How can you use time-frequency analysis for biomedical data?

Time-frequency analysis is a powerful tool for extracting meaningful information from biomedical data, such as electroencephalograms (EEGs), electromyograms (EMGs), or electrocardiograms (ECGs). It allows you to study how the frequency content of a signal changes over time, revealing patterns, trends, and events that are not visible in the time or frequency domain alone. In this article, you will learn how to use time-frequency analysis for biomedical data, what are the main methods and challenges, and what are some applications and benefits.

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1 What is time-frequency analysis?

Time-frequency analysis is a branch of signal processing that aims to represent a signal in both the time and frequency domains simultaneously. A time-frequency representation (TFR) is a two-dimensional function that shows how the energy or amplitude of a signal varies with time and frequency. A TFR can be obtained by applying a windowed Fourier transform, a wavelet transform, or other methods to a signal. A TFR can be displayed as a spectrogram, a scalogram, or other visualizations.

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Dr. Jorge Garza-Ulloa

CEO at Research Consulting Services garzaulloa.org
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Data signals analysis techniques are based on the following: • Time domain to frequency domain, it is the analysis of mathematical functions or signals with respect to frequency, rather than time and vice versa; • Frequency domain to time domain, it is applied when the results are obtained in frequency domain, and need to be converted to time domain, as practical/conventional solutions. • Applying different mathematical transformations. For example: – Fourier transform, which converts the time function into a sum of sine waves of different frequencies, each of which represents a frequency component. In Biomechanics, there are a lot of applications based on the changes of the signals frequencies.

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2 Why use time-frequency analysis for biomedical data?

Biomedical data often contain non-stationary signals, meaning that their frequency characteristics change over time. For example, EEG signals reflect the brain's electrical activity, which can vary depending on the cognitive state, the task, or the stimuli. EMG signals measure the muscle contractions, which can change depending on the force, the fatigue, or the movement. ECG signals record the heart's electrical activity, which can change depending on the heart rate, the arrhythmia, or the ischemia. Time-frequency analysis can help you detect and quantify these changes, and identify features and events that are relevant for diagnosis, monitoring, or intervention.

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Dr. Jorge Garza-Ulloa

CEO at Research Consulting Services garzaulloa.org
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one main application is the study of muscle fatigue, based on the fact the muscles that are fatigued absorb less energy, and it is reflected in the shifting to lower frequencies. – Wavelet transform, where a wavelet series is a representation of a square integrable (real-or complex-valued) function by a certain orthonormal series generated by a wavelet. Wavelet analysis allows the signals used in Biomechanics to be encoded, compressed, reconstructed, described, simplified, modeled, distinguished, and located; allowing the detection of transitory characteristics of non-stationary signals as: drift, trends, abrupt changes, and beginnings and ends of transitory events. – And, Others.

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3 How to choose a time-frequency method for biomedical data?

When selecting a time-frequency method, it is important to consider the characteristics of the signal, the research question, and the computational resources. Short-time Fourier transform (STFT) divides the signal into short segments, applies a window function, and computes the Fourier transform of each segment. The result is a spectrogram that shows the frequency spectrum of the signal over time. However, it has a fixed resolution and is not suitable for signals that have a rapid change in frequency content. Wavelet transform (WT) decomposes the signal into a set of wavelets, which are scaled and shifted versions of a mother wavelet. The result is a scalogram that shows the coefficients of the wavelet decomposition over time and scale. It has a variable resolution and can capture high-frequency details with a high temporal resolution and low-frequency details with a high frequency resolution. Other methods, such as Wigner-Ville distribution, Hilbert-Huang transform, empirical mode decomposition, or synchrosqueezing can handle non-linear, non-stationary, or noisy signals but may also introduce artifacts, cross-terms, or mode mixing. Thus, it is important to compare different methods and evaluate their performance and suitability for your data.

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Dr. Jorge Garza-Ulloa

CEO at Research Consulting Services garzaulloa.org
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A wavelet can be defined as a small wave, and wavelet transform the application of the wavelet to analyze a signal. There are many wavelets that can be used for both continuous and/or discreet analysis. The most common items include orthogonal wavelets as the Daubechies’ extremal phase(dbN), Daubechies’ least asymmetric wavelets (symN), Meyer wavelets (meyr), gaussian wavelets (gaus), and Mexican hat wavelet (mexh).

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4 How to interpret and analyze a time-frequency representation?

A Time-Frequency Representation (TFR) can provide valuable insights into the dynamics and features of a biomedical signal, but it also requires careful interpretation and analysis. Preprocessing is often necessary, such as removing noise, artifacts, outliers, or trends. Additionally, parameters must be selected for the window size, the window function, the wavelet type, the wavelet scale, or the decomposition level. These parameters can affect the resolution, accuracy, and complexity of the TFR. Visualizing a TFR as a color-coded image is also important for enhancing visibility and readability. Feature extraction is another step in using a TFR to describe the time-frequency characteristics of a signal. Features such as peak frequency, bandwidth, energy, entropy, phase, or coherence can be used for further analysis.

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Dr. Jorge Garza-Ulloa

CEO at Research Consulting Services garzaulloa.org
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For each research of a specific patient's illness is very common to analyze data and results with many charts and compare the results with a healthy patient data. i.e. Detect transition to fatigue in sEMG of tibialis anterior from both limbs in diabetic subject using wavelet analysis multiple-level filtering. Response variables to calculate in this research The generation of the following actions: • Chart with 4 plots for the diabetic subject data, and • Chart with another 4 plots for the healthy normal subject. The four plots required in each chart are: • Analyzed signal sEMG TA right. • Discrete transform of absolute coefficients TA right. • Analyzed signal sEMG TA left. • Discrete transform of absolute coefficients TA left.

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5 What are some applications and benefits of time-frequency analysis for biomedical data?

Time-frequency analysis is a powerful tool for biomedical data analysis that can be applied to various domains, such as neuroscience, cardiology, or rehabilitation. It can help with diagnosis by identifying abnormal patterns or events in biomedical signals, such as epileptic seizures or cardiac arrhythmias. Time-frequency analysis can also be used for monitoring changes in signals over time, such as brain activity or heart rate. Additionally, it can help design and optimize interventions that modulate or stimulate biomedical signals, like neurofeedback or electrical stimulation. Ultimately, this analysis can help explore and understand complex and dynamic signals from living systems, as well as discover new knowledge, solve problems, and improve outcomes in bioengineering and biomedicine.

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