ECE 802-603 Take Home Exam 1 02/23/2010-02/25/2010
Instructions
This exam is due on Thursday February 25, 2010 at 8:30 am. Please
hand in your exam to me, do not leave it under a door or in a mailbox.
During the exam you may use the lecture notes, the i
ECE 802-603 Homework 2
Spring 2010
Due February 11, 2010
Please turn in all of your MATLAB code and your outputs with your solutions.
You should turn in a hard copy on the due date of the assignment.
1. One way to address the issue of time-frequency resol
ECE 802-603 Homework 2 Solutions
1. a)
Averaged Spectrogram
120
100
80
60
40
20
500
1000
1500
2000
2500
Time Samples
3000
3500
Figure 1: The average of the four spectrograms
b)The spectrogram with the window length 128 provides the best time and frequency
ECE 802-603 Homework 1
Spring 2010
Due January 26, 2010
1. [25] Consider the space of square integrable functions on the interval [ , ] ,
cos(nx) sin(nx)
L2 [ , ] , and the associated othonormal basis given by 1,
,
, n 1,2,.
Consider the following two s
ECE 802-603 Homework 1 Solutions
1. a) It is known that the symmetric (even) part of a signal can be obtained
as:
f (x) + f (x)
fs (x) =
(1)
2
Similarly, the antisymmetric (odd) part of a signal can be written as:
f (x) f (x)
2
fa (x) =
(2)
Therefore, f (
ECE 802-603 Homework 3
Spring 2010
Due March 4, 2010
1. The DWT of a signal f(t) can be written as f (t )
d
j k
j ,k (t ) :
j ,k
a. Show that the DWT is a linear transformation.
b. Is DWT shift-invariant, i.e. does DWT ( f (t ) d j ,k imply
DWT ( f (t
ECE 802-603 Homework 4
Spring 2010
Due March 25, 2010
1.
This problem is about designing Daubechies filters, scaling functions and
wavelets.
a) Design the minimum-phase Daubechies filter of length 6. Find the
corresponding wavelet filter.
b) Using the sca
ECE 802 Review Paper 2
Due: April 1, 2010
For this review paper, you are given three recent papers on extensions of wavelet decompositions to overcomplete sets. The rst paper by Gribonval and Bacry introduce harmonic
matching pursuit for audio signal anal
ECE 802-603 Review Paper 1
due February 18, 2010
Reading: Higher Order Time-Frequency Distributions
For this review paper, you are given three papers on extensions of Wigner distribution for
analyzing higher order time-varying spectra. Wigner distribution
ECE 802 Homework 5
Due: April 22, 2010
1. Wavelet Denoising: Let f (t) = sin(8t)cos(3t) + n(t) with n(t) being the noise. Numerically, you can model n(t) using MATLABs randn
(for white Gaussian noise). Take 1500 samples on [2, 3] of f and do an
analysis w