Homework _5 Spring 11

Homework _5 Spring 11 - BME6360 Neural Engineering Homework...

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Unformatted text preview: BME6360 Neural Engineering Homework #5 Spring 2011 Prof. Wheeler The goals of this exercise are: 1. To give you experience in linear system identification at a basic level. You should be able to create a transfer function which accounts for the data with reasonable accuracy, but which has complexity appropriate for a biological system. You should start to develop an intuitive understanding of what kind of accuracy is reasonable. 2. To demonstrate that the same data can be modeled with different functions. Although this is necessarily true, it is often forgotten. Usually it is possible to argue that one model is better than the others by appealing to other aspects of the biology (although not in the limited information you have for this exercise.) Your report should be concise and should include the transfer function which you have identified from the data, plus plots of the data superimposed on the model predictions. Files available for the exercise: h6logplt.m flist.mat h6linplt.m dblist.mat h6compar.m phlist.mat lap2tdel.m lap2tim.m bodedela.m polemult.m polezero.m 1. In experiments performed on the catfish retina, a light of variable intensity covered the retinal surface. The response was the potential change of a horizontal cell recorded intracellularly. A sine wave stimulus was used which had a modulation depth of 0.8. Modulation depth is the ratio of Im/Iav where Im is the amplitude of the sine wave modulation and Iav is the average intensity; i.e. I(t) = Iav + Imcos(ωt). Find a suitable transfer function for this system, whose frequency (in Hz), gain (in dB) and phase shift (in degrees) are given by the following: flist = [ 1 1.5 2.5 3 4 7 9 10 12 14 15 18 20 23 27 35] dblist = [-7 -4 -4 0 -1 1 -2 -2 -2 -8 -9 -10 -16 -22 -30 -36] phlist = [ 0 -3 -10 -30 -70 -120 -170 -180 -230 -270 -300 -330 -360 -420 -450 -540] These values have been stored in the files and you may recall them by executing: load flist load dblist load phlist Note that there are several possible models and ranges of parameters. You should choose something reasonable yet simple. These are real data: they were measured, not simulated by adding noise. This implies that there is no entirely satisfactory answer. The functions plot(flist, dblist), semilogx(flist,dblist), and plot(phlist, flist) will generate plots to get you started. To get the gain slope (dB/decade), try plot(log10(flist),dblist), then grid, and you will be easily able to measure fractional changes in "decade" (which is another name for the horizontal axis of this plot, i.e. base ten log units). Try printing the result and then using old fashioned technology -- a straightedge -- to estimate the slope. The same technology should work for measuring the slope of the phase vs. frequency (on a linear scale) so that you can estimate the pure time delay. You should use the two functions h5linplt.m and h5logplt.m which will save you a lot of time. Investigate either of these m files and figure out how they work. The purpose is to encourage you to create short .m files to help you with your work.) 2. In the course lecture notes are descriptions of figures from Stark's paper on the response of a photosensitive ganglion of the crayfish. The model in the paper is: (a) Ga(s) = K exp[-T1 s] / (s T2 + 1)2 , where T1=1 second and T2=1.3 seconds. An alternate model is suggested by (b) Gb(s) = K / (s Tn + 1) n, where Tn = 0.8 seconds and n=4. Let K=1 for simplicity. Compare the step responses of Ga, Gb, and the data reported (a copy will be made available in class). Compare also the impulse responses and the magnitude and phase Bode plots. Can you think of any tests which could distinguish between the two models? (This is a very difficult question -- you are asked for suggestions; there are no tests guaranteed to work.) You should use the function h5compar.m which will save you a lot of time on this problem. Investigate the code in the .m file. Again, the purpose is to reinforce the manipulation of the transfer function to create impulse and step responses, and, as above, to encourage you to write your own functions when you need them. ...
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This note was uploaded on 01/23/2012 for the course EEL 6502 taught by Professor Principe during the Spring '08 term at University of Florida.

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