The McGill Physiology Virtual Lab

Biomedical Signals Acquisition

A/D basics
  In the process of analogue to digital conversion, an analogue signal is converted into a digital signal which can then be stored in a computer for further processing. Analogue signals are "real world" signals - for example physiological signals such as electroencephalogram, electrocardiogram or electrooculogram. In order for them to be stored and manipulated by a computer, these signals must be converted into a discrete digital form the computer can understand.


example of an A/D board which performs the analogue to digital conversion. This board is placed inside the computer where it communicates with the rest of the computer hardware and software. An alternate way to acquire a signal is to use an integrated device which comprises the electronics necessary to acquire as well as amplify the signals (shown to the right).

Powerlab* recording system has an A/D board as well as amplifiers and communicates with the computer through its USB port.



Using A/D conversion and a computer to analyze data has many advantages over older non-computerized methods. Computer data is easily transported and manipulated. Computer analysis of signals is far more efficient than analysis by hand and paper. Most importantly, real-time analysis can be performed - this means that signals can be analyzed as they are acquired during the course of an experiment


Consider the signal shown in the figure which is part of an electroencephalogram. It is an analogue signal, since it is continuously changing in time. Any arbitrarily given value that is within the range of the signal can be obtained simply by measuring electrical activity at the right point in time. The object of A/D conversion is to convert this signal into a digital representation, and this is done by sampling the signal. A digital signal is a sampled signal, obtained by sampling the analogue signal at discrete points in time. These points are usually evenly spaced in time, with the time between being referred to as the sampling interval.

In the figure, the sampling interval is 2.5 milliseconds, with samples being taken at the times indicated by the red dots on the waveform.
The electronic circuit that carries out the process of sampling the signal and A/D conversion is called an analogue-to-digital converter (ADC). Being an electronic device, it requires an electrical signal at its input. Thus the first step in the process of A/D conversion is to convert the analogue (non-voltage) signal into an analogue voltage signal. The device that carries out this function is called a transducer. For signals which are inherently voltages such as the electrocardiogram from the heart, the electrooculogram from the eyes, or the electromyogram from muscle, transduction is of course not necessary.

The ADC we are using is a 16 bit board. This means that when it performs an A/D conversion, the ADC samples the analogue voltage present at its input at that point in time and converts it into a 16-digit binary number. Since each digit of a binary number can take one of the two values 0 or 1, a 16 bit (bit = binary digit) number can take one of 2^16 = 65536 values, representing the integers from 0 to 65535. Our ADC also has an input range of -10 000 millivolts (mV) to +10 000 millivolts (mV). This means that the binary value 0000000000000000, which is equivalent to the decimal number 0, will be returned by the ADC to the computer when a voltage of -10 000 mV is present at its input, and the binary number 1111111111111111, whose decimal equivalent is 65535, will be returned when the input voltage is +10 000 mV. Thus, the input voltage range from -10 000 mV to +10 000 mV is divided into 65536 levels, with each level being 20 000 mV/65536 = 0.305 mV wide. This value will determine the resolution of the sampled signal.

In the example above, the resolution is 0.305 millivolts. An input voltage lying within one of these 0.305mV wide ranges is converted into a specific binary number: for example, any voltage lying in the range from
-10 000 to -9 999.695 will be converted to the binary number:
0000000000000000, while any voltage in the range between +9 999.695 and +10 000 mV will be converted to the decimal number 65535.

click here to see an example of conversion from binary to decimal

Input Voltage (mV)
(Real Value)
Binary (Base 2) Value Decimal (Base 10) Value
-10 000 to
-9 999.695
0000000000000000 0
... ... ...
... 111111111111110 32766
0.0 to +0.305 1000000000000000 32768
... 1000000000000001 32769
... ... ...
+9 999.695 to +10 000 1111111111111111 65535

How would the resolution for an 8-bit converter compare to the 12-bit case?
What is the answer?
Click here for an interactive applet which will further help you visualize and understand the process of A/D conversion.

As mentioned previously, one important step when carrying out A/D conversion is to keep the input signal within the input voltage range of the ADC. In our case, should the input signal exceed 10 000 mV a 16 bit binary number with an equivalent decimal value of 65535 would still be returned to the computer. The computer would thus interpret the voltage being sent to be +10 mV, which would be in error. This error is called saturation of the ADC. However, the input signal should span as much of the ADC input voltage range as possible, without saturating the ADC, since this increases the signal to noise ratio. Thus if the voltage range of the input signal is much smaller than +/-10 000 mV, the signal should be amplified before being fed to the input of the ADC.

However, the input signal to the ADC should also spanas much of the ADC input voltage range as possible, without saturating the ADC, since this increases the signal resolution.
For example, if the signal to be recorded is much smaller than +/- 10 000 mV, say +/- 5 000 mV, then the range over which the board operates should be decreased. By changing the hardware gain from 10 000 mV (10 V) to 5 V, the operating range of the board is changed from +/- 10 000mV to +/-5 000 mV. This allows the experimenter to record a +/- 2V signal with a significant improvement in signal resolution ( 2 times greater). This occurs because the minimum resolvable voltage would be 10 000 mV/65536 or 0.152 mV versus 0.305 mV when the board's operating range was set to +/-10 volts.

Sampling Rate and Aliasing

Another consideration to be kept in mind during the process of A/D conversion is the choice of sampling rate. The sampling rate is the frequency expressed in Hertz (Hz) at which the ADC samples the input analogue signal. As mentioned before, the sampling interval is the time between successive samples: the sampling rate is thus the inverse of the sampling interval. Generally speaking, the faster the rate at which a signal changes, the higher the frequency content of the signal, and the higher is the sampling rate needed to reproduce it faithfully.

This can be appreciated from the figure, which shows that the rapidly rising phase of the wave form is not represented as well in the sampled waveform as is the more slowly changing part. In fact, it can be proven mathematically that the sampling rate to be used must be greater than twice the highest frequency contained in the analogue signal. This critical sampling rate is called the Nyquist Sampling rate.
The figure to the right below illustrates the sampling of a sine wave using two different sampling rates. The times at which A/D conversion are made are given by the vertical lines beneath the signal, while the red asterisks on the waveform show the voltages that are sampled. The highest frequency present in this signal is the frequency of the signal itself, since it is a simple sine wave, and so contains only one frequency.
Note that the sampling rate in the upper figure is about ten times higher than the highest frequency present in the signal and so is about five times the Nyquist rate. The sampled signal is thus a reasonable approximation of the analogue signal.
The lower figure above shows the situation that results when the sampling rate is reduced to about 1.2 times the highest frequency contained in the analogue signal. This sampling rate is thus lower than the Nyquist rate, and the sampled signal (dashed line) bears little resemblance to the analogue signal. Note that the frequency of the sampled signal is much smaller than that of the analogue signal. This artifactual result due to improper choice of the sampling rate is called aliasing.
Why not always sample at the highest rate possible?
It is critical that the sampling rate be sufficiently high. For example, in experiments in which the resting membrane potential of skeletal muscle is measured, a sampling rate of about 25-50 Hz is sufficiently high. In contrast, when measuring action potentials in nerve axons, which are much more rapidly changing events, a sampling rate of 10-20 kHz is required. However, for a signal of given frequency content, increasing the sampling rate beyond a certain point does not significantly increase the fidelity with which the signal is rendered. In addition, the cost of an ADC increases as higher sampling rates are desired. Finally, more computer processing time and storage space in memory or disk are needed to process the larger number of data points produced when the sampling rate is increased. Thus there is a tradeoff between fidelity of reproduction on the one hand, and computer storage space, computing time, and cost on the other.

Any ADC has a maximum sampling rate. In some circumstances, this maximum sampling rate is not high enough to satisfy the Nyquist conditions mentioned above. In that case, one can pass the analogue signal through a low-pass filter before sending it on to the ADC. This filter acts to remove some of the high-frequency content of the signal that would otherwise alias down in frequency, producing spurious low-frequency content along the lines illustrated above. Note that this anti-alias filtering could remove high frequency information of physiological importance to the phenomenon under investigation. If it is important to retain these higher frequencies, one has no choice but to use a better data acquisition system that has a higher sampling rate.

A biological signal can be broken down into fundamental frequencies, with each frequency having its own intensity. Display of the intensities at all frequencies is a power spectrum. Usually we are interested in signals of a particular frequency range or bandwidth. The bandwidth is determined by filters, which are devices that alter the frequency composition of the signal.

Ideal frequency-selective filter: is a filter that exactly passes signals at one set of frequency and completely rejects the rest.
There are three types of filter:

  • Low frequency or in old terminology high pass. Filters low frequencies.
  • High frequency or in old terminology low pass. Filters high frequencies.
  • Notch filter. Filters one frequency, usually 60 Hz.

Real filters or hardware filters alter the frequency composition of the signal. It means after filtering the signal, we cannot recover the frequencies that have been filtered.
Digital filters change the frequency of the signal by performing calculations on the data. It means you can record all the frequency components of your signal and by digitally filtering it, eliminate the unwanted frequencies.


Any unwanted signal that modifies the desired signal is noise. It can have multiple sources.

  • Thermal noise: the random motion of atoms generates this random, uniformly distributed noise.
    Thermal noise is present everywhere and has a nearly constant Power Spectral Density (PSD).
  • Interference: imposition of an unwanted signal from an external source on the signal of interest.
  • Sampling noise: another artifact of the acquisition process, sampling noise occurs when you digitize a continuous signal with an A/D converter that has finite number of steps. It is interesting to note that you can dither (add white noise: i.e.: does not vary with frequency) your signal to reduce the overall sampling noise.
  • Narrowband/broadband: two general categories of noise. Narrowband noise confines itself to a relatively small portion of the overall signal bandwidth as defined by Nyquist. Broadband noise occupies a significant portion of the Nyquist bandwidth. For example, 60Hz-hum is narrowband because it typically limits itself to a 60 Hz component. Thermal noise is definitely broadband because its PSD is constant, meaning that it distributes its energy over nearly the entire spectrum.

Signal to Noise Ratio (SNR): it is a measurement of the amplitude of variance of the signal relative to the variance of the noise. The higher the SNR, the better can you distinguish your signal from the noise.

A few definitions to remember
  • Desired signal: a signal that is not corrupted by noise
  • Signal sampling: the process of obtaining a sequence of instantaneous values of a particular signal characteristic, usually at regular time intervals.
  • Sampling frequency: it is the frequency at which the ADC samples the analogue signal (usually in number of samples per second (Hz))
  • Sampling period: the reciprocal of the sampling frequency, i.e., the interval between corresponding points on two successive sampling pulses of the sampling signal.
  • sampling range: the range between the minimal and maximal values at which you sample the signal (if you sample between -10 V and +10 V the sampling range is 20 V)
  • Offset: a fluctuation in the baseline value of the signal
  • gain and amplification: it is the factor by which you multiply your signal. If a gain is one, the signal remains unchanged; if the gain is higher than 1, the signal is amplified. If the gain is lower than one, the signal is reduced.
  • amplitude saturation: it occurs when the intensity of the signal exceeds the values within the sampling range. For example, if we acquire a signal which intensity is +20 V and we are sampling between -5V and +5 V. It produces a distortion of the signal, i.e., over the interval in which the signal reaches +20V, the output of our ADC will be +5V.
  • Nyquist interval: the maximum time interval between equally spaced samples of a signal that will enable the signal waveform to be completely determined.
    ----the Nyquist interval is equal to the reciprocal of twice the highest frequency component of the sampled signal.
    ----in practice, when analogue signals are sampled for the purpose of digital transmission or other processing, the sampling rate must be more frequent than that defined by Nyquist theorem, because of quantization error introduced by the digitizing process. The required sampling rate is determined by the accuracy of the digitizing process.
  • Nyquist Sampling rate: is the value of the sampling frequency equal to twice the maximal frequency of the signal we are acquiring.

To continue to the next topic, Computerized recording system, click here