EE 1563 - Digital Signal Processing Laboratory
Solutions Sample Exam 2
Fall, 2010
1. You have designed the following digital low-pass filters with the same cutoff frequency (3
dB attenuation) of 4000 Hz and a stopband starting at 5000 Hz with a minimum of
EE 1563 - Digital Signal Processing Laboratory
Solutions Exam 1
March 1, 2010
1. Use backward differences to derive a discrete system estimate of the differential equation:
dy
dx
, y ( 0) = 0
+ 10 y =
dt
dt
Find the transfer function of the discrete syste
EE 1563 - Digital Signal Processing Laboratory
Sample Exam 2
Closed book. One sheet (two sides) of notes - Be sure to show your work.
Fall, 2010
1. You have designed the following digital low-pass filters with the same cutoff frequency (3
dB attenuation)
EE 1563 - Digital Signal Processing Laboratory
Sample Exam 1
Open Notes (and Books) - Be sure to show your work.
Fall, 2010
1. Use backward differences to derive a discrete system estimate of the differential equation:
dy
dx
+ 10 y =
, y ( 0) = 0
dt
dt
Fi
Linear Systems Analysis
JR Boston, August 21, 2007
page 1
Review of Continuous Linear Systems Analysis
We define systems in terms of their effects on signals. We generally consider signals to be
functions of time, such as the sinusoid
x1(t) = A cos t
or t
Linear Control
JR Boston
January 5, 2009
page 1
Notes on Linear Feedback Control
EE/BIOENG 1680/2680
Spring, 2009
J.R. Boston
A commonly encountered example of a control system is a room thermostat for a forced hot
air heating system. When the room temper
1.
So
So
So
2. A)
B)
3. N = 8
4.
(
)
()
5. By sampling 8 points on the result of problem 4 from 0 to
We have
This is exactly the same with the result of problem 3.
1.
a) Y[0] = 0
Y[1] = X[0] Y[0]/4 = 1
Y[2] = -X[0]/2 Y[1]/4 +Y[0]/8 = -3/4
Y[3] = -Y[2]/4 + Y[1]/8 = 5/16
b)
()
()
()
()
()
()
()
()
(
)(
)
Both the poles are inside the unit circle, so the system is stable
c) Do partial fraction expansion
()
()
(
)
(
)
(
1.
(
(
)
(
)
)
(
()
)
(
()
)
()
()
()
The pole is z = 1-aT, for the system to be stable, we should have |1-aT| < 1, so 0<T<2/a
2. (a) x[n-1] y[n-1] = y[n]
So , for [ ]
[ ] we have y[1] = x[0]+y[0] = 1, y[n] = -y[n-1] for n>1
()
(b)y[n] = 1-y[n-1] for n>0,
ECE 1563 Fall, 2010
Solutions to Homework 4: Spectral Analysis
1. Assume that you have sampled a 1000 Hz sine wave at 5000 samples per second for 10
milliseconds. You then implement a discrete Fourier transform (fft) on the data.
a) How many points are in
October 12, 2010
EE 1563 - Digital Signal Processing Laboratory
Exam 1 Solutions
1. You are given a discrete system with transfer function
H(z) =
Y(z)
1 + 0.7z 1
=
X (z) (1 + 0.9z 1 )(1 0.9z 1 )
a) Sketch the pole-zero diagram for H(z).
Zeros are at 0 and
EE 1563 - Digital Signal Processing Laboratory
Exam 2 - Solutions
Fall, 2010
1. Consider a filter with discrete impulse response h(n) = [0 A A 0]. Evaluate a 4-point
discrete Fourier transform and find the value of A that makes the maximum value of the
fr
Notes on the discrete Fourier transform
J.R. Boston
January, 2006
page 1
Notes on the discrete Fourier transform
These notes provide a brief overview of the discrete Fourier transform (DFT). The DFT is used
in computer processing of discrete signals in th