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Did you carefully complete the reading assignment?
When you Fourier transform a function, the result is a sum over sines
and cosines. The picture above shows one possible result---the
coefficients for the sine terms is zero and the terms for the cosines
decay as the square of the sinc function. Note that the
argument for the coefficients is the wave vector k. Type the above
code into Mathematica (use Remote Desktop Connection if it's not
convenient to go to the computer lab). Verify that this particular
cosine sum yields a periodic "tent" function. Play around with other
forms for the coefficients. For example, try things like 1/k^2, 1/k,
exp(-k). Try using only odd (or even) values of k. Play around and
then describe your results here. (Can you choose the coefficients so
that they make square pulse? Like Fig. 6.3?)
Take a look at Fig. 6.2 again. Do you understand what the two plots
are showing? If so, explain. If not, ask a question here.
The math was kind of thick and heavy in 6.4. Read it again and keep
the following in mind---there are really only two main steps: 1)
multiply by another cosine (but of a different frequency), and 2)
integrate the product over a period. (When I was a student, my friend
York called this process "multigrating", a nice mnemonic.) And the
important thing to realize is that the product of two cosines, of different
frequecies, integrated over an integral number of periods, will give
you zero. So you can pick off the terms one by one just by changing
the frequency of the cosine you used in step one. If you still have
questions after re-reading, ask them here.
Was there anything that you didn't understand in the reading
assignment? If so, explain.
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