Rethinking Magnitude Compression in Spectral Losses for DDSP Parameter Estimation

Byunghoo Park; Jayeon Yi; Minje Kim

cs.SDOct 16, 2026

Rethinking Magnitude Compression in Spectral Losses for DDSP Parameter Estimation

Authors: Byunghoo Park, Jayeon Yi, Minje Kim

Organizations: University of Illinois Urbana-Champaign, Siebel School of Computing and Data Science, USA 61801

Abstract

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	–
$f_{c}$	filter cutoff	1	1
$f_{0}$	fundamental	–	1
$\kappa$	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	$\mathcal{C}_{\mathrm{lin}}$	$\mathcal{C}_{\mathrm{log}}$	difference	$t$
Plate	0.773	0.756	$+0.017\pm 0.007$	$+2.5$
Synth.	0.781	0.771	$+0.010\pm 0.003$	$+3.5$
Reverb	0.711	0.748	$-0.037\pm 0.005$	$-7.8$

Table 2: Concordance of each loss term over the full spectrum, across 100 targets. The difference

\mathcal{C}_{\mathrm{lin}}-\mathcal{C}_{\mathrm{log}}

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.

Panel of Figure 2 — 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

\alpha=0.05

. The last column gives the number of listeners preferring the linear variant.

Parameter Estimation

Parameter estimation studies how to infer unknown quantities in statistical, physical, and machine-learning models from observed data.

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Parameter Estimation

Open paper AskPDF arXiv

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.

Abstract

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