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Homework answers / question archive / BIOINSTRUMENTATION I Your Name_____ Ameen Mohamed Midterm Exam Questions related to basic concepts (50 points) 1

BIOINSTRUMENTATION I Your Name_____ Ameen Mohamed Midterm Exam Questions related to basic concepts (50 points) 1

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BIOINSTRUMENTATION I Your Name_____ Ameen Mohamed Midterm Exam Questions related to basic concepts (50 points) 1. (15 points) Introduce the typical components in an intrisic measurement system and an extrinsic measurement system, respectively, and discuss the functions of each component. Intrinsic measurement system that convert internal energy into electrical signal and extrinsic measurement system requires external energy to measure inputs.It is a sort of transducer. transducers convert non-electrical energy into an electronic signal. Output of a transducer is voltage or current signal whose amplitude is proportional to the measured energy. 2. (15 points) What is a linear system and what is a linear time-invariant system? Based on the given input and output signals, are the following systems linear or nonlinear: System 1 VInput = 3*cos(2*pi*20*t+pi/2), Voutput = 24*cos(2*pi*40*t+pi/2) System 2 VInput = 5*sin(2*pi*10*t), Voutput = 10*sin(2*pi*10*t+pi/3) Answer If a system is linear, this means that when an input to a given system is scaled by a value, the output of the system is scaled by the same amount. A time-invariant system has the property that a certain input will always give the same output (up to timing), without regard to when the input was applied to the system. System 1 is nonlinear and system 2 is linear. 3. (10 points) what is the sensitivity, dynamic range, and rise time of a measurement system. 1 BIOINSTRUMENTATION I Your Name_____ Answer Sensitivity is defined as the ratio of the incremental output and the incremental input. The quotient between the measuring range and resolution is often expressed as dynamic range. Rise time is the time required for the response to rise from 10% to 90% of its final value. 4. (10 points) What are the impulse response function (IRF) and the transfer function (TF) of a measurement system? If you are given the IRF, how can you convert it into TF? Answer Impulse response function (IRF), of a measurement system is its output when presented with a brief input signal, called an impulse. A Transfer Function is the ratio of the output of a system to the input of a system. The impulse response of a system is given by the transfer function. If the transfer function of a system is given by H(s), then the impulse response of a system is given by h(t) where h(t) is the inverse Laplace Transform of H(s). Questions related to calculations (50 points) 5. (25 points) If the signal you will measure can be mathematically represented in time-domain using the following equation: V=5*sin(2*pi*f1*t)+10*cos(2*pi*f2*t) (1) Answer the following questions: (a) (5 Pts) If f1=30 Hz and f2=250 Hz, what is the lowest sampling frequency you should select to acquire the signal correctly (based on Nyquist theorem)? Answer To acquire the signal correctly , the lowest sampling frequency is =2*250=500 Hz. (b) (10 Pts) If your team member already acquired the signal and the time increment in the data acquisition is ?t=0.001 second, ? What is the sampling frequency? 2 BIOINSTRUMENTATION I Sampling Frequency = Your Name_____ 1 1 = −3 = 1000 Hz ?t 10 ? What is the Nyquist frequency? Nyquist Frequency=2000Hz ? Do you think your team member can correctly acquire the signal (if yes, please explain why. If no, what are the aliasing frequencies and how to correctly acquire the data)? No, there is the phenomenon of aliasing. (c) (10 Pts) If your team member changes the time increment ?t down to 0.01 second, ? What is the sampling frequency? Sampling Frequency = 1 1 = −2 = 100 Hz ?t 10 ? What is the Nyquist frequency? Nyquist Frequency=200 Hz ? Do you think your team member can correctly acquire the signal (if yes, please explain why. If no, what are the aliasing frequencies and how to correctly acquire the data)? Team member can correctly acquire the signal as there is no aliasing. 6. (25 points) If you have a bio-instrument and its impulse response function is h(n)=[0.5, 0.2, 0.4] ? (15 Pts) What is the output signal of the system when the input isx(n)=[3, 2]? Y[n]=1.5+0.4=1.9 ? (10 Pts) What is the Z-transform of the system’s impulse response function if assuming h=0.5 when n=0? (i.e. h(n)=[0.5, 0.2, 0.4]) H(z)=0.5+0.2Z^(-1)+0.4z^(-2) 3 BIOINSTRUMENTATION I Your Name_____ 4

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