentation of SACD products, we want the master's band to extend to 30kHz or even 50kHz+ — not for the ear to "hear" it (the human limit is about 20kHz), but so the filter transition band in the audible range is gentler, high-frequency intermodulation distortion is lower, and most importantly: to push the DSD modulator's noise shaping further into the ultrasonic region, creating a cleaner background in the 2k-8kHz band where the ear is most sensitive.
The traditional approach is plain upsampling — using high-quality FIR filters to double or quadruple the sample rate. But upsampling produces no new information; it only changes how information is presented. A 44.1kHz/16bit MP3 upsampled to 88.2kHz still has an empty 16-22kHz range (only smooth interpolation transitions, no real harmonic structure).
DSEE takes a different approach: generate high-frequency harmonics from the existing low-frequency harmonics.
Technical Principle: SSB Frequency Shifting
The core of DSEE is single-sideband (SSB) frequency shifting based on the Hilbert transform — a classic technique from communications engineering: modulating a baseband signal onto a higher carrier frequency while keeping only the upper sideband (LSB suppressed).
The Mathematics
Given a real signal x(t), its Hilbert transform is:
x_h(t) = H{x(t)}
The Hilbert transform is equivalent to a -90° phase shift: -90° for positive-frequency components, +90° for negative-frequency components.
Construct the complex analytic signal:
x_a(t) = x(t) + j·x_h(t)
This signal's spectrum exists only at positive frequencies; negative frequencies are zero. Multiply the analytic signal by the complex exponential e^{jωt}:
x_a(t)·e^{jωt} = (x(t) + j·x_h(t))·(cos(ωt) + j·sin(ωt))
Taking the real part yields the upper-sideband (USB) shifted signal:
y(t) = Re{x_a(t)·e^{jωt}} = x(t)·cos(ωt) - x_h(t)·sin(ωt)
This formula neatly shifts every frequency component of x(t) upward by ω. If x(t) contains components at 1kHz, 5kHz and 8kHz, the output contains 1+Δf, 5+Δf and 8+Δf — high-frequency harmonics thus "grow" out of the original signal.
DpdoEngine's Implementation
The DSEE processor extends the basic SSB principle:
- 8× frequency-shift stacking — instead of shifting once, shift 8 times: Δf, 2Δf, 3Δf … 8Δf, forming a dense extended harmonic layer
- Exponential decay — each shift's gain decays exponentially (decay=0.5); farther shifts are weaker, matching the natural decay of real instrument harmonics
- 3kHz pre-HPF — filters low-band energy before the SSB chain so large low-frequency amplitudes don't dominate modulation, letting mid/high frequencies lead harmonic generation
- 16kHz post-HPF — keeps only SSB products above 16kHz, ensuring the extension layer doesn't pollute the audible mid/low band of the original signal
- Adaptive gain — the extension layer's peak never exceeds 50% of the original signal, avoiding harsh high-frequency overboost
- Wet/dry mixing — the full-chain group delay (pre-HPF + LPF + Hilbert + post-HPF) is aligned with the dry signal for phase-coherent mixing
The 14kHz pre-LPF: A Necessary Trade-off
Why add an LPF?
The Hilbert transform is implemented in practice as a finite-order FIR filter (DpdoEngine uses a 63-tap Kaiser-windowed Hilbert FIR). An ideal Hilbert needs infinite impulse response — the finite approximation introduces imperfect transition response at high frequencies.
The DSD conversion chain typically includes an 88.2kHz upsampling stage (44.1kHz→88.2kHz). Upsampling interpolation produces image-frequency residues near Nyquist — even after high-quality FIR filtering, stopband attenuation cannot be infinite. When these image residues enter the SSB modulator along with the original signal, they produce lower-sideband intermodulation products that fold back into the audible band (20Hz-20kHz).
This leakage shows up on the spectrum as a stretch of continuous broadband noise — especially in passages with no signal (silence), where this noise "floats above the noise floor," harming background blackness.
What the LPF does
Applying a low-pass filter to the signal before the Hilbert transform — blocking content above 14kHz from entering the SSB chain — is precisely to prevent this intermodulation leakage. DpdoEngine uses a Kaiser-windowed FIR LPF (161 taps @88.2kHz, ~60dB stopband attenuation) with cutoff near 14kHz and a complete transition band of 14-16kHz.
This means DSEE only works when the original signal has content at ≤14kHz. Original content in 14-22kHz does not participate in SSB shifting — but that content is already polluted by image residues during upsampling, so better left out.
The Inherent Trade-off
The LPF's side effect is removing material that could be used for SSB intermodulation. In our tests:
- No LPF: DSEE produces about +5.4dB enhancement in the 12-16kHz range
- Correct LPF (161-tap Kaiser): enhancement drops to about +1.6dB
- Delayed-pulse placeholder (delay only, no filtering): enhancement recovers to +5.2dB → proving delay itself doesn't affect DSEE; the reduction comes from the high-frequency material removed by the LPF
This is an inherent trade-off, not a bug: removing upsampling artifacts (the source of SSB leakage) necessarily reduces the material available for SSB intermodulation. On real full-band music signals (rather than test sine sweeps), the LPF's reduction is partially compensated by broadband intermodulation, because the spectral density of 20Hz-12kHz is far higher than test signals.
SSB cos/sin alignment fix
In the initial DSEE implementation, the cos term used the raw signal (unfiltered) while the sin term used the Hilbert-transformed signal (full LPF + Hilbert path). The filter-path difference between the two branches caused a measurable deviation in the SSB formula — the cos term represented "signal with LPF" and the sin term "signal with LPF + Hilbert," inconsistent in time alignment and spectral response.
DpdoEngine's current implementation fixes this: both the cos and sin terms use the same post-LPF signal (d_lpf), and the cos term additionally passes through filterDelayHilb_ delay alignment to match the Hilbert output's group delay. This fix makes the SSB modulation mathematically self-consistent, with clean SSB USB output.
Effect Metrics
| Test signal | Band | No LPF enhancement | Correct LPF enhancement |
|---|---|---|---|
| 1kHz sine MP3 320kbps | 14-22kHz | ~+6.3dB | ~+1.6dB |
| 1kHz sine MP3 320kbps | 6-12kHz | ~+8.8dB | ~+8.8dB |
| Real music (broadband) | 16kHz+ | pending | expected better than sine tests |
Key observation: enhancement in the 6-12kHz band is unaffected by the LPF (+8.8dB with or without LPF), because the original signal in that band itself participates in SSB intermodulation, and its products land in the 20kHz+ ultrasonic region, untouched by the 14kHz LPF. The LPF's impact is concentrated on the transition band near 14kHz and SSB products above it.
Conclusion
DSEE is not magic — it cannot create overtones that don't exist in the instrument. It is signal processing: starting from an existing signal, generating high-frequency extension consistent with its harmonic structure via Hilbert SSB frequency shifting.
The 14kHz pre-LPF illustrates a general principle: any signal enhancement technique must balance "adding content" against "avoiding introduced noise." DSEE's LPF chooses the latter — sacrificing some extreme-high-frequency enhancement rather than allowing imperfect SSB modulation to leave audible pollution in the audible band.
DpdoEngine's DSEE is now integrated into the PCM→DSD mastering chain. To experience DSEE's high-frequency extension on your work, contact us for a trial version.