FFT is an efficient algorithm to compute the discrete Fourier transform (DFT) and convert a time domain signal to its frequency domain representation. Radix-2 FFT is the most common algorithm, in which the input is divided into groups of 2 samples at each stage. FFT algorithms generally have a number of samples that is a power of 2, like 2N, to efficiently compute the DFT. The radix-2 FFT breaks the computation into "butterflies" or decimation in time (DIT) and decimation in frequency (DIF) structures to recursively compute the DFT. Twiddle factors representing complex roots of unity are used to compute the outputs of each butterfly operation.
UNIT II DISCRETE TIME SYSTEM ANALYSIS 6+6
Z-transform and its properties, inverse z-transforms; difference equation – Solution by ztransform,
application to discrete systems - Stability analysis, frequency response –Convolution – Discrete Time Fourier transform , magnitude and phase representation
Although eigenvalues are one of the most important concepts in linear algebra, some of us eigen-struggle with them without understanding their usefulness and beauty. In this talk I'll briefly review the definition of eigenvalues emphasizing the associated geometric idea and I'll show how can they be used in some applications.
From the Un-Distinguished Lecture Series (http://ws.cs.ubc.ca/~udls/). The talk was given Mar. 16, 2007
Slide for study session given by Ryosuke Sasaki at Arithmer inc.
It is a summary of recent methods for object pose estimation in robotics using deep learning.
He entered Ph.D course at Univ. of Tokyo in April 2020.
Arithmer株式会社は東京大学大学院数理科学研究科発の数学の会社です。私達は現代数学を応用して、様々な分野のソリューションに、新しい高度AIシステムを導入しています。AIをいかに上手に使って仕事を効率化するか、そして人々の役に立つ結果を生み出すのか、それを考えるのが私たちの仕事です。
Arithmer began at the University of Tokyo Graduate School of Mathematical Sciences. Today, our research of modern mathematics and AI systems has the capability of providing solutions when dealing with tough complex issues. At Arithmer we believe it is our job to realize the functions of AI through improving work efficiency and producing more useful results for society.
A detailed note on the Fourier Transform of the Unit Step Signal. This text explains the various approaches used in the evaluation of the Fourier transform of the unit step signal.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
This method, Newton raphson helps to approximate the root of a non linear equation.
The presentation also tells about the Advantages and disadvantages of the method.
UNIT II DISCRETE TIME SYSTEM ANALYSIS 6+6
Z-transform and its properties, inverse z-transforms; difference equation – Solution by ztransform,
application to discrete systems - Stability analysis, frequency response –Convolution – Discrete Time Fourier transform , magnitude and phase representation
Although eigenvalues are one of the most important concepts in linear algebra, some of us eigen-struggle with them without understanding their usefulness and beauty. In this talk I'll briefly review the definition of eigenvalues emphasizing the associated geometric idea and I'll show how can they be used in some applications.
From the Un-Distinguished Lecture Series (http://ws.cs.ubc.ca/~udls/). The talk was given Mar. 16, 2007
Slide for study session given by Ryosuke Sasaki at Arithmer inc.
It is a summary of recent methods for object pose estimation in robotics using deep learning.
He entered Ph.D course at Univ. of Tokyo in April 2020.
Arithmer株式会社は東京大学大学院数理科学研究科発の数学の会社です。私達は現代数学を応用して、様々な分野のソリューションに、新しい高度AIシステムを導入しています。AIをいかに上手に使って仕事を効率化するか、そして人々の役に立つ結果を生み出すのか、それを考えるのが私たちの仕事です。
Arithmer began at the University of Tokyo Graduate School of Mathematical Sciences. Today, our research of modern mathematics and AI systems has the capability of providing solutions when dealing with tough complex issues. At Arithmer we believe it is our job to realize the functions of AI through improving work efficiency and producing more useful results for society.
A detailed note on the Fourier Transform of the Unit Step Signal. This text explains the various approaches used in the evaluation of the Fourier transform of the unit step signal.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
This method, Newton raphson helps to approximate the root of a non linear equation.
The presentation also tells about the Advantages and disadvantages of the method.
Dynamic stiffness and eigenvalues of nonlocal nano beams - new methods for dynamic analysis of nano-scale structures. This lecture gives a review and proposed new techniques.
Computing f-Divergences and Distances of\\ High-Dimensional Probability Densi...Alexander Litvinenko
Talk presented on SIAM IS 2022 conference.
Very often, in the course of uncertainty quantification tasks or
data analysis, one has to deal with high-dimensional random variables (RVs)
(with values in $\Rd$). Just like any other RV,
a high-dimensional RV can be described by its probability density (\pdf) and/or
by the corresponding probability characteristic functions (\pcf),
or a more general representation as
a function of other, known, random variables.
Here the interest is mainly to compute characterisations like the entropy, the Kullback-Leibler, or more general
$f$-divergences. These are all computed from the \pdf, which is often not available directly,
and it is a computational challenge to even represent it in a numerically
feasible fashion in case the dimension $d$ is even moderately large. It
is an even stronger numerical challenge to then actually compute said characterisations
in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose
to approximate density by a low-rank tensor.
Introduction to Information Technology Lecture 2MikeCrea
Number Systems
Types of number systems
Number bases
Range of possible numbers
Conversion between number bases
Common powers
Arithmetic in different number bases
Shifting a number
In this work we discuss how to compute KLE with complexity O(k n log n), how to approximate large covariance matrices (in H-matrix format), how to use the Lanczos method.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
1. DFT and FFT
• FFT is an algorithm to convert a time domain
signal to DFT efficiently.
• FFT is not unique. Many algorithms are
available.
• Each algorithm has merits and demerits.
• In each algorithm, depending on the sequence
needed at the output, the input is regrouped.
• The groups are decided by the number of
samples.
2. FFTs
• The number of points can be nine too.
• It can be 15 as well.
• Any number in multiples of two integers.
• It can not be any prime number.
• It can be in the multiples of two prime
numbers.
3. FFTs
• The purpose of this series of lectures is to
learn the basics of FFT algorithms.
• Algorithms having number of samples 2N,
where N is an integer is most preferred.
• 8 point radix-2 FFT by decimation is used
from learning point of view.
• Radix-x: here ‘x’ represents number of
samples in each group made at the first
stage. They are generally equal.
• We shall study radix-2 and radix-3.
4. Radix-2: DIT or, DIF
• Radix-2 is the first FFT algorithm. It was
proposed by Cooley and Tukey in 1965.
• Though it is not the efficient algorithm, it lays
foundation for time-efficient DFT calculations.
• The next slide shows the saving in time
required for calculations with radix-2.
• The algorithms appear either in
(a) Decimation In Time (DIT), or,
(b) Decimation In Frequency (DIF).
• DIT and DIF, both yield same complexity and
results. They are complementary.
• We shall stress on 8 to radix 2 DIT FFT.
5. Other popular Algorithms
Besides many, the popular algorithms are:
• Goertzel algorithm
• Chirp Z algorithm
• Index mapping algorithm
• Split radix in prime number algorithm.
have modified approach over radix-2.
Split radix in prime number does not use even the twiddles.
We now pay attention to 8/radix-2 butterfly FIT FFT algorithm.
6. Relationship between exponential forms
and twiddle factors (W) for Periodicity = N
Sr.
No.
Exponential form Symbolic form
01 e-j2n/N = e-j2(n+N)/N WN
n = WN
n+N
02 e-j2(n+N/2)/N = - e-j2n/N WN
n+N/2= - WN
n
03 e-j2k = e-j2Nk/N = 1 WN
N+K = 1
04 e-j2(2/N) = e-j2/(N/2) WN
2 = WN/2
8. DFT calculations
• The forward DFT, frequency domain output in the
range 0kN-1 is given by:
• While the Inverse DFT, time domain output, again, in
the range 0kN-1 is denoted by
X k
( )
0
n 1
n
x n
( ) W
N
nk
x n
( )
1
N
0
n 1
k
X k
( ) W
N
nk
9. Matrix Relations
• The DFT samples defined by
can be expressed in NxN matrix as
where
T
N
X
X
X ]
[
.....
]
[
]
[ 1
1
0
X
T
N
x
x
x ]
[
.....
]
[
]
[ 1
1
0
x
1
0
,
]
[
]
[
1
0
N
k
W
n
x
k
X
N
n
kn
N
x(n)
X(k)
1
0
n
N
nk
N
W
10. Matrix Relations
can be expanded as NXN DFT matrix
2
)
1
(
)
1
(
2
)
1
(
)
1
(
2
4
2
)
1
(
2
1
1
0
1
1
1
1
1
1
1
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
k
nk
N
W
W
W
W
W
W
W
W
W
W
1
0
N
k
nk
N
W
11. DFT:
For N of length 4,range of n, k = [0 1 2 3] each.
Hence X(n) = x(0)WN
n.0+x(1)WN
n.1+x(2)WN
n.2 + x(3)WN
n.3
X k
( )
0
n 1
n
x n
( ) W
N
nk
x
x(0) x(1) x(2) x(3)
X(0) = W4
0x0 W4
0x1 W4
0x2 W4
0x3
X(1) = W4
1x0 W4
1x1 W4
1x2 W4
1x3
X(2) = W4
2x0 W4
2x1 W4
2x2 W4
2x3
X(3) = W4
3x0 W4
3x1 W4
3x2 W4
3x3
15. Matrix Relations
• Likewise, the IDFT is
can be expressed in NxN matrix form as
1
0
,
]
[
]
[
1
0
N
n
W
k
X
n
x
N
k
n
k
N
X(k)
1
0
n
x
1
N
n
nk
N
W
16. Matrix Relations
can also be expanded as NXN DFT matrix
2
)
1
(
)
1
(
2
)
1
(
)
1
(
2
4
2
)
1
(
2
1
1
0
1
1
1
1
1
1
1
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
k
nk
N
W
W
W
W
W
W
W
W
W
W
1
0
N
k
nk
N
W
Observe:
1
0
N
k
nk
N
W
1
0
1
*
1
0
N
n
nk
N
W W
N
N
k
nk
N
The inversion can be had by Hermitian conjugating j by –j and dividing by N.
23. The Process of Decimation
• First step of process of decimation is splitting a
sequence in smaller sequences.
• A sequence of 15 can be splitted in five
sequences of threes or three sequences of fives.
• A sequence of 16 numbers can be splitted in 2
sequences of 8. Further,
each sequence of 8 can be be splitted in two
sequences of 4;
Subsequently each sequence of 4 can be splitted in
two sequences of two;
There can be various combinations and varied
complexities.
24. 4-point DFT
X 0
( )
X 1
( )
X 2
( )
X 3
( )
1
1
1
1
1
j
1
j
1
1
1
1
1
j
1
j
x 0
( )
x 1
( )
x 2
( )
x 3
( )
Can be, by interchanging col. 2 and 3, seen as
X 0
( )
X 1
( )
X 2
( )
X 3
( )
1
1
1
1
1
1
1
1
1
j
1
j
1
j
1
j
x 0
( )
x 2
( )
x 1
( )
x 3
( )
26. Matrix manipulation to get the desired
input sequence from the actual
x 0
( )
x 2
( )
x 1
( )
x 3
( )
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
x 0
( )
x 1
( )
x 2
( )
x 3
( )
27. Process of decimation: example
X[n]
-1
-2 1
2 3 4
5
6
7 n
X[1]
X[3]
X[5]
X[7]
X[n]
-1
-2 1
2 3 4
5
6
7 n
X[1]
X[2]
X[3] X[4]
X[5]
X[6]
X[7]
X[0]
X[n]
-1
-2 1
2 3 4
5
6
7 n
X[2]
X[4]
X[6]
X[0]
Separating the above sequence for +ve ‘n’ in even and odd sequence numbers .
28. Process of decimation: example
X[n]
-
- 1
2 3 4
5
6
7 n
X[1]
X[3]
X[5]
X[7]
2 3 4 6
X[n]
- 1 5 7 n
X[2]
X[4]
X[6]
X[0]
Compress the even sequence by two.
Shift the sequence to left by one and
compress by two
X[n]
-
1 2 3
n
X[2]
X[4]
X[6]
X[0]
X[n]
2
4 6 n
X[1]
X[3]
X[5]
X[7]
The compression is also called decimation
29. x 0
( ) x 2
( )
x 0
( ) x 2
( )
x 1
( ) x 3
( )
x 1
( ) x 3
( )
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
x 0
( )
x 2
( )
x 1
( )
x 3
( )
X 0
( )
X 1
( )
X 2
( )
X 3
( )
1
0
1
0
0
1
0
1
1
0
1
0
0
j
0
j
x 0
( ) x 2
( )
x 0
( ) x 2
( )
x 1
( ) x 3
( )
x 1
( ) x 3
( )
X 0
( )
X 1
( )
X 2
( )
X 3
( )
1
0
1
0
0
1
0
1
1
0
1
0
0
j
0
j
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
x 0
( )
x 2
( )
x 1
( )
x 3
( )
First stage of
realization
Second
stage
30. Decimation of 4 point DFT into 2xradix-2
• The values of
W4
0= 1; W4
2 = -1; W4
1= -j; and W4
3 = j
X[0]
x0
x2
x1
x3
x0+x2
xo -x2
x1+x3
x1-x3
X[1]
X[2]
X[3]
Wo
w1
W2
W3
-1
-1
31. Decimation of 4 point DFT into 2xradix-2
• The values of
W4
0= 1; W4
2 = -1; W4
1= -j; and W4
3 = j
X[0]
N/4 point
DFT
even
N/4 point
DFT
odd
x0
x2
x1
x3
x0+x2
xo -x2
x1+x3
x1-x3
X[1]
X[2]
X[3]
Wo
w1
W2
W3