Math 414 - Spring 2002

Assignment 1

• Read sections 0.1-0.5.
• Problems

  §0.8: 1, 4, 5, 6, 7, 12, 13

• Due Thursday, 1/24/02

Assignment 2

• Read sections 0.6-0.7.
• Problems

  §0.8: 15, 18(a,b), 19, 26, 28

• Due Thursday, 1/31/02

Assignment 3

• Read sections 1.1-1.3.
• Problems (Use any software you like. Questions? Email me at fnarc@math.tamu.edu.)

§0.8: 29

§1.4: 1, 8

• Due Thursday, 2/7/02

Assignment 4

• Read section 1.3.
• Problems

  §1.4: 3, 4, 7, 9, 10, 11, 24

• Due Thursday, 2/14/02

• Read section 1.3.
• Problems

  §1.4: 15, 16, 17, 26, 28(a,b,c,d)

• Due Thursday, February 21

• Read sections 2.1, 2.2.
• Problems
  1. §1.4: 28(e,f,g), 29; §2.6: 1
  2. Let s be real. Find the complex Fourier series for f(x) = e^-isx on [-pi,pi]. Use Parseval's theorem to show that
     csc²(pi s)= (1/pi)² SUM_k=-inf^inf (s+k)^-2
  3. Use MATLAB and the coefficients in Example 1.13, p. 54, to plot partial sums for the FSS of 1+x². Calculate the size of the overshoot at 0. Does this agree with what we got in class?
• Due Thursday, February 28

• Read sections 2.3, 2.4.
• Problems
  1. §2.6: 2, 3, 4, 5, 6
  2. Let f(t) = e^{-| t |} cos(t).
     1. Find the Fourier transform of f.
     2. Find the Fourier transform of tf'(t-1).
  3. For your projects, begin forming groups and picking topics. This should be done a week or so after spring break.
• Due Thursday, March 21

• Read sections 2.5, 3.1, 3.2
• Problems
  1. §2.6: 10, 11, 12 (typo - h(s) should be h(t)), 14
  2. Project groups should have been formed. Each group should write a paragraph explaining what the group's project is.
• Due Thursday, March 28

• Read sections 3.1, 3.2, 4.1
• Problems

  §3.3: 7 (Note: integers should run from 0 to 255, not 1 to 256 or 0 to 256.), 8, 15(a,b,c). (Another error. In the 1st printing this is labeled as 14(e), (i)-(iii).)

• Due Thursday, April 4

• Read sections 4.1-4.3
• Problems
  1. Let f(t)=t*exp(-2*t) if t > 0 and let f(t)=0 otherwise. Take n to be a positive integer and also take T>0. (Here, T will be the interval between samples and 2ⁿ*T is the duration of the signal.) Finally, set y_j=f(j*T) for j=0,...,2ⁿ-1.
     1. Using property 8 on pg. 100 and a table of Laplace transforms, find the Fourier transform of f
     2. Take T=0.0025 and n=11. Find the fft of the y_j's, j=0,..,2ⁿ-1. Approximate the Fourier transform of f using (3.6) on pg. 142. Plot the magnitude of the difference between this approximation and the actual Fourier transform. Where does the approximation break down?
     3. Repeat (b) with T=0.0025 and n=10.
     4. Repeat (b) with T=0.00125 and n=12.
  2. §4.4: 1, 2, 5.
• Due Thursday, April 11

Assignment 11

• Read sections 5.1 and 5.2.
• Problems

  §4.5: 7, 9, 10. (You may use the Wavelet Toolbox in MATLAB to do the numerical parts of problems.)

• Due Thursday, April 18.