Biomedical Signals Acquisition

Signals are functions of one or more independent variables and typically contain information about the behaviour or nature of some phenomenon. Systems usually respond to particular signals by producing other signals. The representation of a signal as a plot of amplitude versus time constitutes the waveform. The pattern of variations contained in the waveforms gives us information about the signal; for example, the human vocal mechanism produces speech by creating fluctuations in acoustic pressure.

Deterministic signals: a signal is deterministic if it is exactly predictable for the time span of interest. Deterministic signals can be described by mathematical models. A sinusoidal signal is described by :

V(t)= A* sin(w * t),

where V(t) is the signal over time
A (=amplitude) and w are the model parameters (2pf=w).
f is the frequency of the sine wave.
l is the period of the sine wave and is the inverse of the frequency (1/f)

So: V(t) = A sin(2pft)

Stochastic or random signals: a signal whose value has some element of chance associated with it, therefore it cannot be predicted exactly. Consequently, statistical properties and probabilities must be used to describe stochastic signals. In practice, biological signals often have both deterministic and stochastic components.

Signal amplitude statistics
A number of statistics may be used as a measure of the location or "centre" of a random signal:

• the mean is the average amplitude of the signal over time
• the median is the value at which half of the observations in the sample have values smaller than the median and half have values larger than the median. The median is often used as the measure of the "centre" of a signal because it is less sensitive to outliers.
• the mode is the most frequently occurring value of the signal
• maximal and minimal amplitude are the maximal and minimal value of the signal during a given time interval
• range: the range or peak-to-peak amplitude is the difference between the minimum and maximum values of a signal.

Continuous time signals versus discrete time signals
The signals are continuous time signals when the independent variable is continuous, therefore the signals are defined for a continuum of values of the independent variable X(t). An analogue signal is a continuous time signal. Discrete time signals are only defined at discrete times; the independent variable takes on only a discrete set of values X(n). A digital signal is a discrete time signal.
A discrete time signal may represent a phenomenon for which the independent variable is inherently discrete (e.g., amount of calories per day on a diet). On the other hand, a discrete signal may represent successive samples of an underlying phenomenon for which the independent variable is continuous (e.g., a visual image captured by a digital camera is made of individual pixels that can assume different colours).

Measuring signal frequency using spectral analysis
There are quantitative methods to measure the frequency and amplitude of a waveform. One of the most well known is called spectral analysis: any waveform can be mathematically decomposed in a sum of different waveforms. This is what the so-called Fourier analysis does; it decomposes the waveform in different components and measure the amplitude (power) of each frequency component. What is plotted is a graph of power (amplitude) vs. frequency.
 

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