001_BME343_Signals_Systems

001_BME343_Signals_Systems - Introduction to Biological and...

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Signals and Systems 1-1 Introduction to Biological and Biomedical Systems and Signals • Signal is a set of data that carries information – Often is a function of time – Not limited to time / 1D • System acts on a signal to change the properties of the signal in some way
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Signals and Systems 1-2 Objectives • Be able to compute the energy and power of a signal • Be able to plot signals for different operations (time shifting, time scaling, time reversal, combination of the above) • Be able to classify signals as continuous or discrete, digital or analog, periodic or aperiodic, and energy or power • Be able to classify systems as linear or nonlinear, time invariant or time varying, instantaneous or dynamic, causal or noncausal, continuous-time or discrete-time, analog or digital, invertible or non-invertible, memoryless or with memory, BIBO stable, asymptotically stable, or unstable
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Signals and Systems 1-3 Examples of Biomedical Signals • Electrocardiogram (ECG) – cardiac dynamics • Electroencephalogram (EEG) – brain electrical activity recorded from scalp • Time-varying voltages in a circuit • Blood flow • Respiration • Temperature • Sequences of bases in a gene
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Signals and Systems 1-4 Examples of Systems • Hardware – circuit that processes a voltage signal • Software – application that processes a signal • Biological systems – Pancreas: regulates glucose levels Physiological System Input Output Stimulus Response () xt yt
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Signals and Systems 1-5 Biological Systems • Nervous system • Musculoskeletal • Respiratory • Circulatory • Immune • Digestive • Reproductive •A u d i t o r y • Visual •O l f a c t o r y Organ-level Cellular-level •N e u r o n • Cell cycle regulation • Genes •P r o t e i n • Cell receptors • Muscle tissue • Red blood cell • Ion transport •T r a n s c r i p t i o n
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Signals and Systems 1-6 • Generally, need a measure of signal size – include both time and amplitude • Signal energy • Signal power • Discussion – rms (root-mean-square) – periodic signal or statistical regularity – (ramp vs. unit step function) – units of energy and power – power and rms of sinusoid Size of signal 2 () x Ex t d t −∞ = 2 x t d t −∞ = /2 2 1 lim ( ) T x T T P xt d t T →∞ = 2 1 lim ( ) T x T T P xt d t T = Complex valued signal Real valued signal
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Signals and Systems 1-7 Discussion – rms (root-mean-square) – periodic signal or statistical regularity – (ramp vs. unit step function) – units of energy and power – power and rms of sinusoid Size of signal
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Signals and Systems 1-8 Power or Energy signal? z t Interesting observations Power is the time average of energy Averaging is over infinitely large interval (time or space) Signal with finite energy has zero power Signal with finite power has infinite energy 2 () x Ex t d t −∞ = /2 2 1 lim ( ) T x T T P xt d t T →∞ =
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Signals and Systems 1-9 Signal operations: Time shifting
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This note was uploaded on 09/28/2009 for the course BME 343 taught by Professor Emelianov during the Fall '09 term at University of Texas.

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001_BME343_Signals_Systems - Introduction to Biological and...

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