**By Munshi Imran Hossain, Software Affiliate at Cytel**

Biomedical signals are electrical signals collected from the body. Some of the most common ones are the electrocardiogram (ECG) and the electroencephalogram (EEG). These signals are of great value because they can be used for diagnostic purposes. Importantly, most of them can be collected using non-invasive methods. These attributes, together with the tremendous recent advances in electronic and digital processing technology, have made biomedical signal data an important source of data used in medical diagnostics.

Why do biomedical signals need processing?

Most real-world signals include noise. Noise, in this case, is any unwanted signal that corrupts the signal of interest. There are different sources of noise. The heat generated in the electronics, static electrical signals in the surroundings and movement between the subject and sensors are some of the sources of noise. In order to extract useful information from the signal, noise has to be eliminated. Filtering of signals is, therefore, one of the first steps in the processing of biomedical signals.

*[Figure 1] A representative noisy signal. The underlying pattern can be seen but with noise overlaid on it.*

**Time-domain and frequency-domain representations of signal**

A signal that is a function of time, i.e., essentially a time series, can also be expressed as a function of frequency. This can be achieved using a mathematical transformation called the Fourier transformation.

The Fourier transformation expresses the signal using the sinusoidal basis. In other words, the signal is expressed as a function of sines and cosines. This is just one of the many ways of transforming the signal. There are other bases in which a signal can be expressed. The theory of wavelets provides other suitable bases.

The obvious question is why would we want to transform the signal from the time domain into the frequency domain? There is a lot of information to be gained from such a transformation. The frequency domain representation essentially tells us what the component frequencies in a signal are, and the strength (the amplitudes) of these frequencies. This distribution of amplitudes across frequency can be used for filtering out noise from the signal.

*[Figure 2] Amplitude versus frequency plot for the noisy signal shown above.*

**Filtering signals in the frequency domain**

From a priori knowledge it is known that noise signals are typically high frequency signals. There is another kind of noise signal- a drift in the signal. This is a low frequency noise signal. Both these kinds of noises can be eliminated using a digital bandpass filter.

A bandpass filter is one that retains signals in a certain frequency band and attenuates any signal outside the band. The upper and lower cut-off frequencies of this filter can be suitably chosen to eliminate noise and only retain frequency components that correspond to the signal of interest.

[Figure 3] Frequency response of a typical bandpass filter via Wikipedia

The filtered signal can be transformed back into a function of time using an inverse Fourier transform. However it is easier to process the signal in the frequency domain. Therefore the signal is usually retained in the frequency domain for further processing.

**Conclusion**

In this post we have discussed about transforming biomedical signals into functions of their component frequencies for removing noise.

In a future blog post we will look at ways of using this processed signal to gain insights such as classifying the signal based on whether it originates from a normal versus an impaired physiological process.

*Munshi Imran Hossain is a Software Affiliate at Cytel and currently works as a data scientist for strategic consulting assignments. He has 5 years of experience working in the areas of software development and data science. He holds an M. Tech in Biomedical Engineering, from IIT Bombay. His interests include processing and analysis of biomedical data. Outside of work, he enjoys reading.*

Cytel's data science team regularly works with customers on a variety of biomarker discovery, signal detection, and data mining projects. To check out our data science brochure click the button below.

Further reading