**2 Weeks**

The impulse response *h(t)* for a particular LTI system is shown below. All parts of this lab make use of this
*h(t)*.

- Plot the impulse response for
*h(t)*directly from the above equation by creating a time vector. -
Use the
*residue*function to determine the transfer function*H(s)*. Determine the locations of the poles and zeros of*H(s)*with the*roots*function, and plot them in the*s*-plane (x for poles, o for zeros). Compare the pole locations with the terms in the expression for*h(t)*. Is there any obvious relation between the zeros in the transfer function of*H(s)*and terms in*h(t)*? -
Use the
*logspace*function to create a frequency vector from 0.01 to 100 r/s, using at least 200 frequency points. Use the*bode*or*freqresp*function (or*polyval*,*abs*, and*angle*functions) with this frequency vector to determine the magnitude and phase of the transfer function. -
Use the
*subplot*,*semilogx*, and*log10*functions to create plots of magnitude (db) vs. frequency and phase (deg) vs. frequency. -
Repeat step 4 using the
*subplot*and*loglog*functions to create plots of magnitude (absolute value) vs. frequency and phase (deg) vs. frequency. -
Repeat step 5 using the
*subplot*and*semilogx*functions to create plots of magnitude (absolute value) vs. frequency and phase (deg) vs. frequency. -
Use the
*linspace*function to create a frequency vector from 0 to 100 r/s, using the same number of frequency points as in step 3. Calculate the magnitude and phase of the transfer function with this new frequency vector. -
Use the
*subplot*and*plot*functions to create plots of magnitude (absolute value) vs. frequency and phase (deg) vs. frequency with the new magnitude and phase arrays. At the lowest frequency in your arrays, compare the magnitudes of the transfer function in absolute value and in decibels. How can this low frequency (0 r/s) magnitude (absolute value) be obtained from*H(s)*by doing only a simple calculation? -
Document your work in a typed report. Discuss the similarities and differences in the various frequency-domain
plots which were made. Give your opinions on which type of plot might be the most useful to you. Discuss the change
in value in phase shift from low frequency to high frequency and compare that change to the number of poles and
zeros in the transfer function. If the Fourier transform for this system exists, write down that transform directly
from
*H(s)*.

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*Latest revision on
Friday, May 19, 2006 10:57 AM
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