FAST HAAR TRANSFORM BASED FEATURE EXTRACTION FOR MULTIMODAL BIOMETRIC SYSTEM ABSTRACT In many realworld applications, unimodal biometric systems often face signiﬁcant limitations due to sensitivity to noise, interclass variability, data quality, non universality, and other factors. Attempting to improve the performance of individual matchers in such situations may not prove to be highly effective. Multibiometric systems seek to alleviate some of these problems by providing multiple pieces of evidence of the same identity. These systems help achieve an increase in performance that may not be possible using a singlebiometric indicator. In this project we use multimodal biometric fast recognition method. Subspace learning is the process of ﬁnding a proper feature subspace and then projecting highdimensional data onto the learned lowdimensional subspace. The projection operation requires many ﬂoatingpoint multiplications and additions, which makes the projection process computationally expensive. To tackle this problem, this project proposes two simplebuteffective fast subspace learning and image projection methods, fast Haar transform (FHT) based principal component analysis. The advantages of this methods result from employing both the FHT for subspace learning and the integral vector for feature extraction. Experimental results on face,iris and fingerprint databases demonstrated their effectiveness and efficiency.
LIST OF ABBREVIATIONS
FHT Fast Haar Transform
PCA Principal Component Analysis
FLD Fisher’s Linear Discriminant
DSP Digital Signal Processing
RGB Red Green Blue
FAR False Accept Rate
FRR False Reject Rate
FTE Failure To Enroll rate
GAR Genuine Accept Rate
EER Equal Error Rate
DET Detection Error Tradeoff
CCD Charge Coupled Display
JPEG Joint Photographic Expert Group
GIF Graphics Interchange Format
BMP Bit MaP
EPS Encapsulated Post Script
PNG Portable Netwoks Graphics
HDF Hierarchial Data Format
AVI Audio Video Interface
OOP Object Oriented Programming
TIFF Tagged Image File Format
1.INTRODUCTION
Software and computer systems are recognized as a subset of simulated intelligent behaviors of human beings described by programmed instructive information. According to Wang, computing methodologies and technologies are developed to extend human capability, reachability, persistency, memory, and information processing speed. Biometric information system is one of the ﬁnest examples of computer system that tries to imitate the decisions that humans make in their everyday life, speciﬁcally concerning people identiﬁcation and matching tasks. In this quest, the biometric systems evolved from simple singlefeaturebased models to a complex decisionmaking mechanism that utilize artiﬁcial intelligence, neural networks, complex decision making schemes, and multiple biometric parameters extracted and combined in an intelligent way. The main goal and contribution of this Project is to present a comprehensive analysis of various biometric fusion techniques in combination with advanced biometric feature extraction mechanisms that improve the performance of the biometric information system in the challenging and not resolved problem of people identiﬁcation. A biometric identiﬁcation (matching) system is an automatic pattern recognition system that recognizes a person by determining the authenticity of a speciﬁc physiological and/or behavioral characteristic (biometric) possessed by that person. Physiological biometric identiﬁers include ﬁngerprints, hand...
...Queen Mary, University of London 
Lab 1: DFT,FFT and STFT 
ELEM018: Advanced Transform Methods 

Arsal Javid 
12/1/2011 
[Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.] 
Section 2:
The following code was used to calculate perform the DFT Function in Matlab:
function sw = dft(st)
% DFT  Discrete Fourier Transform
M = length(st);
N = M;
WN = exp(2*pi*j/N);
%Main Loop
for n=0:N1
temp = 0;
for m=0:M1
s = st(m+1);
temp = temp + (s* (WN ^ (n*m)));
end
sw(n+1) = temp;
end
The DFT function created was performed on the following signals and a graph was plotted using the function stem4.
The function used to display the results was as follows:
function stem4(s)
% STEM4  View complex signal as real, imag, abs and angle
subplot(4,1,1); stem(real(s)); title('Real');
subplot(4,1,2); stem(imag(s)); title('Imag');
subplot(4,1,3); stem(abs(s)); title('Abs');
subplot(4,1,4); stem(angle(s)); title('Angle');
end
The stem4 function was applied to the DFT function of the following signals.
Uniform Function:
S = ones(1,64)
From the figure above, the Real axis displays a nonzero value at the fundamental frequency; the same is also true when observing...
...Lecture 11 Fast Fourier Transform (FFT)
Weinan E1,2 and Tiejun Li2
1
Department of Mathematics,
Princeton University,
weinan@princeton.edu
2
School of Mathematical Sciences,
Peking University,
tieli@pku.edu.cn
No.1 Science Building, 1575
Examples
Fast Fourier Transform
Outline
Examples
Fast Fourier Transform
Applications
Applications
Examples
Fast FourierTransform
Applications
Signal processing
Filtering: a polluted signal
1.5
1
0.5
0
−0.5
−1
−1.5
0
200
400
600
800
1000
1200
High pass and low pass filter (signal and noise)
1.5
1
0.5
0
−0.5
−1
−1.5
0
200
400
600
800
1000
1200
How to obtain the high frequency and low frequency quickly?
Examples
Fast Fourier Transform
Solving PDEs on rectangular mesh
Solving the Poisson equations
−∆u = f in Ω
u = 0 on ∂Ω
in the rectangular domain
After discretization we will obtain the linear system with about N 2
unknowns
−
ui+1,j + ui−1,j + ui,j+1 + ui,j−1 − 4ui,j
= fij
4h2
The FFT would give a fast algorithm to solve the system above with
computational efforts O(N 2 log2 N ).
Applications
Examples
Fast Fourier Transform
Applications
Computing convolution (
)
Suppose
2π
f (x − y)g(y)dy
h(x) =
0
is the convolution of f and g, where f (x), g(x) ∈ C2π are period 2π
functions.
Take xj = jδ, j = 0, 1,...
...The Discrete Cosine Transform
(DCT):
Theory and Application
1
Syed Ali Khayam
Department of Electrical & Computer Engineering
Michigan State University
March 10th 2003
1
This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is
assumed. Interested readers should follow the references for advanced material on DCT.
ECE 802 – 602: Information Theory and Coding
Seminar 1 – The Discrete CosineTransform: Theory and Application
1. Introduction
Transform coding constitutes an integral component of contemporary image/video processing
applications. Transform coding relies on the premise that pixels in an image exhibit a certain
level of correlation with their neighboring pixels. Similarly in a video transmission system,
adjacent pixels in consecutive frames2 show very high correlation. Consequently, these
correlations can be exploited to predict the value of a pixel from its respective neighbors. A
transformation is, therefore, defined to map this spatial (correlated) data into transformed
(uncorrelated) coefficients. Clearly, the transformation should utilize the fact that the information
content of an individual pixel is relatively small i.e., to a large extent visual contribution of a
pixel can be predicted using its neighbors.
A typical image/video transmission system is outlined in Figure 1. The objective of the source
encoder is to...
...Preprint, February 1, 2004
1
Computation of the Fractional Fourier Transform
Adhemar Bultheel and H´ctor E. Mart´ e ınez Sulbaran 1
Dept. of Computer Science, Celestijnenlaan 200A, B3001 Leuven
Abstract In this note we make a critical comparison of some matlab programs for the digital computation of the fractional Fourier transform that are freely available and we describe our own implementation that ﬁlters the best out of the existing ones. Two types of transforms are considered: First the fast approximate fractional Fourier transform algorithm for which two algorithms are available. The method is described in H.M. Ozaktas, M.A. Kutay, and G. Bozda˘i. Digital computation of the fractional Fourier transform. g IEEE Trans. Signal Process., 44:2141–2150, 1996. There are two implementations: one is written by A.M. Kutay the other is part of package written by J. O’Neill. Secondly the discrete fractional Fourier transform algorithm described in the master thesis C. Candan. The discrete fractional Fourier transform, ¸ Bilkent Univ., 1998 and an algorithm described by S.C. Pei, M.H. Yeh, and C.C Tseng: Digital fractional Fourier transform based on orthogonal projections IEEE Trans. Signal Process., 47:1335–1348, 1999. Key words: Fractional Fourier transform
1
Introduction
The idea of fractional powers of the Fourier...
...BEGE.104
Bachelor's l)egree Programme
(BDPI
ASSIGNMENT
(For July
2013  2014
2013 and January 2014 sessions)
ELECTTVE COURSE IN ENGLISH (BEGE104)
English for B usiness Communication
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School of Humanities
Indira Gandhi National Open University
Maidan Garhi, New Delhil10 068
Elective Course in English (BEGE _rc4)
E ng lis h
.for
B us i n es s C omm unicctti o n
Programme Code: BDp
Course Code: BEGE 104120131 4
Dear Student,
You need to attempt one assignment forthe Elective
course in English (BEGE104): English for
Business comrnunication. This assignment is Tutor
Marked tirranl ancl carries 100 marks. The
TMA is concerned mainly with assessing your application
and your understanding of the colrrse
nraterial. It aims to teach as lvell as to assess your performance.
lnstructions: Before attempting the assignment please
read the following instructions carefirlly.
l'
Read the detailecl instructions about the assignr.nerrts
given in the progranrnre Guide for
Elective Courses.
2'
write your Roll NLrmber, Name, FLrll Address and Date
on tlre top right corner of the flrst
page olyoLrr respoltse sheet(s).
3'
write the Course Title, Assignment Number and the Name
of the StLrdy centre yolr are
attaclred to in the centre of the first page of you,
,"rponr" ,h.;(;j.'
4'
Do not plan to take the terminal examination for the
course if you have...
...2. Analysis of Signals
Figure 2.45.: Approximate FTs of two bandlimited signals
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The Hilbert transform of a function is by deﬁnition,
H {x(t)} = xh (t) =
∞
x(τ )
dτ
t −τ
−∞
1
π
(2.171)
which is the convolution of x(t) with 1/π t,
H {x(t)} = xh (t) = x(t) ∗
1
πt
(2.172)
if we take the FT of this convolution,
Xh (ω ) = X (ω ) × F
1
πt
(2.173)
From Example 2.24,
F {sgn(t)} =
2
jω
(2.174)
and using duality from Equation (2.126) and Example 2.26,
j
⇔ sgn(ω )
πt
therefore
F
(2.175)
1
πt
(2.176)
= − jsgn(ω )
87
2. Analysis of Signals
(a)
(b)
Figure 2.46.: −90◦ Phaseshifter
therefore
Xh (ω ) = − jX (ω )sgn(ω )
jXh (ω ) = X (ω )sgn(ω )
(2.177)
From the deﬁnition of the Hilbert transform and its FT, we may infer the following properties.
1. The function and its Hilbert transform have the same magnitude spectrum. This property
may inferred from the following facts.
x(t) ⇔ X (ω )
xh (t) ⇔ − jsgn(ω )X (ω )
(2.178)
therefore,
Xh (ω ) = − jsgn(ω )X (ω )
=  − jsgn(ω )X (ω )
= X (ω )
2. For a real time function, if we pass it through a −π /2 phase shifter, the output of the ﬁlter
is the Hilbert transform of the input. Referring to Figure 2.46 (a), x(t) is the input to the
phase shifter whose output is y(t). The phase shifter only has an effect on the phase, while...
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