Spectral losses for differentiable digital signal processing (DDSP) commonly compress magnitudes, for example by using log-magnitude terms. Such compression mimics human perception, but whether it helps the optimization is less clear, and is usually found only by comparing trained models. In this work, we show that whether compression helps depends on the system's informative region: the region of its dynamic range that carries the information pointing toward the target. To indicate where this region lies without having to train, we introduce concordance, which measures how well a loss orders candidate parameter settings by their distance from the target. We then compare uncompressed, compressed, and combined losses by fitting a modal plate reverb and a subtractive synthesizer model to target sounds. A third system, selected for its low-energy informative region, tests the relationship in the opposite direction. In every system, the loss that matches the informative region performs best: the uncompressed one where the region lies at high energies, and the compressed one where it lies low. Surprisingly, the common combination of both log-magnitude and linear-magnitude terms performs best in none of the systems. Code and audio examples are available at https://github.com/superstem000/compression-analysis
Figures & tables
Synth.
Reverb
a
amplitude
2
–
fc
filter cutoff
1
1
f0
fundamental
–
1
κ
frequency ratio
1
–
m
oscillator mix
2
1
Q
filter resonance
1
1
Table 1: Estimated parameters of the synthesizer and reverb systems. Numbers give how many of each parameter are estimated; amplitude and oscillator mix are estimated per oscillator.
Figure 1: Log concordance as the loss is restricted to bins within F dB of the target’s peak. The rightmost point, past the dotted line, is the unrestricted loss.
System
Clin
Clog
difference
t
Plate
0.773
0.756
+0.017±0.007
+2.5
Synth.
0.781
0.771
+0.010±0.003
+3.5
Reverb
0.711
0.748
−0.037±0.005
−7.8
Table 2: Concordance of each loss term over the full spectrum, across 100 targets. The difference Clin−Clog is paired per target and given with its standard error. t is the difference divided by its standard error.
linear
log
hybrid
Plate
MFCC (rendered)
7.88
8.76
8.35
NMSE
0.036
0.218
0.221
MFCC (real)
13.92
19.01
15.98
Synth.
MFCC (rendered)
6.91
11.80
12.02
NMSE
0.0072
0.0157
0.0161
MFCC (real)
11.45
14.01
12.76
Table 3: MFCC distance and parameter NMSE for each loss variant. Lower is better. NMSE is available for rendered targets only.
Figure 2: Listening test ratings of overall similarity to the reference, over 12 items and seven listeners. Error bars are 95% confidence intervals pooled over all ratings.
System
linear − log
95% CI
p
listeners
Plate
+15.7
[+4.1,+27.3]
0.016
6/7
Synth.
+6.9
[+0.8,+13.1]
0.033
6/7
Table 4: Listening-test contrast in each experiment. Differences are tested with a paired t -test on per-listener means over 12 items and seven listeners, two-sided at α=0.05 . The last column gives the number of listeners preferring the linear variant.
Dynamic Range Compression (DRC) is a widely used nonlinear audio effect whose parameters are often unknown, making blind estimation and inversion challenging. In this work, we formulate DRC parameter estimation as a black-box optimization problem in a perceptually motivated feature space. Given an observed signal and a reference representation, we estimate the parameters that minimize the distance between feature descriptors of the reconstructed and reference signals. Unlike gradient-based approaches, the proposed method does not require differentiability of the DRC model or the feature extraction pipeline, enabling the use of nonlinear and histogram-based descriptors. Experimental results demonstrate that the proposed method achieves competitive performance in blind parameter estimation and dry signal recovery, outperforming or matching state-of-the-art models in terms of reconstruction quality.
Compressed music restoration aims to recover high-fidelity audio from lossy codecs such as MP3 by restoring missing spectral content and reducing coding artifacts. Recently, generative adversarial networks and band-split models have made progress in compressed music restoration. However, existing methods either operate without explicitly modeling phase or rely on predefined frequency partitions, which may limit restoration performance and the use of input-dependent frequency information. To address these issues, we propose MPASCNet, a Magnitude-Phase-Aware Adaptive Spectral Compression network. Instead of using fixed bands, MPASCNet combines magnitude and phase features to guide cross-attention, adaptively compressing full-resolution spectral features into compact tokens. These tokens are then processed by a spectro-temporal backbone to model spectral-temporal dependencies. Finally, separate decoder branches reconstruct the full-resolution magnitude and wrapped phase spectra. Experiments on MP3 restoration show that MPASCNet outperforms the Apollo and AEROMamba baselines across multiple restoration metrics while using only 6.49 M parameters. The code is available at https://github.com/xinghour/MPASCNet.
Xinlong Deng, Yu Xia, Qiuqiang Kong +2
College of Artificial Intelligence, China University of Petroleum, Beijing · Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong, China · Institute of Acoustics, Chinese Academy of Sciences
A differentiable digital signal processing (DDSP) autoencoder reconstructs a monophonic harmonic sound through three types of synthesis parameters: fundamental frequency, loudness, and timbre features. To handle mixtures of harmonic sounds within the DDSP approach, we have previously proposed a DDSP mixture model (DDSPMM). It represents a mixture as the sum of source signals synthesized by the decoders of pretrained DDSP autoencoders. Although DDSPMM enables direct estimation of synthesis parameters of each source from mixtures, it does not explicitly model temporal variations in the synthesis parameters and can produce excessive temporal fluctuations. In this paper, we propose a method for estimating synthesis parameters with temporally plausible trajectories by incorporating a denoising diffusion probabilistic model (DDPM) into the DDSPMM-based estimation. The DDPM is trained as a generative model of synthesis parameters. During estimation, the proposed method guides the DDPM reverse diffusion process with the reconstruction error between the observed mixture and the mixture synthesized by DDSPMM from the current estimates. Experiments on woodwind and string instrument ensembles showed that the DDPM-based regularization improves synthesis parameter estimation by imposing temporal plausibility on the estimated trajectories.