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Wavelet and Signal Analysis

Wavelet transforms and digital signal processing for power, industrial, motion and acoustic signals, often paired with neural networks.

Real measurements rarely stay still. A voltage sag lasts a few cycles, a microcrack shows up as a brief burst in a sensor trace, and a bird call is a short chirp in hours of farm noise. Methods that look at a whole signal at once, such as the ordinary Fourier transform, blur these short events. Wavelet transforms describe a signal in time and frequency together, so a transient can be located and measured where it happens.

This is Prof. Yang’s core field. The lab uses the discrete wavelet transform (DWT) and the short-time Fourier transform (STFT) to extract features from measured signals, then classifies or regresses them with neural networks: probabilistic and radial-basis networks, wavelet neural networks, and more recently LSTMs. Because many of these systems run next to the machine they monitor, the processing is designed to fit on embedded hardware, down to a mixed-signal integrated-circuit design for wavelet-based monitoring.

The same tools have been applied to many kinds of signals: voltage sags, flicker and other power disturbances; wafer microcracks, probe marks and wet-etching flow rates in semiconductor manufacturing; textile production lines; human motion patterns; pest-bird sounds on a grape farm; and speech. Two current lines of work carry this forward: wavelet neural networks for the Industrial Internet of Things, which extract features from machine signals to identify a system’s response and status, and wavelet neural networks for embedded image recognition, from feature extraction to contour identification and object recognition. The papers are listed below. The work feeds directly into the lab’s smart grid and energy storage and biomedical AI directions.

Earlier master’s theses. Students have built these methods into working systems: voltage-sag analysis with the DWT and real-time sag monitoring on an FPGA, an embedded lifting-wavelet power-quality analyzer, lifting wavelets for automatic optical inspection, bearing-vibration analysis on an embedded FPGA, and wavelet neural networks that recognize movement patterns and infant crying or model chiller power consumption.

Featured work

Schematic of wavelet-based disturbance recognition. On the left, a pipeline: measured voltage or current, discrete wavelet transform into details d1 to d5 and approximation a5, energy of each level by Parseval's theorem, a neural network (PNN, RBF, GRNN or LSTM), and the disturbance type. On the right, a sine wave that drops to half amplitude for three cycles; below it the level-1 detail coefficients, flat except for a spike where the sag starts and another where it ends; and a bar chart of the six level energies on a log scale.

Finding a voltage sag with the wavelet transform

The wavelet transform splits a measured waveform into levels. The finest level stays close to zero until the waveform jumps, so it marks where a sag starts and ends, and the energy of each level gives a neural network six numbers to classify instead of the raw samples. The figure is a schematic drawn from synthetic data.

Read more

Related projects

Reads an ECG and tells heartbeat types apart on a low-cost microcontroller.

Wavelet-based preprocessing and feature extraction of ECG heartbeat signals, with ANN and CNN heartbeat classifiers deployed on low-cost microcontrollers (Arduino Nano, ESP8266 with MicroPython).

Jupyter Notebook 0 Updated Feb 13, 2023

Related publications

  1. A Comparative Speech Signal Processing of Taiwanese and Indian Speech Characteristics for ASR and Speaker Verification

    Monica C, Wen-Ren Yang

    2025 IEEE International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan), pp. 349–350

    Compares the speech of Taiwanese Mandarin–English bilinguals with Indian English speakers using MFCCs, pitch contours, spectrograms and wavelet analysis: Taiwanese speech shows more pitch variation and tonal shifts, Indian speech a steadier rhythm. The findings guide the choice of speech-recognition and speaker-verification models for diverse speakers.

  2. Grape farm pest bird sound detection system using embedded systems

    E. Aman, W.-R. Yang

    IET International Conference on Engineering Technologies and Applications (ICETA 2023)

    Detects mynah birds in a vineyard from their calls with deep learning on an RP2040 microcontroller, estimates their distance with ultrasonic sensors, and can send a robot vehicle with red lasers to chase them away.

  3. Textile Production Line Monitoring System Using Wavelet-Regression Neural Network

    Nagaraj V. Dharwadkar, Anagha R. Pakhare, Vinothkumar Veeramani, Wen-Ren Yang, Rajinder Kumar Mallayya Math

    Journal of Cases on Information Technology, vol. 24, no. 3, pp. 1–26, 2022

    Monitors a textile production line mapped to smart-grid standards: the DWT removes noise from the line's operating signals, and their energy distribution feeds a general regression neural network that forecasts the time series.

  4. Enhancement of the Flickermeter for Grid-Connected Wind Turbines

    Chau-Shing Wang, Wen-Ren Yang, Yi-Cheng Hsu

    Energies, vol. 14, no. 18, art. 5734, 2021

    Extends the IEC 61400-21-1 flicker measurement for grid-connected wind turbines so it also gives ΔV10 values, as used in Japan and elsewhere; engineers can then estimate a turbine's flicker before installation and manufacturers can certify faster. Tested on a simulated doubly-fed induction generator turbine.

  5. Motion-Pattern Recognition System Using a Wavelet-Neural Network

    Wen-Ren Yang, Chau-Shing Wang, Chien-Pu Chen

    IEEE Transactions on Consumer Electronics, vol. 65, no. 2, pp. 170–178, 2019

    Recognizes human motion from a three-axis accelerometer for fitness assistance and elderly activity monitoring: the DWT extracts vibration features, their local energy feeds a multi-channel radial-basis neural network, and the wavelet step keeps the computation light.

  6. Discrete Wavelet Transform and Radial Basis Neural Network for Semiconductor Wet-Etching Fabrication Flow-Rate Analysis

    Wen-Ren Yang

    IEEE Transactions on Instrumentation and Measurement, vol. 61, no. 4, pp. 865–875, 2012

    Classifies the flow rate of a single-wafer wet-etching tool automatically: the flow meter's signal is decomposed with the DWT, the coefficient power goes into a radial-basis neural network, and a digital filter with a threshold refines the result, for in-situ monitoring in the fab.

  7. Application of image processing to wafer probe mark area calculation

    Chau-Shing Wang, Wen-Ren Yang, Cheng-Yen Chung, Wen-Liang Chang

    2010 5th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp. 414–419

    Measures the area of the marks that test needles leave on wafer pads from high-magnification microscope images, replacing the manual practice of drawing an oval around each mark; the method is faster, more accurate and does not vary from person to person.

  8. Discrete wavelet transform and short-time fourier transform applications: Wafer microcrack and voltage sag detection

    Wen-Ren Yang, Wen-Xun Yang

    2010 International Conference on System Science and Engineering (ICSSE), pp. 31–35

    Compares the discrete wavelet transform with the short-time Fourier transform on two industrial signals, wafer microcracks and voltage sags, through experiments and simulation.

  9. Optical design and signal processing for a microcrack detection system

    Wen-Ren Yang, Yu-Lin Li

    2010 5th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp. 1780–1785

    Designs the optics of the wafer microcrack detector (a cylindrical lens with a solid immersion lens) and its signal processing: a probabilistic neural network separates vibration-induced deviations, and a short-time discrete wavelet transform identifies the cracks.

  10. Power Disturbance Recognition Using Probabilistic Neural Networks

    Chau-Shing Wang, Wen-Ren Yang, Jing-Hong Chen, Guan-Yu Liao

    Proceedings of the International MultiConference of Engineers and Computer Scientists 2009 (IMECS 2009), Vol. II, Hong Kong, pp. 1573–1577

    Recognizes seven kinds of power disturbance (flicker, harmonics, interruption, dip, surge, swell and a clean sine) by decomposing each waveform with the DWT, reducing each level to its energy with Parseval's theorem, and classifying the energies with a probabilistic neural network; recognition rates are 86% or higher.

  11. Short-Time Discrete Wavelet Transform for wafer microcrack detection

    Wen-Ren Yang

    2009 IEEE International Symposium on Industrial Electronics (ISIE), pp. 2069–2074

    Builds a real-time in-line microcrack detector for wafers that scans line by line instead of processing images, and develops a short-time discrete wavelet transform (STDWT) that picks out a crack's reflection with little computation.

  12. Analysis of equivalent 10-Hz voltage flicker measurement using IEC flickermeter standard

    C.-S. Wang, L.-R. Chen, W.-R. Yang

    2008 IEEE International Conference on Industrial Technology (ICIT), pp. 1–5

    Examines the ΔV10 method, used for decades in several Asian countries to rate voltage flicker and unchanged since 1978, against the IEC flickermeter standard, and shows where its readings become unreliable.

  13. Modeling of a wavelet-based voltage sag monitoring system and design for the mixed-signal integrated circuit implementation

    Wen-Ren Yang, Robert O'Connell, Chau-Shing Wang, Liang-Rui Chen

    2008 IEEE International Conference on Industrial Technology (ICIT), pp. 1–6

    Designs a mixed-signal chip for voltage-sag monitoring at many points of a transmission system: an analog front end for data acquisition and a digital discrete-wavelet-transform core. In simulation on IEEE P1159.2 sag waveforms, the wavelet decides faster than an RMS calculation.

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