MICROLITHOGRAPHY SYSTEMS page 1 of 1
HW#1
1. Determine the Fourier Transform for the following functions and sketch results:
a. rect (x) ; a space
b. 1-rect (x) ; a line
c. rect (4x)
d. rect (x/2)
e. cos (2 u0x)
f. 1.5
g. sinc (2u)
h. comb (2x)
i. rect (x/0.6) * comb (x) NOTE: * denotes the operation of convolution
2. Show how the Fourier Transform of comb(x) is comb(u). Do this by (accurately) plotting a
sum of cosines with appropriate frequency values.
3a. Sketch the following periodic function f(x) and its Fourier transform F(u).
f(x) = rect(2x) * comb(x)
b. Represent the spatial frequency structure of f(x) by calculating the first four terms of the
Fourier series expansion.
4. Plot sinc(x/1.15) for x values from -3.5 to +3.5. Note the x values where the function goes to
zero.