EE630 F11 Solutions/Notes:
10/2011
Problem-1:
(a)
y[n]
x[n]
2012
503
H (z)
630
105
Reduce to:
x[n]
x[n]
4
H (z)
6
y[n]
y[n]
2
x[n]
2
H (z)
2
2
E0(z)
3
3
y[n]
(b) This is not LTI because in the Z domain, the output is not the product of the
input and a tra

ENEE 630 Fall 2011 Homework 7
Material Covered: Parameters in LD Recursion and
Prediction Error
Problem 1 Consider a wide-sense stationary process cfw_u(n) whose autocorrelation function
has the following values for dierent lags:
r (0) = 1
r (1) = 0.8
r (

CHAPTER 1
1.1
Let
ru(k ) = E [u(n)u*(n k )]
(1)
r y(k ) = E [ y(n) y*(n k )]
(2)
We are given that
y(n) = u(n + a) u(n a)
(3)
Hence, substituting Eq. (3) into (2), and then using Eq. (1), we get
r y(k ) = E [(u(n + a) u(n a)(u*(n + a k ) u*(n a k )]
= 2ru

7 M -channel Maximally Decimated Filter Bank
Appendix: Detailed Derivations
Multi-rate Signal Processing
7. M -channel Maximally Decmiated Filter Banks
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides w

2 Discrete Wiener Filter
Appendix: Detailed Derivations
Part-II Parametric Signal Modeling and
Linear Prediction Theory
2. Discrete Wiener Filtering
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were

4 Levinson-Durbin Recursion
Appendix: More Details
Parametric Signal Modeling and
Linear Prediction Theory
4. The Levinson-Durbin Recursion
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on

1 Discrete-time Stochastic Processes
Appendix: Detailed Derivations
Parametric Signal Modeling and
Linear Prediction Theory
1. Discrete-time Stochastic Processes (2)
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: EN

5 Lattice Predictor
Appendix: Detailed Derivations
Parametric Signal Modeling and
Linear Prediction Theory
5. Lattice Predictor
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on class notes

ENEE630 PartENEE630 Part-3
Part 3. Spectrum Estimation
3.2 Parametric Methods for Spectral Estimation
Electrical & Computer Engineering
Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on class notes deve

1 Discrete-time Stochastic Processes
Appendix: Detailed Derivations
Parametric Signal Modeling and
Linear Prediction Theory
1. Discrete-time Stochastic Processes
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE63

ENEE624 Advanced Digital Signal Processing:
Filter Bank Design and Subband Coding for Digital
Audio
Hung-Quoc Lai, Steven Tjoa
Dept. of Electrical and Computer Engineering, University of Maryland
November 2003
Abstract
Multirate lter banks are often used

3 Linear Prediction
Appendix: Detailed Derivations
Part-II Parametric Signal Modeling
and Linear Prediction Theory
3. Linear Prediction
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on cla

ENEE630 PartENEE630 Part-3
Part 3. Spectrum Estimation
3.
3.1 Classic Methods for Spectrum Estimation
Classic
Electrical & Computer Engineering
Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on class no

ENEE 624 Homework #1
Problem 1 For the system in Fig. P-1, nd an expression for y(n) in terms of x(n). Simplify
x(n)
2
3
3
y(n)
2
Figure 1: P-1
the expression as best as you can.
Problem 2 Show that the two systems shown in Fig. P-2(a) (where k is some in

ENEE 624 Homework #2
Problem 1 Suppose the analysis lters in a two-channel QMF bank are given by the following
set of equations:
H0 (z) = 2 + 6z 1 + z 2 + 5z 3 + z 5
H1 (z) = H0 (z)
Find a set of stable synthesis lters which result in perfect reconstructi

1 Basic Multirate Operations
2 Interconnection of Building Blocks
Multi-rate Signal Processing
Prof. Min Wu
University of Maryland, College Park
[email protected]
Updated: September 6, 2011
Acknowledgment: ENEE630 slides were based on class notes developed by

1 Basic Multirate Operations
2 Interconnection of Building Blocks
Multi-rate Signal Processing
Prof. Min Wu
University of Maryland, College Park
[email protected]
Updated: September 8, 2011
Acknowledgment: ENEE630 slides were based on class notes developed by

6 Quadrature Mirror Filter (QMF) Bank
Appendix: Detailed Derivations
Multi-rate Signal Processing
6. Quadrature Mirror Filter (QMF) Bank
Electrical & Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on cl

(1) Relation between 2nd order statistics of x[n] and v[n]:
see class notes for Section 2.1 (replace y[n] in the derivation there with v[n])
For a stable H(z), v[n] is w.s.s.
(2) y[n] is no longer w.s.s. (unless y[n] is a constant sequence of zeros)
The e

8 General Alias-Free Conditions for Filter Banks
9 Tree Structured Filter Banks and Multiresolution Analysis
Appendix: Detailed Derivations
Multi-rate Signal Processing
8. General Alias-Free Conditions for Filter Banks
9. Tree Structured Filter Banks and

ENEE630 PartENEE630 Part-3
Part 3. Spectrum Estimation
3.3 Subspace Approaches to Frequency Estimation
Electrical & Computer Engineering
Computer Engineering
University of Maryland, College Park
Acknowledgment: ENEE630 slides were based on class notes dev

Review of Discrete-Time System
Prof. Min Wu
University of Maryland, College Park
[email protected]
Updated: August 31, 2011
Acknowledgment: ENEE630 slides were based on class notes developed by Profs. K.J. Ray Liu and Min Wu.
The LaTeX version includes contri

4 Multistage Implementations
5 Some Multirate Applications
Multi-rate Signal Processing
4. Multistage Implementations
5. Multirate Application: Subband Coding
Prof. Min Wu
University of Maryland, College Park
[email protected]
Updated: September 20, 2011
Ackn

ENEE630 ADSP
RECITATION 5
Material Covered: General Conditions on Alias-Free, Amplitude Distortion Free
and P.R. in Multirate Systems, Pseudo-Circulant Representation
1.
Consider a 4-channel lter bank which is alias-free. If we know part of the matrix P (

ENEE630 Fall 2010 Midterm Exam
This is a close-book close-notes exam. There are three problems for a total of 60 points. Write legibly and
show the necessary intermediate steps of your solutions. You will be graded based on what you write down
on the exam

ENEE630 ADSP
RECITATION 9
Material Covered: Wiener Filter
1.
[Problem 8.3 continued] Assume v (n) and w(n) are white Gaussian random processes with
zero mean and variance 1. The two lters in Fig. R9.1 are G(z ) =
1
10.4z 1
and H (z ) =
2
.
10.5z 1
Figure