EE 261 The Fourier Transform and its Applications
Fall 2007
Problem Set Seven Due Wednesday, November 14
1. (15 points) DFT basics.
(a) Prove the shift theorem for the discrete Fourier transform:
F (p f ) = p F f .
where
p f [n] = f [n p].
(b) Replication
EE 261 The Fourier Transform and its Applications
Fall 2007
Problem Set 6
Due Wednesday, November 7
1. (20 points) Nyquist rate. The signal f (t) has the Fourier transform F (s) as shown below.
F (s)
s
-B2
-B1
0
B1
B2
The Nyquist frequency is 2B2 since th
EE 261 The Fourier Transform and its Applications
Fall 2007
Problem Set Five
Due Wednesday, October 31
1. (30 points) Evaluating integrals with the help of Fourier transforms Evaluate the following
integrals using Parsevals Theorem and one other method. (
EE 261 The Fourier Transform and its Applications
Fall 2007
Problem Set Nine
Due Wednesday, December 5
1. (10 points) 2D Convolution
lution:
Find and sketch the function dened by the following convog(x, y ) = (x)(y ) (x)(y )
2. (10 points) 2D Radial Stret
EE 261 The Fourier Transform and its Applications
Fall 2007
Problem Set Eight Due Wednesday, November 28
1. (20 points) A True Story : Professor Osgood and a graduate student were working on a
discrete form of the sampling theorem. This included looking a