GG 652: Homework 8:
Fourier-Domain Modeling
Reading: Blakeley Ch. 11, p. 258-288 , Due: Friday 8 March
For the first five problem, do following exercises in Ch. 11.
(1) 11.1
(2) 11.5
(3) 11.10
(4) 11.12
(5) 11.15
For the last 3 problems use hw8fft.m to familiarize yourself with “fast Fourier transforms” (fft’s) in Matlab. This routine produce a cosine and a sine function, each with a wavelength that you specify, and then allows you to see how these functions or the sum of the functions appears as an fft in the “Fourier domain” (i.e., the Fourier coefficient versus wave number). This allows you to see how fft's work and where Matlab puts the coefficients of these periodic functions
(6) First set the amplitudes of the cosine function, A, and the sine function, B to zero and set the function to a constant by setting h0 = 1. Run the program and have a look at the function in the Fourier domain. Describe what the results mean and why they make sense.
(7) Fft of a cosine function: Set h0 = 0 and set A =1. Start with ncycles1 =1, run the program (with iwhich= 1) and describe the results and why they make sense. Vary ncycles1 and do the same. Change A to a different positive number and a negative number. Describe the results and why they make sense.
(8) Fft of a sine function: Now set h0 = 0, A=0, and B =1. Start with ncycles2 =1, run the program (with iwhich= 2) and describe the results and why they make sense. Vary ncycles2, B as you did for (8).
(9) Combined cosine and sine function. How try adding a cosine and sine function by setting non-zero values for A, B, ncycles1, and ncycles2 and set iwhich = 3. Discuss the results.