The Illinois Society of Electroneurodiagnostic Technologists (ISET) Fall Meeting: Electronics Crash Course for Technologists Saturday, November 9, 2013 Michael A. Stein, MD

Digital EEG System: Transformation PART 3: PART 3: ‘BlackBox’ Analog-to-Digital Transformation ‘BlackBox’ Analog-to-Digital Transformation

Digital EEG System: Analog to Digital Transformation Input: Input: Electric Field at Scalp Electric Field at Scalp Sensors/Transducers: Sensors/Transducers: EEG electrodes. EEG electrodes. Transformation: Transformation: Filters Filters Analog-to-Digital Converter (ADC) Analog-to-Digital Converter (ADC) Amplifier Amplifier Digital-to-Analog Converter (DAC) Digital-to-Analog Converter (DAC) Output: Output: Computer Display Computer Display Memory/Digital Storage Media Memory/Digital Storage Media

Analog vs Digital EEG System Comparison Advantages of Digital Advantages of Digital Data can be re- montaged Data can be re- montaged Data can be re- filtered Data can be re- filtered Sensitivity can be adjusted Sensitivity can be adjusted Data can be post- processed Data can be post- processed (e.g. frequency/spectral analysis) (e.g. frequency/spectral analysis) Advantage of Analog: Slightly higher fidelity reproduction of true electric field detected at the scalp.

Digital EEG System: Analog to Digital Transformation

The true EEG signal at the scalp is a continuous (analog) and continuously changing electric field signal. The true EEG signal at the scalp is a continuous (analog) and continuously changing electric field signal. To be utilized in a digital system, this analog signal needs to be converted to discrete levels of amplitude after being sampled at a defined time interval. To be utilized in a digital system, this analog signal needs to be converted to discrete levels of amplitude after being sampled at a defined time interval. In other words there are two domains that are approximated to convert a true analog signal to a digital representation: In other words there are two domains that are approximated to convert a true analog signal to a digital representation: (1) Time/frequency domain  Sampling Rate (1) Time/frequency domain  Sampling Rate (2) Amplitude  Bit number (2) Amplitude  Bit number

Digital EEG System: Analog to Digital Transformation (1) Time/frequency domain  Sampling Rate The sampling rate or sampling frequency is how often the analog signal is analyzed/sampled and converted to a digital number. The sampling rate or sampling frequency is how often the analog signal is analyzed/sampled and converted to a digital number. The example below shows 1 second of EEG data. Ten samples (red dots) are recorded. This represents a sampling rate of 10 per second or 10 Hz. The example below shows 1 second of EEG data. Ten samples (red dots) are recorded. This represents a sampling rate of 10 per second or 10 Hz.

Digital EEG System: Analog to Digital Transformation (1) Time/frequency domain  Sampling Rate The digital representation of an analog signal will only contain the same frequencies as the true analog signal if the sampling rate is at least twice as high as the highest frequency present in the analog signal. This is called the Nyquist theorem. The digital representation of an analog signal will only contain the same frequencies as the true analog signal if the sampling rate is at least twice as high as the highest frequency present in the analog signal. This is called the Nyquist theorem. A frequency of ½ the sampling rate of the digital system is the Nyquist frequency. A frequency of ½ the sampling rate of the digital system is the Nyquist frequency.

Digital EEG System: Analog to Digital Transformation (1) Time/frequency domain  Sampling Rate If the sampling rate is too low, then the resulting digital signal may be distorted by aliasing. If the sampling rate is too low, then the resulting digital signal may be distorted by aliasing. 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 which is not twice as high as the frequency of the signal being sampled. The samples are represented by the black dots. The sampling rate is 5 Hz which is not twice as high as the frequency of the signal being sampled. The superimposed 1 Hz waveform becomes the distorted output of this digital system. The superimposed 1 Hz waveform becomes the distorted output of this digital 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.

Digital EEG System: Analog to Digital Transformation (1) Time/frequency domain  Sampling Rate The signal to the left is a 1 second sample of a 1 Hz analog sine wave. The red dots are the samples. In this case the sampling rate is 2 Hz, which is twice as high as the signal being sampled. This image illustrates why the sampling rate needs to be at least twice as high as the highest frequency being sampled. If the sampling rate was lower than this, then only one direction of inflection (up or down) may be sampled with each cycle of the sine wave. This would lead to an alias that is half of the frequency of the true signal.

Digital EEG System: Analog to Digital Transformation (1) Time/frequency domain  Sampling Rate Importantly, although the Nyquist Theorem states that all of the frequencies of the true analog signal will be reproduced in the digital reproduction if the sampling rate is at least twice as high as the highest frequency in the analog signal, this does not imply that the digital reproduction will be an accurate/high fidelity copy of the true signal. Importantly, although the Nyquist Theorem states that all of the frequencies of the true analog signal will be reproduced in the digital reproduction if the sampling rate is at least twice as high as the highest frequency in the analog signal, this does not imply that the digital reproduction will be an accurate/high fidelity copy of the true signal. The higher the sampling rate beyond twice the highest frequency (or the more over-sampled the signal), the more the digital version will approximate the true analog form. The higher the sampling rate beyond twice the highest frequency (or the more over-sampled the signal), the more the digital version will approximate the true analog form.

Effects of Sampling Rate Digital 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.

Digital EEG System: Analog to Digital Transformation (2) Amplitude  Bit number For each digital sample of the analog EEG signal, the amplitude is approximated to one of a finite number of discrete levels. For each digital sample of the analog EEG signal, the amplitude is 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 digital representation will approximate the true analog EEG signal. As with sampling rate, the higher the bit number, the more accurately the 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 values that can be represented is therefore 2 N, where N is the number of bits in the system. Since each bit can have 2 values, this is a base 2 system and the number of values that can be represented is therefore 2 N, where N is the number of bits in the system.

Digital EEG System: Analog to Digital Transformation (2) Amplitude  Bit number For example: For example: A 3 bit system is characterized by 2 3 = 2x2x2 = 8 levels. A 3 bit system is characterized by 2 3 = 2x2x2 = 8 levels.

Digital EEG System: Analog to Digital Transformation (2) Amplitude  Bit number A 4 bit system has 16 possible levels. A 4 bit system has 16 possible levels. The red tracing to the right is the continuous analog signal. The red tracing to the right is the continuous analog signal. The black stair-like waveform is the 4-bit digital representation of this waveform. The black stair-like waveform is the 4-bit digital representation of this waveform. At each sample point in time the analog and digital signals have nearly the same amplitude/voltage value. At each sample point in time the analog and digital signals have nearly the same amplitude/voltage value. In between samples though, there is no true data and the digital waveform is interpolated by straight lines between the sampled data points. In between samples though, there is no true data and the digital waveform is interpolated by straight lines between the sampled data points.

Effects of Bit Number Digital 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) 7-bits (128 levels, values of +/- 64) 8-bits (256 levels, values of +/- 128)

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

Digital EEG System: Output Input: Input: Electric Field at Scalp Electric Field at Scalp Sensors/Transducers: Sensors/Transducers: EEG electrodes. EEG electrodes. Transformation: Transformation: Filters Filters Analog-to-Digital Converter (ADC) Analog-to-Digital Converter (ADC) Amplifier Amplifier Digital-to-Analog Converter (DAC) Digital-to-Analog Converter (DAC) Output: Output: Computer Display Computer Display Memory/Digital Storage Media Memory/Digital Storage Media

Digital EEG System: Output

The digital representation of the analog EEG signal can be either directly sent to digital storage media or further processed and sent to a digital monitor for viewing. An additional output high frequency filter can be used to smooth out the remaining stair-like appearance of the waveforms if needed due to limitations in the bit number of the system.

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

Summary Input: Input: Electric Field at Scalp Electric Field at Scalp Sensors/Transducers: Sensors/Transducers: EEG electrodes. EEG electrodes. Transformation: Transformation: Filters Filters Analog-to-Digital Converter (ADC) Analog-to-Digital Converter (ADC) Amplifier Amplifier Digital-to-Analog Converter (DAC) Digital-to-Analog Converter (DAC) Output: Output: Computer Display Computer Display Memory/Digital Storage Media Memory/Digital Storage Media