ECE-600 Homework #4
Introduction to Digital Signal Processing
Winter 2011 Feb. 5, 2011
HOMEWORK ASSIGNMENT #4 Due Fri. Feb. 11, 2011 (in class)
1. Say that a signal x(t) is sampled at rate 1/T1 Hz, producing x[n], and then sinc-reconstructed at 1 rate 1/T
ECE-600 Homework #3
Introduction to Digital Signal Processing
Winter 2011 Jan. 21, 2011
HOMEWORK ASSIGNMENT #3 Due Fri. Jan. 28, 2011 (in class)
1. The following matlab routine helps to visualize the sampling of a complex sinusoid:
f0 = 1; T = 0.1; n = [0
ECE-600 Homework #7
Introduction to Digital Signal Processing
Autumn 2010 Nov. 19, 2010
HOMEWORK SOLUTIONS #7
1. For this problem, we can use the IDFT denition plus a variable change (l = N 1 k ): y [n] = 1 N 1 N
N 1
Y [k ]ej N nk =
k=0 N 1
2
2
1 N
N 1
X
ECE-600 Homework #1
Introduction to Digital Signal Processing
Winter 2011 Jan. 12, 2011
HOMEWORK SOLUTIONS #1
1. Here, the input/output relationship of H is y [n] = (a) For H to be linear, we need that
2 m=0
x[n m] = x[n] + x[n 1] + x[n 2].
Hcfw_x[n] + w[
ECE-600
Introduction to Digital Signal Processing
Autumn 2011
Homework #1
Sep. 28, 2011
HOMEWORK SOLUTIONS #1
1. Here, the input/output relationship of H is y [n] =
2
m=0 (3m)x[nm]
= 3x[n]+2x[n1]+x[n2].
(a) For H to be linear, we need that
Hcfw_x[n] + w[n
ECE-600 Homework #4
Introduction to Digital Signal Processing
Winter 2011 Feb. 11, 2011
HOMEWORK SOLUTIONS #4
1. For rate-1/T1 sampling, the relationship between the CTFT of the continuous-time signal x(t) and the DTFT of the discrete time signal x[n] is
ECE-600 Homework #8
Introduction to Digital Signal Processing
Autumn 2010 Nov. 24, 2010
HOMEWORK ASSIGNMENT #8 Due Fri. Dec. 4, 2010 (in class)
1. Using Matlab, you are to design a bandpass lter that suppresses the signal over the frequency ranges [0, 0.2
Chapter 8
8.1
Analyzing Figure P8.1, we get w[n] = A( X [n] + CDu[n]) and
y[n] = C ( ABx[n] + u[n]). A direct implementation of these two equations leads to
the structure shown below which has no delay-free loop.
A
w[n]
x[n]
AB
CD
y[n]
8.2
C
u[n]
(a) Figu
Home Assignment 8
Due on July 30, 2008
Exercise 1
A Chebyshev-I lter of order N = 3 and 0 = 1 is known to have a pole at s = 1 rad/s. a) Find the other two poles of the lter and its parameter . b) The lter is transformed to the z domain using a bilinear t
Home Assignment 6
Due on July 9, 2008
Exercise 1
A causal LTI system has impulse response h[n], for which the z-transform is H(z) = 1 + z 1 1 (1 1 z 1 )(1 + 4 z 1 ) 2
a) What is the region of convergence of H(z)? b) Is the system stable? Explain. c) Find
Home Assignment 5
Due on June 30, 2008
Exercise 1
Consider the window w[n] = sin4 n N 1 .
Explore the properties of this window: main-lobe width and side-lobe level. How is this window related to the Hann window?
Exercise 2
We are given 128 samples of the
Home Assignment 1
Due on May 20, 2008
Exercise 1
In this problem we derive the Fourier transforms of the sign function and the unit-step function.
Part A
Find the Fourier transform of the signal (for > 0) et , t > 0, x(t) = 0, t = 0, t e , t < 0.
Part B
T
Home Assignment 4
Due on June 16, 2008
Exercise 1
Let 0 = 16 . Consider three values N = 16, N = 64, and N = 256. Let xN [n] = cos(0 n) for n = 0, . . . , N 1, and XN [k] be its N-point DFT coecients.
a) Plot |XN [k]| for the above three values of N . Us
Home Assignment 8
Due on July 17, 2008
Exercise 1
Design a symmetric FIR lter with group delay N/2 according to the ideal magnitude response 1, 0 | , 3 f |Hd ()| = 0, < | < 2 , 3 3 0.5, 2 | . 3 A. Compute hd [n]. B. If the lter is designed with the Hammin
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EE600 Assignment #3 Solutions & Comments
Autumn 2003
1. Sampling and nonlinearities
Let us denote yc (t) = x3 (t) + 0.5x(t). Then, the multiplication x(t) x(t) x(t) is a
convolution in the frequency domain:
Yc (j ) =
1
cfw_X X X (j ) + 0.5X (j )
4 2
Hence
EE600 Assignment #2 Solutions & Comments
Autumn 2003
1. Execution of the given Matlab commands gives both a time-domain and a frequency-domain view
of a linear time-invariant system. This system, described by the coecients in b, is a nite impulse
response
EE600, Autumn 2003: Assignment #1 Solutions & Comments
1. Median lter: The median lter is an example of order statistic ltering. The median
lter is a useful, simple processing technique that is nonlinear and dicult to implement
with analog circuits. The m
ECE 413
Solution to assignment 5
Solutions to assignment'
J
Exercise 1
tj
5
N
Page I of3
ECE 413
Solution to assignment 5
Exercise 2
t
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T
Exercise 3 a)
The rectanglIl;:u' wincklws 7J)1 and Ul2 , [n] [n], differ only in their lengths, which an) ~:i2
and
Assignment #7 Solutions
Page 1 of 2
Exercise 1
(A) From the general multiband filter formula we get
hd [n]
sin[(n 0.5 N 0( / 3)]
sin[cfw_n 0.5 N )(2 / 3)]
0.5
, n 0.5 N
(n 0.5 N )
(n 0.5 N )
and
hd [0.5 N ] 0.5
(B) Using the Hamming window parameters,