The Illinois Society of Electroneurodiagnostic Technologists (ISET) Fall Meeting: Electronics Crash...

The Illinois Society of The Illinois Society of Electroneurodiagnostic Electroneurodiagnostic

Technologists (ISET)Technologists (ISET)Fall Meeting:Fall Meeting:

Electronics Crash Course for Electronics Crash Course for TechnologistsTechnologists

Saturday, November 9, 2013Saturday, November 9, 2013

Michael A. Stein, MDMichael A. Stein, MD

Digital EEG System:Digital EEG System:TransformationTransformation

PART 3:PART 3: ‘‘BlackBox’ Analog-to-Digital TransformationBlackBox’ Analog-to-Digital Transformation

Digital EEG System:Digital EEG System:Analog to DigitalAnalog to Digital TransformationTransformation

InputInput:: Electric Field at ScalpElectric Field at Scalp Sensors/Transducers:Sensors/Transducers:

EEG electrodes.EEG electrodes. TransformationTransformation::

FiltersFilters Analog-to-Digital Analog-to-Digital

Converter (ADC)Converter (ADC) AmplifierAmplifier Digital-to-Analog Digital-to-Analog

Converter (DAC)Converter (DAC) OutputOutput::

Computer DisplayComputer Display Memory/Digital Storage Memory/Digital Storage

MediaMedia

Analog vs Digital EEG Analog vs Digital EEG SystemSystem

ComparisonComparison Advantages of Advantages of

DigitalDigital Data can be re-Data can be re-

montagedmontaged Data can be re-Data can be re-

filteredfiltered Sensitivity can Sensitivity can

be adjustedbe adjusted Data can be Data can be

post-processedpost-processed (e.g. (e.g.

frequency/spectrafrequency/spectral analysis)l analysis)

Advantage of Advantage of Analog:Analog: Slightly higher Slightly higher

fidelity fidelity reproduction reproduction of true electric of true electric field detected field detected at the scalp.at the scalp.



The true EEG signal at the scalp is a The true EEG signal at the scalp is a continuous (analog) and continuously continuous (analog) and continuously changing electric field signal.changing electric field signal.

To be utilized in a digital system, this analog To be utilized in a digital system, this analog signal needs to be converted to discrete levels signal needs to be converted to discrete levels of amplitude after being sampled at a defined of amplitude after being sampled at a defined time interval.time interval. In other words there are two domains that are In other words there are two domains that are

approximated to convert a true analog signal to a approximated to convert a true analog signal to a digital representation:digital representation:

(1) Time/frequency domain(1) Time/frequency domain Sampling Rate Sampling Rate (2) Amplitude (2) Amplitude Bit number Bit number

Digital EEG System:Digital EEG System:Analog to Digital TransformationAnalog to Digital Transformation

(1)(1) Time/frequency domainTime/frequency domain Sampling Rate Sampling Rate

The sampling rate or sampling frequency is how often The sampling rate or sampling frequency is how often the analog signal is analyzed/sampled and converted the analog signal is analyzed/sampled and converted to a digital number.to a digital number.

The example below shows 1 second of EEG data. Ten The example below shows 1 second of EEG data. Ten samples (red dots) are recorded. This represents a samples (red dots) are recorded. This represents a sampling rate of 10 per second or 10 Hz.sampling rate of 10 per second or 10 Hz.



The digital representation of an analog The digital representation of an analog signal will only contain the same signal will only contain the same frequencies as the true analog signal if frequencies as the true analog signal if the sampling rate is the sampling rate is at leastat least twice as twice as high as the highest frequency present in high as the highest frequency present in the analog signal. This is called the the analog signal. This is called the Nyquist theoremNyquist theorem..

A frequency of ½ the sampling rate of A frequency of ½ the sampling rate of the digital system is the the digital system is the Nyquist Nyquist frequencyfrequency..



If the sampling rate is too low, then the resulting digital signal may be If the sampling rate is too low, then the resulting digital signal may be distorted by distorted by aliasingaliasing. .

In the example below:In the example below: The true analog signal has a frequency of 5 Hz.The true analog signal has a frequency of 5 Hz. The samples are represented by the black dots. The sampling rate is 5 Hz The samples are represented by the black dots. The sampling rate is 5 Hz

which is which is notnot twice as high as the frequency of the signal being sampled. twice as high as the frequency of the signal being sampled. The superimposed 1 Hz waveform becomes the distorted output of this digital The superimposed 1 Hz waveform becomes the distorted output of this digital

system.system.

This type of signal distortion is referred to as aliasing, because one frequency is assuming the identity of another or acting as its alias.

In this case the true 5 Hz signal has an alias of a 1 Hz signal.



The signal to the left is a 1 The signal to the left is a 1 second sample of a 1 Hz analog second sample of a 1 Hz analog sine wave.sine wave.

The red dots are the samples. In The red dots are the samples. In this case the sampling rate is 2 this case the sampling rate is 2 Hz, which Hz, which isis twice as high as the twice as high as the signal being sampled.signal being sampled.

This image illustrates why the This image illustrates why the sampling rate needs to be at least sampling rate needs to be at least twice as high as the highest twice as high as the highest frequency being sampled.frequency being sampled.

If the sampling rate was lower If the sampling rate was lower than this, then only one direction than this, then only one direction of inflection (up or down) may be of inflection (up or down) may be sampled with each cycle of the sampled with each cycle of the sine wave. This would lead to an sine wave. This would lead to an alias that is half of the frequency alias that is half of the frequency of the true signal.of the true signal.



ImportantlyImportantly, although the Nyquist Theorem , although the Nyquist Theorem states that all of the frequencies of the true states that all of the frequencies of the true analog signal will be reproduced in the digital analog signal will be reproduced in the digital reproduction if the sampling rate is at least reproduction if the sampling rate is at least twice as high as the highest frequency in the twice as high as the highest frequency in the analog signal, this analog signal, this does notdoes not imply that the imply that the digital reproduction will be an accurate/high digital reproduction will be an accurate/high fidelity copy of the true signal.fidelity copy of the true signal.

The higher the sampling rate beyond twice the The higher the sampling rate beyond twice the highest frequency (or the more over-sampled highest frequency (or the more over-sampled the signal), the more the digital version will the signal), the more the digital version will approximate the true analog form.approximate the true analog form.

Effects of Sampling RateEffects of Sampling RateDigital reproductions of 1 Hz analog signal

1 Hz analog signal

For the images on the right, from top to bottom, the sampling rates are: 4 Hz, 6 Hz, 8 Hz, 128 Hz.


(2)(2) Amplitude Amplitude Bit number Bit number

For each digital sample of the analog EEG signal, the amplitude is For each digital sample of the analog EEG signal, the amplitude is approximated to one of a finite number of discrete levels.approximated to one of a finite number of discrete levels.

The number of levels available is determined by the bit number of the system. The number of levels available is determined by the bit number of the system. As with sampling rate, the higher the bit number, the more accurately the As with sampling rate, the higher the bit number, the more accurately the

digital representation will approximate the true analog EEG signal.digital representation will approximate the true analog EEG signal. Digital systems are binary and each bit can have two values (1’s and 0’s).Digital systems are binary and each bit can have two values (1’s and 0’s). Since each bit can have 2 values, this is a base 2 system and the number of Since each bit can have 2 values, this is a base 2 system and the number of

values that can be represented is therefore 2values that can be represented is therefore 2NN, where N is the number of bits , where N is the number of bits in the system.in the system.



For example:For example: A 3 bit system is A 3 bit system is

characterized by 2characterized by 233 = 2x2x2 = 8 levels.= 2x2x2 = 8 levels.



A 4 bit system has 16 A 4 bit system has 16 possible levels.possible levels. The red tracing to the right The red tracing to the right

is the continuous analog is the continuous analog signal.signal.

The black stair-like waveform The black stair-like waveform is the 4-bit digital is the 4-bit digital representation of this representation of this waveform. waveform.

At each sample point in time At each sample point in time the analog and digital signals the analog and digital signals have nearly the same have nearly the same amplitude/voltage value.amplitude/voltage value.

In between samples though, In between samples though, there is no true data and the there is no true data and the digital waveform is digital waveform is interpolated by straight lines interpolated by straight lines between the sampled data between the sampled data points.points.

Effects of Bit NumberEffects of Bit NumberDigital reproductions of 1 Hz analog signal

1 Hz analog signal

For the images on the right, from top to bottom, the bit numbers are: 4-bits (16 levels, values of +/- 8)

6-bits (64 levels, values of +/- 32)



The example below shows one second of a The example below shows one second of a single channel of analog scalp EEG that is single channel of analog scalp EEG that is sampled at rate of 32 Hz and an sampled at rate of 32 Hz and an reconstructed with a 4-bit system.reconstructed with a 4-bit system.

Digital EEG System:Digital EEG System:OutputOutput

InputInput:: Electric Field at ScalpElectric Field at Scalp Sensors/Transducers:Sensors/Transducers:





Computer DisplayComputer Display Memory/Digital Memory/Digital

Storage MediaStorage Media



The digital representation The digital representation of the analog EEG signal of the analog EEG signal can be either directly sent can be either directly sent to digital storage media to digital storage media or further processed and or further processed and sent to a digital monitor sent to a digital monitor for viewing.for viewing.

An additional output high An additional output high frequency filter can be frequency filter can be used to smooth out the used to smooth out the remaining stair-like remaining stair-like appearance of the appearance of the waveforms if needed due waveforms if needed due to limitations in the bit to limitations in the bit number of the system.number of the system.

Digital EEG System:Digital EEG System:Output:Output:

Digital to Analog ConversionDigital to Analog Conversion

The digital to analog The digital to analog convertor (DAC) is the convertor (DAC) is the part of the circuit part of the circuit which converts the which converts the strings of binary data strings of binary data (1’s and 0’s) back to (1’s and 0’s) back to discrete levels and discrete levels and interpolates the data interpolates the data between sample between sample points to create the points to create the stair-like output stair-like output signal. signal.

SummarySummary InputInput::

Electric Field at ScalpElectric Field at Scalp Sensors/Transducers:Sensors/Transducers:





Computer DisplayComputer Display Memory/Digital Memory/Digital

Storage MediaStorage Media

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