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

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.

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.

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.

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.