ECE 158 Gibson Homework #2 Solutions
Fall 2010
Problem 1: 5.2 b) x[n] = [-1 5 3 0 3] h[n] = [-2 0 5 3 -2]
By adding the columns above each Yc component, you should obtain Yc[n] = [1 -1 -2 16 26]. If you have the 4th edition with x[n] = [-1 5 3 0 3] and h[
ECE 158 Gibson Homework #5 Solutions
Fall 2010
Problem 2: The direct form DFT is given as
The DFT is calculated as follows:
Therefore
Problem 3: A basic decimation-in-time FFT butterfly computation is given below
Using the butterfly graph above, we can ex
ECE 158 Gibson Homework Assignment #6 1. Problem 13.3 (3rd ed) and 13.1 (4th ed) in the text.
Fall Quarter 2010 Due: 12/02/10
2. For the two-channel QMF filter bank below, (a) If the analysis filters are H 0 ( z ) = 3 + 4 z 1 and H1 ( z ) = 1 + 2 z 1 , fi
ECE 158
Gibson
Fall 2010
Homework #6 Solutions
Problem 2:
a)
With H0(z) = 3+4z-1 and H1(z) = 1 +2z-1, G0(z) and G1(z) can be found as
H0(z) G0(z) + H1(z) G1(z) = 2z-L
H0(-z) G0(z) + H1(-z) G1(z) = 0
(perfect reconstruction condition)
(alias cancellation c
ECE 158 Fall 2010: Lab Instructions
And some tips on getting a good grade
1. Lab reports are due at the start of the lab in which you are enrolled on the
following week.
2. There are three options for submitting a lab report: (1) Hand a printed version
to
ECE 158 Gibson Mid-Term Exam
Fall Quarter 2008 11/03/08
Instructions: Do all problems. Show all work. Problems are weighted as shown. 1. (15) Let x(t ) be an analog signal with a bandwidth of 3,000 Hz. (a) What is the minimum sampling rate for this signal
Polyphase Decompositions and QMF Channel Banks
(Slides adapted from S. Mitra to accompany the text, Digital Signal Processing)
Jerry D. Gibson
ECE 158 Fall 2010
12/1/2010
Polyphase Decomposition
The Decomposition Consider an arbitrary sequence cfw_x[n] wi
Upsampling
ECE 158 Fall 2010
Temporal Domain: M zeros inserted between samples of x[n]. (M=1, N=10)
Intuition: Higher frequencies needed to represent jumps in the signal
Periodic with period N
Upsampling increases the size of the DFT to 2N, but does not c
ECE 158 Gibson Homework Assignment #5 1. Problem 11.16 (3rd or 4th edition) from the text.
Fall Quarter 2010 Due: 11/16/10
1111 2. Compute the 8-point DFT of the sequence x[n] = cfw_ , , , , 0, 0, 0, 0 using the 2222 direct expression for the DFT. 3. Repe
ECE 278A - HW #5: Wavelets Transform (DUE Wed. November 14th) 1. Write two Matlab functions to implement the 2D Wavelets (using the Haar transform). Your functions (one for the analysis and one for the synthesis) should have the following format:
[F]=Wave
Digital Signal Processing: A Computer-Based Approach
3rd Edition
by
Sanjit K. Mitra
Errata List
Chapter 1
1. Page 4, Eq. (1.1): Replace the lower limit of the integral with .
Chapter 2
1. Page 45, line 2 below Eq. (2.9): Insert for a length-N sequence, af
ECE 158, Digital Signal Processing, Fall 2010
Schedule: Tuesday/Thursday 3:30-4:45, Phelps 3523 http:/www.ece.ucsb.edu/courses/ECE158/158_F10Gibson/default.html Department of Electrical and Computer Engineering
University of California, Santa Barbara
Inst
ECE 158 Gibson Homework Assignment #1
Fall Quarter 2010 Due: 10/05/10
All problems are from the text. The problem numbers correspond to the 3rd or 4th edition as shown. 3rd Edition 1. 2. 3. 4. 5. 6. 7. Problem 2.67 Problem 2.82 Problem 2.87 Problem 3.5 Pr
ECE 158 Gibson Homework Assignment #2 Problems are from the text: 1. Problem 5.2 (b)both 3rd and 4th editions
Fall Quarter 2010 Due: 10/19/10
2. Calculate the linear convolution corresponding to Problem 5.2 (b) both 3rd and 4th editions 3. Problem 5.9 (a)
ECE 158 Gibson Homework Assignment #3
Fall Quarter 2010 Due: 10/26/10
All problems are from the text. The problem numbers correspond to the 3rd or 4th edition as shown. 3rd Edition 1. 2. 3. Problem 5.30(c) Problem 5.45 Problem 5.61(c) 4th Edition Problem
ECE 158 Gibson Homework Assignment #4 Problems are from the text: 3rd Edition 1. Problem 6.37 2. Problem 6.43(a) 3. Problem 6.47 4. Problem 6.48 5. Problem 6.54 4th Edition Problem 6.42 Problem 6.47(a) Problem 6.65 Problem 6.66 Problem 6.71
Fall Quarter 2
ECE 158 Gibson Homework #4 Solutions
Fall 2010
6.37/6.42
For the 4th edition, we have
6.43(a)/6.47(a)
For 6.47(a) in the 4th edition, the z transform is given by Hence,
6.47/6.65
6.48/6.66
R=6
R=5
6.54/6.71