## Using wavelet transform in biomedical engineering – heart signal analysis

In previous post, we cleared out that wavelet transform is used to analyze short-time and non-stationary signals. Since base wavelet function has to parameters – translation and scaling, it is possible to achieve good time and frequency localization. In other words, we can equally analyze the slow signal and fast signal structures without losing resolution and so evaluate signal frequency characteristics and time dynamics. Heart signal analysis is one of the most common problems in biomedical engineering. Practically every part of ECG signal carries some sort of information about heart conditions, possible pathologies, and diseases. So equally, frequency and timing characteristics of ECG signal is essential. As you know standard ECG signal consists of several typical waveforms like P-QRS-T, where in P and T waves low frequency component dominates, and in QRS, mid and high. The common condition of hear is myocardial ischemia when blood flow through coronary arteries to the heart is reduced, what prevents receiving enough oxygen. This can damage the heart muscle and lead to a heart attack. In order to notice this pathology it is we need to analyze S-T segment of ECG waveform. Insignificant changes in the signal can indicate ischemia. In order to find…

## Wavelet transform – the basics

Recently I’ve been reviewing wavelet transform. I think some points are worth sharing. In this first post, I would like to mention the basics of wavelet transform and its main features. A probably most important question that comes to mind is why we need another transform when we already have Fourier transform. The answer lies in the signals that we want to analyze. If we take any periodic signal that is stationary (e.g., Pulse train) then Fourier transform is the right tool because its frequency components don’t change in time. Let’s take another case when the signal changes in time (chirp signal). Classical Fourier transform cannot determine frequency components of such signal because it doesn’t carry any information about signal time scale. Of course, it is possible to cheat with Short Time Fourier Transform (STFT) when the signal is analyzed in short chunks, but again there is a problem of resolution – the shorter chunks give better time resolution, and longer – better frequency resolution. You can find more info on this by looking for Heisenberg’s Uncertainty Principle. So there is always a tradeoff between both. A fundamental limitation of Fourier transform is in its base function, which is a…