This preview shows pages 1–3. Sign up to view the full content.
1
Kyung Hee University
Department of Electronics and Radio Engineering
C1002900
Random Processing
Homework 3: Sinusoid Estimation
Spring 2010
Professor Hyundong Shin
Issued:
May 3, 2010
Due:
May 17, 2010
(No acceptance of overdue submission)
Reading:
Course textbook Chapter 8
In this homework, we explore a basic problem involving sinusoid estimation. Specifically, given
noisy observation of the form
cos
,
, ,
,
nn
YA
n
W
n
N
0
01
1
(3.1)
we wish to estimate one or more of the nonrandom parameters
A
,
0
, or
, where
A
0 and
0
0
. In (3.1), we assume that the noises
n
W
are i.i.d.
,
2
0
random variables. This
model arises in a number of applications: analog communications, Doppler radar, noise cancel
lation, interference suppression, radio astronomy, and sonar directionfinding, for example.
○
Analog Communication
Amplitude Modulation (AM):
In AM systems, the frequency
0
is known, but the am
plitude
A
varies with time and carries the information. In such systems, we can gener
ally approximate the amplitude as constant over the block of
N
samples, and consider
the problem of recovering the amplitude for each block as an estimation problem. In
such problems, the phase
may be known, but more typically is an unknown parame
ter that, while not of interest, must be simultaneously estimated.
Phase Modulation (PM):
In PM systems, it is the phase
that carries the information
while the frequency
0
remains essentially fixed (and known). In such problems, the
amplitude
A
is generally distorted by the channel and while similarly not of interest,
must be jointly estimated as well.
Frequency Modulation (FM):
In FM systems, the frequency
0
carries the information
and varies with time accordingly. In such systems, we then wish to estimate
0
, which
is modeled as essentially constant over the block of length
N
. Typically, the communi
cation channel distorts both the amplitude
A
and phase
, so these quantities must be
simultaneously (i.e., jointly) estimated.
○
Noise and Interference Cancellation
A wide variety of noise and interference encountered in practice is inherently sinusoidal in
nature. Examples include 60 Hz (linefrequency) interference in systems due to AC power
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
supplies, noise from rotating machinery, propeller noise in aircraft or on ships, and nar
rowband jamming
―
hostile or inadvertent
―
in wireless communication systems. In such
cases, the sinusoidal term in (3.1) may be the unwanted interference and
n
W
may represent
the (broadband) signal of interest. For these scenarios, an effective interference suppression
strategy involves estimating the parameters of the sinusoidal interferer, then subtracting it
out from the observations to recover the signal of interest.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '10
 HyungdongShin

Click to edit the document details