{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:21:15Z","timestamp":1760059275392,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Slovak Research and Development Agency","doi-asserted-by":"publisher","award":["APVV-22-0508","VEGA 1\/0039\/24"],"award-info":[{"award-number":["APVV-22-0508","VEGA 1\/0039\/24"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education, Research, Development, and Youth of the Slovak Republic","award":["APVV-22-0508","VEGA 1\/0039\/24"],"award-info":[{"award-number":["APVV-22-0508","VEGA 1\/0039\/24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A spectrogram is one of the most effective tools for visualizing dynamic signal changes in industrial processes. In many cases, these signals exhibit certain forms of symmetry\u2014whether in time, frequency, or statistical properties. This paper proposes a novel visualization methodology based on an adaptive nonlinear quantization framework, which intentionally introduces asymmetry to enhance diagnostic-critical features of the power spectrum. Unlike conventional linear quantizers that preserve uniform sensitivity across the range, the nonlinear approach enables selective emphasis of transient or low-energy components, improving visibility under varying signal-to-noise conditions. The design of both symmetric (linear) and asymmetric (nonlinear) quantizers is presented, including their mathematical foundations and visual effects on deterministic, stochastic, and pulsed signals. Entropy-based metrics are used to evaluate information content in the visualized spectrograms. The results demonstrate the proposed technique\u2019s potential for enhancing fault detection, monitoring, and industrial diagnostics.<\/jats:p>","DOI":"10.3390\/sym17060876","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T10:10:16Z","timestamp":1749031816000},"page":"876","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Visualization of Industrial Signals Using Symmetry-Aware Spectrogram Quantization"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9175-1189","authenticated-orcid":false,"given":"Patrik","family":"Flegner","sequence":"first","affiliation":[{"name":"Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Ko\u0161ice, N\u011bmcovej 3, 04200 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1498-447X","authenticated-orcid":false,"given":"J\u00e1n","family":"Ka\u010dur","sequence":"additional","affiliation":[{"name":"Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Ko\u0161ice, N\u011bmcovej 3, 04200 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3784-3450","authenticated-orcid":false,"given":"Milan","family":"Durd\u00e1n","sequence":"additional","affiliation":[{"name":"Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Ko\u0161ice, N\u011bmcovej 3, 04200 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1874-5038","authenticated-orcid":false,"given":"Marek","family":"Laciak","sequence":"additional","affiliation":[{"name":"Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Ko\u0161ice, N\u011bmcovej 3, 04200 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Ma, B., and Chen, B. (2025). A 1D Cascaded Denoising and Classification Framework for Micro-Doppler-Based Radar Target Recognition. Remote Sens., 17.","key":"ref_1","DOI":"10.3390\/rs17091515"},{"doi-asserted-by":"crossref","unstructured":"Ghobber, S., Mejjaoli, H., and Sraieb, N. (2024). Gabor Transform Associated with the Dunkl\u2013Bessel Transform and Spectrograms. Symmetry, 16.","key":"ref_2","DOI":"10.3390\/sym16111410"},{"doi-asserted-by":"crossref","unstructured":"Orozco-Reyes, L., Alonso-Ar\u00e9valo, M.A., Garc\u00eda-Canseco, E., Ibarra-Hern\u00e1ndez, R.F., and Conte-Galv\u00e1n, R. (2025). A Deep-Learning Approach to Heart Sound Classification Based on Combined Time-Frequency Representations. Technologies, 13.","key":"ref_3","DOI":"10.3390\/technologies13040147"},{"doi-asserted-by":"crossref","unstructured":"Scarpiniti, M. (2024). Arrhythmia Detection by Data Fusion of ECG Scalograms and Phasograms. Sensors, 24.","key":"ref_4","DOI":"10.3390\/s24248043"},{"doi-asserted-by":"crossref","unstructured":"Liu, Z., Fan, L., Liu, J., Liu, N., Jin, J., and Xing, J. (2022). Accurate Frequency Estimator for Real Sinusoid Based on DFT. Electronics, 11.","key":"ref_5","DOI":"10.3390\/electronics11193042"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.sigpro.2014.02.015","article-title":"Spectral estimation in frequency-domain by subspace techniques","volume":"101","year":"2014","journal-title":"Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Zhang, Z., Bian, X., and Li, M. (2022). Joint Channel Estimation Algorithm Based on DFT and DWT. Appl. Sci., 12.","key":"ref_7","DOI":"10.3390\/app12157894"},{"doi-asserted-by":"crossref","unstructured":"Kim, S.Y., Lee, H.M., Lim, C.Y., and Kim, H.W. (2025). Detection of Abnormal Symptoms Using Acoustic-Spectrogram-Based Deep Learning. Appl. Sci., 15.","key":"ref_8","DOI":"10.3390\/app15094679"},{"doi-asserted-by":"crossref","unstructured":"Chen, P., Zhang, X., Zhao, H., Cao, H., Chen, X., and Liu, X. (2025). Fusion Classification Method Based on Audiovisual Information Processing. Appl. Sci., 15.","key":"ref_9","DOI":"10.3390\/app15084104"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2892","DOI":"10.3390\/make6040138","article-title":"An End-to-End Adaptive Method for Remaining Useful Life Prediction of Rolling Bearings Using Time\u2013Frequency Image Features","volume":"6","author":"Chen","year":"2024","journal-title":"Mach. Learn. Knowl. Extr."},{"doi-asserted-by":"crossref","unstructured":"Chen, X., Wang, M., Kan, R., and Qiu, H. (2024). Improved Patch-Mix Transformer and Contrastive Learning Method for Sound Classification in Noisy Environments. Appl. Sci., 14.","key":"ref_11","DOI":"10.3390\/app14219711"},{"doi-asserted-by":"crossref","unstructured":"Liu, P., Li, C., Zhang, N., Yang, J., and Wang, L. (2025). Efficient Integer Quantization for Compressed DETR Models. Entropy, 27.","key":"ref_12","DOI":"10.3390\/e27040422"},{"doi-asserted-by":"crossref","unstructured":"Yao, Z., Fang, L., Yang, J., and Zhong, L. (2025). Nonlinear Quantization Method of SAR Images with SNR Enhancement and Segmentation Strategy Guidance. Remote Sens., 17.","key":"ref_13","DOI":"10.3390\/rs17030557"},{"doi-asserted-by":"crossref","unstructured":"Min, T.H., Lee, J.H., and Choi, B.K. (2025). CNN-Based Fault Classification in Induction Motors Using Feature Vector Images of Symmetrical Components. Electronics, 14.","key":"ref_14","DOI":"10.3390\/electronics14081679"},{"doi-asserted-by":"crossref","unstructured":"Wu, Z.T., and Hung, J.W. (2025). Improving the Speech Enhancement Model with Discrete Wavelet Transform Sub-Band Features in Adaptive FullSubNet. Electronics, 14.","key":"ref_15","DOI":"10.3390\/electronics14071354"},{"doi-asserted-by":"crossref","unstructured":"Smietanka, L., and Maka, T.E. (2025). Enhancing Embedded Space with Low\u2013Level Features for Speech Emotion Recognition. Appl. Sci., 15.","key":"ref_16","DOI":"10.3390\/app15052598"},{"doi-asserted-by":"crossref","unstructured":"Tyburek, K. (2025). Analysis of the Fundamental Frequency F0 of Oesophageal Speech in Patients Following Total Laryngectomy Surgery. Appl. Sci., 15.","key":"ref_17","DOI":"10.3390\/app15084402"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.measurement.2015.10.006","article-title":"Optimization of the periodogram average for the estimation of the power spectral density (PSD) of weak signals in the ELF band","volume":"78","year":"2016","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S0263-2241(00)00013-0","article-title":"On windowing effects in estimating averaged periodograms of noisy signals","volume":"28","author":"Jokinen","year":"2000","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"unstructured":"Shannon, C., and Weaver, W. (1964). The Mathematical Theory of Communication, The University of Illinois Press.","key":"ref_21"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.jtbi.2016.12.010","article-title":"Shannon information entropy in the canonical genetic code","volume":"415","author":"Nemzer","year":"2017","journal-title":"J. Theor. Biol."},{"doi-asserted-by":"crossref","unstructured":"Delgado-Bonal, A., and Mart\u00edn-Torres, J. (2016). Human vision is determined based on information theory. Sci. Rep., 6.","key":"ref_23","DOI":"10.1038\/srep36038"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.measurement.2016.06.058","article-title":"Relational measurements and uncertainty","volume":"93","author":"Krechmer","year":"2016","journal-title":"Measurement"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.measurement.2017.10.053","article-title":"Relative measurement theory, The unification of experimental and theoretical measurements","volume":"116","author":"Krechmer","year":"2018","journal-title":"Measurement"},{"doi-asserted-by":"crossref","unstructured":"Yin, H., Chen, H., Feng, Y., and Zhao, J. (2023). Time\u2013Frequency\u2013Energy Characteristics Analysis of Vibration Signals in Digital Electronic Detonators and Nonel Detonators Exploders Based on the HHT Method. Sensors, 23.","key":"ref_26","DOI":"10.3390\/s23125477"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"33","DOI":"10.14311\/AP.2018.58.0339","article-title":"Evaluation of sensor signal processing methods in terms of information theory","volume":"58","author":"Flegner","year":"2018","journal-title":"Acta Polytech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s40808-021-01103-w","article-title":"Artificial neural network for prediction of rock properties using acoustic frequencies recorded during rock drilling operations","volume":"8","author":"Kumar","year":"2022","journal-title":"Model. Earth Syst. Environ."},{"doi-asserted-by":"crossref","unstructured":"Puliafito, V., Vergura, S., and Carpentieri, M. (2017). Fourier, Wavelet, and Hilbert-Huang Transforms for Studying Electrical Users in the Time and Frequency Domain. Energies, 10.","key":"ref_29","DOI":"10.3390\/en10020188"},{"doi-asserted-by":"crossref","unstructured":"Bantilas, K., Kavvadias, I., Tyrtaiou, M., and Elenas, A. (2023). Hilbert\u2013Huang-Transform-Based Seismic Intensity Measures for Rocking Response Assessment. Appl. Sci., 13.","key":"ref_30","DOI":"10.3390\/app13031634"},{"doi-asserted-by":"crossref","unstructured":"Jeon, G., and Chehri, A. (2020). Entropy-Based Algorithms for Signal Processing. Entropy, 22.","key":"ref_31","DOI":"10.3390\/e22060621"},{"doi-asserted-by":"crossref","unstructured":"Yang, F., Shi, D., Lo, L.Y., Mao, Q., Zhang, J., and Lam, K.H. (2023). Auto-Diagnosis of Time-of-Flight for Ultrasonic Signal Based on Defect Peaks Tracking Model. Remote Sens., 15.","key":"ref_32","DOI":"10.3390\/rs15030599"},{"doi-asserted-by":"crossref","unstructured":"Huang, B., Xu, H., Yuan, M., Aziz, M., and Yu, X. (2022). Exploiting Asymmetric EEG Signals with EFD in Deep Learning Domain for Robust BCI. Symmetry, 14.","key":"ref_33","DOI":"10.3390\/sym14122677"},{"doi-asserted-by":"crossref","unstructured":"Celeghini, E., Gadella, M., and del Olmo, M.A. (2021). Hermite Functions and Fourier Series. Symmetry, 13.","key":"ref_34","DOI":"10.3390\/sym13050853"},{"doi-asserted-by":"crossref","unstructured":"Huerta-Rosales, J.R., Granados-Lieberman, D., Amezquita-Sanchez, J., Camarena-Martinez, D., and Valtierra-Rodriguez, M. (2020). Vibration Signal Processing-Based Detection of Short-Circuited Turns in Transformers: A Nonlinear Mode Decomposition Approach. Mathematics, 8.","key":"ref_35","DOI":"10.3390\/math8040575"},{"doi-asserted-by":"crossref","unstructured":"Gao, N., Xu, F., and Yang, J.A. (2024). A High-Resolution Imaging Method for Multiple-Input Multiple-Output Sonar Based on Deterministic Compressed Sensing. Sensors, 24.","key":"ref_36","DOI":"10.3390\/s24041296"},{"doi-asserted-by":"crossref","unstructured":"Liu, G., Zhu, J., Wang, Y., and Wang, Y. (2025). Improved Model-Free Adaptive Predictive Control for Nonlinear Systems with Quantization Under Denial of Service Attacks. Symmetry, 17.","key":"ref_37","DOI":"10.3390\/sym17030471"},{"doi-asserted-by":"crossref","unstructured":"Xing, L., Luo, Z., Deng, K., Wu, H., Ma, H., and Lu, X. (2025). FedHSQA: Robust Aggregation in Hierarchical Federated Learning via Anomaly Scoring-Based Adaptive Quantization for IoV. Electronics, 14.","key":"ref_38","DOI":"10.3390\/electronics14081661"},{"doi-asserted-by":"crossref","unstructured":"Xu, L., Yu, J., Hu, C., Xiong, K., and Shi, T. (2025). Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks. Fractal Fract., 9.","key":"ref_39","DOI":"10.3390\/fractalfract9010047"},{"doi-asserted-by":"crossref","unstructured":"Peric, Z., Denic, B., Savic, M., and Despotovic, V. (2025). Design and Analysis of Binary Scalar Quantizer of Laplacian Source with Applications. Information, 11.","key":"ref_40","DOI":"10.3390\/info11110501"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/876\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:46:25Z","timestamp":1760031985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/876"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,4]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060876"],"URL":"https:\/\/doi.org\/10.3390\/sym17060876","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,6,4]]}}}