Introduc2on/Mo2va2on Today: many examples & applica2ons of signal & system analysis. Course will be much more mathema2cal than this intro! Remember the skill vs fame plot... Note about today s lecture: Don t worry if you don t understand everything! 1
Electrocardiography (ECG or EKG) Measurement of electrical ac2vity of heart using noninvasive skin sensors (electrodes). Electrical impulses produced by sinoatrial node travel through the heart muscles, causing contrac2on. ECG signal analysis is used to diagnose abnormal rhythms and damage to heart 2ssue/muscle. 2
ECG waves: P wave QRS complex T wave Electrocardiography (ECG) List of diagnoses... 3
Electrocardiography (ECG) Willem Einthoven researched the P,Q,R,S,T deflec2ons and described the ECG features of many cardiovascular disorders. He got the Nobel Prize in medicine for this! An ac2ve area of research is to find more accurate methods of using ECG payerns to detect dangerous heart arrhythmia. Researchers hope to build implantable devices that measure heart signals and process them. These devices can s2mulate nerves, deliver drugs, or defibrillate the heart. 4
Measured ECG signals are not clean : they need to be filtered to separate disturbances, ar2facts, & noise. Sources of disturbances are: breathing 50 60 Hz power network... Electrocardiography (ECG) Filtering: raw ECG measurement filter signal used for diagnosis 1 1 0 0.2 Hz 0 50 60 Hz 5
Electrocardiography (ECG) How fast should our measurement device take samples? Too many samples huge data sets, difficult to store & process. Too few samples important informa2on about signal is lost. More on sampling later... 6
Electroencephalography (EEG) Measurement of electrical ac2vity of brain using noninvasive sensors (electrodes) placed on scalp. Electrical impulses are produced by firing neurons in the brain. EEG signal analysis is used to diagnose epilepsy and other brain abnormali2es (tumors, stroke, etc). EEG can be even superior to MRI due to its higher temporal resolu2on (on order of mili seconds rather than seconds). 7
Electroencephalography (EEG) Delta 0--4 Hz sleep Theta 4--7 Hz idling/ meditation Alpha 7--12 Hz reflecting Beta 12--30 Hz alert working/ anxious thinking Gamma 30--100 Hz motor functions 8
Electroencephalography (EEG) Pathologies in each wave can help diagnose a par2cular disorder. Measured EEG signals are not clean : they need to be filtered to separate disturbances, ar2facts, & noise. Sources of disturbances are: 50 60 Hz power network (this mostly corrupts the Gamma wave) blinking & eye movement heart beat jaw & neck muscle ac2va2on (this mostly corrupts the Delta wave) Filtering performed to clean measured signal. 9
Audio Signals Spelling over the phone difficult to dis2nguish between b, d, p, t, v f, s my cousin is sailing in college vs my cousin is failing in college Most of the energy in vowels is in the lower frequencies (< 3 khz), whereas for consonants the energy is in the higher frequencies. Difference between f & s lies en2rely above 3.3 khz. Phone network severely ayenuates frequencies above 3 khz. 1 0 3 3.3 khz 10
Audio Signals signal lower limit upper limit phone 300 Hz 3 khz AM radio 50 Hz 5 khz FM radio 30 Hz 15 khz CD audio 20 Hz 20 khz human hearing range professional audio 20 Hz 22 khz (human ear most sensitive around 3.3 khz) 11
To digi2ze an audio signal, we sample it quan2ze it Digi2zing Audio Signals itunes now uses 256 kbps! We now consider the effects of different sampling rates... 12
Sampling Rate Ques2on: To capture the signal well, for which one of the signals below do we need to take faster samples? 13
Sampling Rate 14
Sampling Rate 15
Sampling Rate 16
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Sampling Rate Ques2on: Given signal we need to digi2ze, how fast do we sample it? Shocking result: Nyquist Shanon sampling theorem : For no loss of informa2on sampling frequency > 2 * maximum signal frequency Example: limit of human hearing approximately 20 khz by Nyquist, sampling frequency must be > 40,000 samples/sec. CD & mp3 sample rate = 44,100 samples/sec. (click Get Info for music you ve bought from itunes!) telephone uses 8,000 samples/sec. 18
Sampling Rate Signal analysis methods can also be applied to problems where 2me axis is replaced with a spa2al coordinate (e.g. image processing) 19
Sampling Rate 20
Sampling Rate 21
Sampling Rate 22
The Fourier Transfrom Whenever we talk about frequency, we need the Fourier transform or Fourier series The Fourier transform takes a 2me signal, and gives a signal that does not live in the real world, but is very informa2ve about the original 2me signal. It shows the frequency content of the 2me signal. 23
Summary Examples of systems and signal processing in: biomedical applica2ons audio imaging Filtering of signals Frequency content of signals Sampling and reconstruc2on of signals 24
Appendix ECG Diagnoses Shape and dura2on of the P waves may indicate atrial enlargement. Absence of the P wave may indicate atrial fibrilla2on. Saw tooth formed P wave may indicate atrial fluyer. Dura2on, amplitude, and morphology of the QRS complex is useful in diagnosing cardiac arrhythmias, conduc2on abnormali2es, ventricular hypertrophy, myocardial infarc2on, electrolyte derangements, and other disease states. Q waves greater than 1/4 the height of the R wave, greater than 0.04 sec (40 ms) in dura2on, or in the right precordial leads are considered to be abnormal, and may represent myocardial infarc2on. PR interval of over 200 ms may indicate a first degree heart block. Short PR interval may indicate a pre excita2on syndrome via an accessory pathway that leads to early ac2va2on of the ventricles, such as seen in Wolff Parkinson White syndrome. Variable PR interval may indicate other types of heart block. PR segment depression may indicate atrial injury or pericardi2s. Variable morphologies of P waves in a single ECG lead is sugges2ve of an ectopic pacemaker rhythm such as wandering pacemaker or mul2focal atrial tachycardia. Inverted (or nega2ve) T waves can be a sign of coronary ischemia, Wellens' syndrome, lep ventricular hypertrophy, or CNS disorder. Tall or "tented" symmetrical T waves may indicate hyperkalemia. Flat T waves may indicate coronary ischemia or 25
Appendix Audio Signals Human voice uses different mechanisms to form consonants compared to vowels. Vibra2on of vocal cords, when unfiltered, is a raw buzzing sound! Vowels are produced by filtering (shaping) the frequencies in this buzzing through the vocal tract. Consonants are unvoiced clicks, puffs, breaths. They are not created from vocal cords, but by colliding, snapping, and hissing through combina2ons of tongue, cheeks, and teeth. 26