Time constant and filters

Biosignal Filters
The process of anaylsing and processing biosignals is a field of crucial importance concerning medical literature and practice. Information embedded in biosignals are challenging to observe from the raw data obtained. It has propelled biomedical engineers to develop and apply certain techniques such as the time constants and relative filters.

Signals may be interfered with by noise distortions or artifacts which may originate at the skin electrode interface, unstable dc offset or muscle noise. Fortunately, filters attempt at removal of these unwanted noises while allowing passage of certain signal frequencies through.

The time constant, represented by the Greek letter τ (tau), is a specific parameter which characterises the speed taken to respond to a step input of a first order, linear time invariant. It is usually equivalent to the time taken for a specified parameter to vary by a factor of 1− 1/ e (approx. 0.6321).

Importance in Clinical Medicine
Filters are involved with non-invasive medical diagnostic testing utilized to identify and diagnose diseases affecting the heart. It is also involved in the scope of Electrophysiology and Kinesiology. Electrocardiography (ECG), electroencephalography (EEG) electromyography (EMG) contain filters which highlight crucial aspects of cardiovascular systems by removing unwanted noise and distortion. Filters and time constants are focal in retrieving efficient information, helping to achieve higher quality assurance of detection, prevention for early or onset stages of heart abnormalities and avoid erroneous readings of the signal. Filters and time constants are involved in a systematic process to monitor and evaluate information. It is important for diagnostic purposes to remove noise since the signal should be accurately interpreted for further analysis and development. These tools are also used in intensive care, ambulatory etc.

Types of Filters

 * Low pass filter

A low-pass filter passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. Exist as digital filters or smoothing sets    of data, acoustic barriers,

The combination of resistance and capacitance gives the time constant of the filter  (represented by the Greek letter tau). The break frequency, also called the turnover frequency or cutoff frequency (in hertz), is determined by the time constant: or equivalently (in radians per second):

High pass filter A high-pass filter is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency fc, that is, where fc is in hertz, τ is in seconds, R is in ohms, and C is in farads.

short term pulses, the effects of high pass filters on waveforms are not so easy to visualise. In particular, it is possible to get negative voltages out of a positive pulse waveform, and also peak to peak values exceeding the input. These effects cannot occur with a low pass filter.

For long term periodic waveforms the main effect is to shift or keep the waveform around the centerline, known as the "baseline" in ECG.Most test engineers have little problem to understand this side of high pass filters.

Function of Time constant
In the time domain, the usual choice to explore the time response is through the step response to a step input, The time constant is also used to characterize the frequency response of various signal processing systems such as digital filters – which can be modeled or approximated by first-order LTI systems. A signal can be analysed and processed in two domains, time and frequency typically seen in ECGs.

Limitations
The main limitation of hardware filters is that t hey rely on capacitors, the value of which cannot be controlled well both in production and in normal use. Thus software filtering is usually relied on for filter cut-off points that can be controlled accurately, allowing also advanced filter models and user selected filters to be implemented.

Future Developments
Conclusively, a balance has to be found between removing noise and preserving the original signal to avoid disparities in diagnosis and ease the acquiring of information. For different purposes the balance shifts, so we end up with a range of filters adjusted to get the best balance. Ultimately, the final decision would require a careful study of the effects of the AC filters on waveforms found in real clinical situations, which also depends in the intended purpose

Béla G. Lipták (2003). Instrument Engineers' Handbook: Process control and optimization (4 ed.). CRC Press. p. 100. ISBN 0-8493-1081-4.