Biomedical Data Acquisition and Signal Processing Lecture Notes PDF

Biomedical data acquisition and signal processing Lecture 1-Data acquisition. Introduction to data acquisition, devices, sensors, registration of 1D signals Ilias K. Kitsas, Ph.D., E&CE, AUTh MSc in BioMedical Engineering (BME-AUTh) BIOMEDICAL DATA ACQUISITION A...

Biomedical data acquisition and signal processing Lecture 1-Data acquisition. Introduction to data acquisition, devices, sensors, registration of 1D signals Ilias K. Kitsas, Ph.D., E&CE, AUTh MSc in BioMedical Engineering (BME-AUTh) BIOMEDICAL DATA ACQUISITION A lot of data is being collected from patients Patients in critical care units/ cared for in intensive care units Clinician does not have the opportunity to screen all of this data A lot of the data is put up on a screen Rudimentary algorithms might be applied to this data... …but largely that data is being discarded! MSc in BioMedical Engineering (BME-AUTh) WHAT IS A SIGNAL? A signal, technically yet generally speaking, is a formal description of a phenomenon evolving over time and/or space Still, the term signal can refer to other symbolic or abstract forms of information, such as: sequence of million combinations of the four symbols of the genetic code (bases A, C, G, T of the DNA) in genes form and uncoded sections or abstract forms of information attributes, such as "cold", "warm", "high", "low". MSc in BioMedical Engineering (BME-AUTh) WHAT IS A SIGNAL? Some examples of signals include data or sequences of properties or numerical quantities from the areas of audio, video, speech, gestures, image, multi-media, communication, sensors, geophysics, Sonar, radar, biology, chemistry, molecular and/or genomics, medicine, music … MSc in BioMedical Engineering (BME-AUTh) WHAT IS PROCESSING? By processing we denote any manual or “mechanical” operation which modifies, analyzes or otherwise manipulates an information It includes functions of: representation filtering, coding, transmission, estimation, detection, modeling, discovery, recognition, synthesis, recording, or reproduction of signals from digital or analog devices, techniques or algorithms in the form of software, hardware, or firmware MSc in BioMedical Engineering (BME-AUTh)  WHAT IS SIGNAL PROCESSING? Putting it together, we can say that signal processing is an enabling technology that encompasses the fundamental theory, applications, algorithms, and implementations of processing or transferring information contained in many different physical, symbolic, or abstract formats broadly designated as signals, and uses mathematical, statistical, computational, heuristic, and/or linguistic representations, formalisms, and techniques for representation, modeling, analysis, synthesis, discovery, recovery, sensing, acquisition, extraction, learning, security, or forensics. MSc in BioMedical Engineering (BME-AUTh) What do your really ‘see’ in this image? MSc in BioMedical Engineering (BME-AUTh) WHAT IS BIOMEDICAL SIGNAL? a signal being obtained from a biologic system / originating from a physiologic process (human or animal) (medical -> patients) MSc in BioMedical Engineering (BME-AUTh) WHAT IS BIOMEDICAL SIGNAL PROCESSING? all treatment (of biomedical signals) which occurs between their origin in a physiological process and their interpretation by their observer (e.g. clinician) application of signal processing methods on biomedical signals All possible processing algorithms may be used It requires understanding the needs (e.g. biomedical processes and clinical requirements) and selecting and applying suitable methods to meet these needs MSc in BioMedical Engineering (BME-AUTh) PROCESSING OF BIOMEDICAL SIGNALS Biomedical Transducers Isolation signals preamplifiers Computer- aided diagnosis Amplifiers and filters and therapy Pattern recognition, Analog-to- classification, and digital diagnostic decision conversion Analysis of events and Detection of events Filtering to waves; feature extraction and components remove artifacts Signal analysis MSc in BioMedical Engineering (BME-AUTh) Signal processing BIOMEDICAL SIGNALS MSc in BioMedical Engineering (BME-AUTh) EEG – MENTAL ACTIVITIES MSc in BioMedical Engineering (BME-AUTh)  EXAMPLE: HEART RATE METERS Sensor Signal processing User Electric potential Detection of events Event series Artifact processing Instantaneous HR HR statistics MSc in BioMedical Engineering (BME-AUTh) MSc in BioMedical Engineering (BME-AUTh) TERMINOLOGY Deterministic: may be accurately described mathematically, usually predictable (not in case of chaos!) Periodic: s(t)=s(t+nT) Almost periodic: patterns repeat with some unregularity Transient: signal characteristics change with time MSc in BioMedical Engineering (BME-AUTh) TERMINOLOGY (cont’) Stochastic: defined by their statistical properties (distribution) Stationary: statistical properties of the signal do not change over time Ergodic: statistical properties may be computed along time distributions White noise: autocorrelation = 0 except for τ=0 where autocorrelation = 1 ; flat spectrum MSc in BioMedical Engineering (BME-AUTh) TERMINOLOGY (cont’) All real (bio)signals may be considered stochastic almost deterministic signals (e.g. ECG – QRS complex): wave shapes that (almost) repeat themselves → characterization by detection of certain measures/waves “strictly” stochastic (e.g. EEG) → characterization by statistical properties MSc in BioMedical Engineering (BME-AUTh) CLASSIFICATION BY SOURCE Bioelectric signals: generated by nerves cells and muscle cells. Single cell measurements (microelectrodes - action potential) “gross” measurements (surface electrodes - action of many cells in the vicinity) Biomagnetic signals: brain, heart, lungs produce extremely weak magnetic fields. Additional information to that obtained from bioelectric signals. Can be measured using SQUIDs. MSc in BioMedical Engineering (BME-AUTh) CLASSIFICATION BY SOURCE (cont’) Bioimpedance signals: tissue impedance reveals info about tissue composition, blood volume and distribution Two electrodes to inject current & two to measure voltage drop. Bioacoustic signals: based on acoustic noise. Flow of blood through the heart, its valves, or vessels Flow of air through upper and lower airways and lungs Digestive tract, joints and contraction of muscles. Recorded using microphones MSc in BioMedical Engineering (BME-AUTh) CLASSIFICATION BY SOURCE (cont’) Biomechanical signals: motion and displacement signals, pressure, tension and flow signals. A variety of measurements (not always simple, often invasive measurements are needed). Biochemical signals: chemical measurements from living tissue or samples analyzed in a laboratory. Ion concentrations/partial pressures (pO2 or pCO2) in blood. Low frequency signals (DC signals) MSc in BioMedical Engineering (BME-AUTh) CLASSIFICATION BY SOURCE (cont’) Biooptical signals: blood oxygenation by measuring transmitted and backscattered light from a tissue, estimation of heart output by dye dilution. Fiberoptic technology. MSc in BioMedical Engineering (BME-AUTh)  BASIC APPROACHES The signal processing included in many applications, e.g., in telecommunications, control systems, biomedical engineering applications, can be seen through two fundamental approaches: Analog (continuous time)-dominant approach for many years (until about the mid-20th century) Digital (discrete time)-domination from mid-20th century up to now (due to computers/microprocessors) Notable contributors: Harry Nyquist (1920): sampling theorem, Alec Reeves (1938): Pulse Code Modulation (PCM), Claude Elwood Shannon (1940-1950): Channel Capacity- Information Theory MSc in BioMedical Engineering (BME-AUTh)  WHY DIGITAL IS BETTER THAN ANALOG? Flexibility: the same material can be used for different functions of signal processing, while the core of the analogue processing must be designed for each individual system operating mode, and Repeatability: the same signal processing operation can be repeated again and again, allowing the same effect, while in analog systems deviations may occur in the results of iterations because of the circuits parameter sensitivities to changes in temperature and/or supply voltage. MSc in BioMedical Engineering (BME-AUTh)  DSP UNDER THE PYRAMIDS Probably the earliest recorded example of digital signal processing dates back to the 25th century BC in Egypt. The floods of the Nile were a rather capricious meteorological phenomenon, with scant or absent floods resulting in little or no yield from the land. The pharaohs quickly understood that they would have to set up a grain buffer with which to compensate for the unreliability of the Nile’s floods. Studying and predicting the trend of the floods (and therefore the expected agricultural yield) was of paramount importance! MSc in BioMedical Engineering (BME-AUTh)  DSP UNDER THE PYRAMIDS (cont’) The floods of the Nile were meticulously recorded by an array of measuring stations called “nilometers” and the resulting data set can indeed be considered a full- fledged digital signal defined on a time base of twelve months. The Palermo Stone is a faithful record of the data in the form of a table listing the name of the current pharaoh alongside the yearly flood level, complying with the modern representation of a flood data set. MSc in BioMedical Engineering (BME-AUTh) THE HELLENIC SHIFT TO ANALOG PROCESSING “Digital” representations of the world (e.g., in Palermo Stone) are adequate for an environment in which quantitative problems are simple: counting cattle, counting bushels of wheat, counting days and so on. As soon as the interaction with the world becomes more complex, so necessarily do the models used to interpret the world itself. In the act of splitting a certain quantity into parts we can already see the initial difficulties with an integer-based world view MSc in BioMedical Engineering (BME-AUTh) THE HELLENIC SHIFT TO ANALOG PROCESSING (cont’) Until the Hellenic period, western civilization considered natural numbers and their ratios all that was needed to describe nature in an operational fashion. In the 6th century BC, Pythagoras realized that the side and the diagonal of a square are incommensurable, i.e., that sqrt(2) is not a simple fraction. The discovery of what we now call irrational numbers “sealed the deal” on an abstract model of the world that had already appeared in early geometric treatises and which today is called the continuum. MSc in BioMedical Engineering (BME-AUTh)  THE IMPORTANT INTERPLAY Communication systems are in general a prime example of sophisticated interplay between the digital and the analog world: while all the processing is undoubtedly best done digitally, signal propagation in a medium (be it the air, the electromagnetic spectrum or an optical fiber) is the domain of differential (rather than difference) equations. MSc in BioMedical Engineering (BME-AUTh)  THE IMPORTANT INTERPLAY (cont’) Even when digital processing must necessarily hand over control to an analog interface, it does so in a way that leaves no doubt as to who’s boss, so to speak: for, instead of transmitting an analog signal which is the reconstructed “real” function as we always transmit an analog signal which encodes the digital representation of the data. This concept is really at the heart of the “digital revolution”. MSc in BioMedical Engineering (BME-AUTh)  THE IMPORTANT INTERPLAY (cont’) Example Imagine an analog voice signal 𝑠(𝑡) which is transmitted over a (long) telephone line; a simplified description of the received signal is where the parameter 𝛼, with 𝛼 < 1, is the attenuation that the signal incurs and where 𝑛(𝑡) is the noise introduced by the system. The noise function is of obviously unknown (it is often modeled as a Gaussian process) and so, once it’s added to the signal, it’s impossible to eliminate it. MSc in BioMedical Engineering (BME-AUTh)  THE IMPORTANT INTERPLAY (cont’) Because of attenuation, the receiver will include an amplifier with gain 𝐺 to restore the voice signal to its original level; with 𝐺 = 1/𝛼 we will have Unfortunately, as it appears, in order to regenerate the analog signal we also have amplified the noise 𝐺 times; clearly, if 𝐺 is large (i.e., if there is a lot of attenuation to compensate for) the voice signal ends up buried in noise. The problem is exacerbated if many intermediate amplifiers have to be used in cascade, as is the case in long submarine cables. MSc in BioMedical Engineering (BME-AUTh)  THE IMPORTANT INTERPLAY (cont’) Consider now a digital voice signal, that is, a discrete-time signal whose samples have been quantized over, say, 256 levels: each sample can therefore be represented by an 8-bit word and the whole speech signal can be represented as a very long sequence of binary digits. We now build an analog signal as a two-level signal which switches for a few instants between, say, −1 V and +1 V for every “0” and “1” bit in the sequence respectively. The received signal will still be but, to regenerate it, instead of linear amplification we can use nonlinear thresholding: MSc in BioMedical Engineering (BME-AUTh) THE IMPORTANT INTERPLAY (cont’) Two-level analog signal encoding a binary sequence: original signal 𝑠(𝑡) (light gray) and received signal 𝑠𝑟 (𝑡) (black) in which both attenuation and noise are visible. As long as the magnitude of the noise is less than 𝛼 the two- level signal can be regenerated perfectly; furthermore, the regeneration process can be repeated as many times as necessary with no overall degradation. MSc in BioMedical Engineering (BME-AUTh)  GENERAL SCOPE OF THE COURSE The course focuses on understanding – what biomedical signals are – what problems and needs are related to their acquisition and processing – what kind of methods are available and get an idea of how they are applied and to which kind of problems getting to know basic digital signal processing and analysis techniques commonly applied to biomedical signals and to know to which kind of problems each method is suited for MSc in BioMedical Engineering (BME-AUTh) TYPES OF SIGNALS Signals can be represented in time or frequency domain MSc in BioMedical Engineering (BME-AUTh) TYPES OF TIME DOMAIN SIGNALS Static = unchanging over long period of time essentially a DC signal Quasistatic = nearly unchanging where the signal changes so slowly that it appears static Periodic Signal = Signal that repeats itself on a regular basis ie sine or triangle wave Repetitive Signal = quasi periodic but not precisely periodic because f(t) /= f(t + T) where t = time and T = period ie is ECG or arterial pressure wave Transient Signal = one time event which is very short compared to period of waveform MSc in BioMedical Engineering (BME-AUTh) TYPES OF TIME DOMAIN SIGNALS a) Static : non-changing signal b) Quasi Static : practically non- changing signal c) Periodic : cyclic pattern where one cycle is exactly the same as the next cycle d) Repetitive : shape of the cycle is similar but not identical (ECG, blood pressure,…) e) Single-Event Transient : one burst of activity f) Repetitive Transient or Quasi Transient : a few bursts of activity MSc in BioMedical Engineering (BME-AUTh) FOURIER SERIES All continuous periodic signals can be represented as a collection of harmonics of fundamental sine waves summed linearly. These frequencies make up the Fourier Series Definition +∞ 1 Fourier: 𝑋 𝜔 = න 𝑥 𝑡 𝑒 −𝑗𝜔𝑡 𝑑𝑡 2π −∞ +∞ 1 𝑥 𝑡 = න 𝑋(𝜔)𝑒 +𝑗𝜔𝑡 𝑑𝜔 Inverse Fourier: 2π −∞ MSc in BioMedical Engineering (BME-AUTh)  Example: x = Xm sin(2ωt) x = instantaneous amplitude of sin wave Xm = Peak amplitude of sine wave ω = angular frequency = 2π f T = time (sec) Fourier Series found using many frequency selective filters or using digital signal processing algorithm known as FFT = Fast Fourier Transform 1 0.8 0.6 0.4 0.2 1 Magnitude 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.1 0.2 0.3 0.4 0.5 Time (Sec) 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 Time (sec) 1 sec Frequency (Hz) Sine Wave in time domain f(t) = sin(23t) MSc in BioMedical Engineering (BME-AUTh) EVERY SIGNAL CAN BE DESCRIBED AS A SERIES OF SINUSOIDS MSc in BioMedical Engineering (BME-AUTh) DC COMPONENT y (t ) = 1 + 4 3 sin( 2t ) + 2 3 sin( 2 3t ) MSc in BioMedical Engineering (BME-AUTh) TIME vs FREQUENCY RELATIONSHIP Signals that are infinitely continuous in the frequency domain (nyquist pulse) are finite in the time domain Signals that are infinitely continuous in the time domain are finite in the frequency domain Mathematically, a finite time and frequency limited signal does not exist. MSc in BioMedical Engineering (BME-AUTh)  SPECTRUM & BANDWIDTH Spectrum: range of frequencies contained in signal Absolute bandwidth: width of spectrum Effective bandwidth (/just bandwidth): Narrow band of frequencies containing most of the energy Used by Engineers to gain the practical bandwidth of a signal DC Component: Component of zero frequency MSc in BioMedical Engineering (BME-AUTh)  EXAMPLES OF BIOMEDICAL SIGNALS ECG vs Blood Pressure Pressure waveform has a slower rise time than ECG →less harmonics to represent the signal Pressure waveform can be ECG represented with 25 harmonics ECG needs 70-80 harmonics MSc in BioMedical Engineering (BME-AUTh)  EXAMPLES OF BIOMEDICAL SIGNALS Square wave theoretically has infinite number of harmonics Approx. 100 harmonics acceptable Time (sec) MSc in BioMedical Engineering (BME-AUTh)  DISCRETE-TIME SIGNALS: SEQUENCES Discrete-Time signals are represented as x = xn, −   n  , n : integer Cumbersome, so just use x  n  In sampling, xn = xa (nT ), T : sampling period 1/T (reciprocal of T) : sampling frequency MSc in BioMedical Engineering (BME-AUTh)  ANALOG TO DIGITAL CONVERSION x[n] = xa (t ) |t = nT = xa (nT ) 256 samples / 32ms= 256 samples / (32/1000) sec= 32.000 samples/sec or Hz MSc in BioMedical Engineering (BME-AUTh) 52 ANALOG TO DIGITAL CONVERSION Sampling Error Quantization Error MSc in BioMedical Engineering (BME-AUTh) SAMPLING RATE Sampling Rate must follow Nyquist’s theorem. Sampling rate must be at least 2 times the maximum frequency. MSc in BioMedical Engineering (BME-AUTh)  QUANTIZATION ERROR Signal digitization → number of bits in the DAQ (data acquisition board) Example is of a 4 bit 24 = 16 level board Most boards have at least 12 bits or 212 = 4096 levels The “staircase” effect is called the quantization noise or digitization noise MSc in BioMedical Engineering (BME-AUTh)  NYQUIST SAMPLING THEOREM ERROR IN SIGNALS 1 Sec 1 Sec 30 samples / 1 sec = 30 Hertz 10 samples / 1 sec = 10 Hertz Signal that is digitized into computer Signal that is digitized into computer MSc in BioMedical Engineering (BME-AUTh) SPECTRAL INFORMATION: SAMPLING WHEN Fs > 2Fm Sampling is a form of amplitude modulation Spectral Information appears not only around fundamental frequency of carrier but also at harmonic spaced at intervals Fs (Sampling Frequency) -Fs-Fm -Fs -Fs+ Fm -Fm 0 Fm Fs-Fm Fs Fs+ Fm MSc in BioMedical Engineering (BME-AUTh) SPECTRAL INFORMATION: SAMPLING WHEN Fs < 2Fm Aliasing occurs when Fs=2Fm MSc in BioMedical Engineering (BME-AUTh)  BASIC SEQUENCE OPERATIONS Sum of two sequences x[n] + y[n] Product of two sequences x[n]  y[n] Multiplication of a sequence by a number α   x[n] Delay (shift) of a sequence y[n] = x[n − n0 ] n0 : integer MSc in BioMedical Engineering (BME-AUTh)  BASIC SEQUENCES Unit sample sequence (discrete-time impulse, impulse) 0 n  0  n =  1 n = 0 MSc in BioMedical Engineering (BME-AUTh) BASIC SEQUENCES A sum of scaled, delayed impulses pn = a−3 n + 3 + a1 n − 1 + a2 n − 2 + a7 n − 7  For an arbitrary sequence: x[n] =  x[k ] [n − k ] k = − MSc in BioMedical Engineering (BME-AUTh)  BASIC SEQUENCES Exponential sequences x[ n] = A n A and α are real: x[n] is real A is positive and 0