EE 230C
Homework #3 Solution
Winter 2005
K. Yao
2
1. Consider the chirp signal x[n] = ei26(n/N ) , n = 1, . . . , N, with N = 200. Fig. 1 shows the magnitude of
the FFT of the signal. Fig. 2 shows the magnitude of the STFT of the signal using a Hanning wi

EE 230C
Homework #3
Due March 12th
Winter 2005
K. Yao
2
1. Consider the analysis of the chirp signal x[n] = ei26(n/N ) , n = 1, . . . , N, by FFT,
STFT, and Wagner-Ville TFD. Pick your own parameters to illustrate the features of
this signal by these thre

EE 230C
Midterm Exam (80 minutes; total 25 pts)
Winter 2003
K. Yao
1. Consider a Pisarenko frequency estimation problem with s[n] = 2ei(2f0 +) , where f0 is a fixed but
unknown real number in (0, 1), is a uniform r.v. on (0, 2], and the observation z[n] =

EE 230C
Homework #2
Due May 2nd
Spring 2013
K. Yao
1. For the following N = 16 windows, find w[n], n = 0, . . . , N 1, and W [k], k = 0, . . . , N 1.
Plot the magnitude of the frequency responses of the windows with few nulls, sidelobe peaks,
etc. Even th

Chapter 5
Time-Frequency Spectral Analysis
5.1
Time-Frequency Signal Representation
Many applications ranging from radar/sonar to speech processing, from seismic surveying, bioacoustical analysis, and condition-based maintenance, all deal with signals wit

Chapter 6
Wavelets and Subband
Decomposition
6.1
Introduction
In this chapter, we consider various aspects of the wavelet transform (WT). On the one hand, WT
is a relatively new analytical method of performing signal decomposition, just as the Fourier ser

Chapter 2
DFT, FFT, and Convolution
2.1
DFT and the classical Fourier Transform
From the classical Fourier transform theory, if we have an integrable continuous time signal x(t)
available on the real line, its Fourier transform can be obtained from
Z
X(f

Chapter 3
Spectral Analysis via
Continuous/Discrete Fourier
Transformation
3.1
Frequency Resolution of Continuous/Discrete Time Data
One of the most basic application of DFT/FFT in communication and radar systems is the detection
of the presence or absenc

N=31, E /N =27 dB, I=2, k=4, User number=8, Time variant P
b
o
D
80
Optimal sequence
Gold code
75
T /
ac D
70
65
60
55
0.4
0.45
0.5
0.55
0.6
Threshold
0.65
0.7
0.75
0.8
Figure 10.31: Acquisition time performance comparison for optimal sequences and Gold

EE 230C
Homework #1
Due April 18th
Spring 2013
K. Yao
1. Derive the Fourier transform F (f ) of the following time-domain signals f (t) by explicit
integrations (show all the steps in your derivations).
a. Consider f (t) = I[a,a] (t), where I[a,b] (t) is

Chapter 4
Parametric Spectral Analysis
In Chapter 3, the spectral analysis techniques based on DFT/FFT and windowing methods are
considered to be non-parametric since no assumptions were made on the spectral sources under consideration. In this chapter, w

Chapter 1
Applications of Spectral Analysis
1.1
Introduction
We want to consider qualitatively some applications of spectral analysis to various signal processing
problems in applied science, communication, control, and avionic/aerospace systems. From the