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lecture 2

# lecture 2 - Wed.May13th,10:30AM 12:30PM 108CHEN...

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Correction to Syllabus Final Exam will take place on: Wed. May 13 th , 10:30AM – 12:30 PM 108 CHEN

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Lecture 2: Outline Time Dependent Signals Signal Classification Signal Operations on the dependent variable Signal Operations on the independent variable Basic Signals
Definition of Signal A signal is the measurement of a physical quantity or event ( dependent variable ) as a function of another physical quantity ( independent variable ). In this course, we will focus on time dependent signals (the independent variable is time). Notation: x(t), y(t) Examples: a. ECG/EEG/EMG (mV vs. t) b. Arterial Blood Pressure (mmHg vs. t) c. Glucose Level (mg/dL vs. t) d. Red blood cells counts (10^12 cells/L vs. t) Other signals can be functions of other variables: a. MRI/Ultrasound (intensity vs. space: I(x,y)) b. Functional MRI (Intensity vs. space and time: I(t,x,y)) c. Cardiac Polarization Map (mV vs. space+time)

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Time Dependent Signal Classification Continuous Time (CT) vs. Discrete Time (DT) Most physiological signals are described over continuous time x(t): However, modern medical instrument usually measure them at discrete times, transforming a CT signal into a DT signal: Interval Sampling Ts t x n x nTs t : ; ) ( ] [ = = The signal is measured only at discrete values of time: t=nTs, n=0,1,2,… The cardiac electric field changes continuously in time: ECG(t)
Time Dependent Signal Classification Even vs. Odd n n x n x t t x t x = = ), ( ] [ , ) ( ) ( EVEN: n n x n x t t x t x = = ), ( ] [ , ) ( ) ( ODD: Any signal x(t) can be expressed as a sum of its even x e (t) and odd x o (t) parts: 2 ) ( ) ( ) ( 2 ) ( ) ( ) ( t x t x t x t x t x t x o e = + = ) . . 2 cos( t f π ) . . 2 sin( t f ) ( ) ( ) ( t x t x t x o e + =

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Dependent Signal Classification Even vs. Odd : Example of even and odd parts of an ECG signal. Run Matlab code: ECG_Even_Odd_parts.m
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lecture 2 - Wed.May13th,10:30AM 12:30PM 108CHEN...

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