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An introduction to convex optimization modelling using cvxopt in an IPython environment. The facility location problem is used as an example to demonstrate modelling in cvxopt.
Convex Optimization Modelling with CVXOPTandrewmart11
An introduction to convex optimization modelling using cvxopt in an IPython environment. The facility location problem is used as an example to demonstrate modelling in cvxopt.
A description about image Compression. What are types of redundancies, which are there in images. Two classes compression techniques. Four different lossless image compression techiques with proper diagrams(Huffman, Lempel Ziv, Run Length coding, Arithmetic coding).
A description about image Compression. What are types of redundancies, which are there in images. Two classes compression techniques. Four different lossless image compression techiques with proper diagrams(Huffman, Lempel Ziv, Run Length coding, Arithmetic coding).
Introduction to Digital Image Processing Using MATLABRay Phan
This was a 3 hour presentation given to undergraduate and graduate students at Ryerson University in Toronto, Ontario, Canada on an introduction to Digital Image Processing using the MATLAB programming environment. This should provide the basics of performing the most common image processing tasks, as well as providing an introduction to how digital images work and how they're formed.
You can access the images and code that I created and used here: https://www.dropbox.com/sh/s7trtj4xngy3cpq/AAAoAK7Lf-aDRCDFOzYQW64ka?dl=0
To Get any Project for CSE, IT ECE, EEE Contact Me @ 09666155510, 09849539085 or mail us - ieeefinalsemprojects@gmail.com-Visit Our Website: www.finalyearprojects.org
This presentation shares some basic concepts about audio processing and image processing using MATLAB and was used as teaching material for an introductory workshop.
This file contains slides that explains the IIR filter design techniques. Especially the time invariance and bilinear transformations. The material found in this presentation was taken from Oppenheim second edition reference book, I hope that anyone who read this presentation to leave a feedback that mention its suitability
Design of Filter Circuits using MATLAB, Multisim, and ExcelDavid Sandy
The purpose of this project was to design crossover active filter circuits, in order to drive music through three different types of speakers. So, high frequencies would be sent through a Tweeter speaker, low frequencies would be sent through a Woofer speaker, and middle frequencies would be sent through a Midbass driver speaker. Three circuits were created to drive these speakers. Multisim, MATLAB, and Excel, were all used in the design process in order to create the filter circuits correctly.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Computational Tools and Techniques for Numerical Macro-Financial ModelingVictor Zhorin
A set of numerical tools used to create and analyze non-linear macroeconomic models with financial sector is discussed. New methods and results for computing Hansen-Scheinkman-Borovicka shock-price and shock-exposure elasticities for variety of models are presented. Spectral approximation technology (chebfun):
numerical computation in Chebyshev functions piece-wise smooth functions
breakpoints detection
rootfinding
functions with singularities
fast adaptive quadratures continuous QR, SVD, least-squares linear operators
solution of linear and non-linear ODE
Frechet derivatives via automatic differentiation PDEs in one space variable plus time
Stochastic processes:
(quazi) Monte-Carlo simulations, Polynomial Expansion (gPC), finite-differences (FD) non-linear IRF
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Direct split-radix algorithm for fast computation of type-II discrete Hartley...TELKOMNIKA JOURNAL
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Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
2. Introduction
In mathematics, Golden Section Transform is a
new class of discrete orthogonal transform. Its
theory involves golden ratio, Fibonacci number,
Fourier analysis, wavelet theory, stochastic
process, integer partition, matrix analysis, group
theory, combinatorics on words, its applied fields
include digital signal (image/audio/video)
processing, denoising, watermarking,
compression, coding and so on. see here.
3. Simple Compression Scheme
Source image is
divided into 8 × 8
blocks of pixels
Apply 2D transform
(LGST, HGST,
Haar, D4) to each
8 × 8 block
4. Set compression ratio, keep largest
abs(elements) in each block, and set all the
others to zero
Apply inverse 2D transform to each 8 × 8 block
to reconstruct the image
Compute PSNR and compare the results.
9. Matlab Code
gstdemo.m % main file
lgst2d.m % 4-level 2d low golden section transform
ilgst2d.m % 4-level inverse 2d low golden section transform
haar2d.m % 3-level 2d haar wavelet lifting scheme
ihaar2d.m % 3-level inverse 2d haar wavelet transform
lword.m % Type-L golden section decomposion of fibonacci number
hgst2d.m % 2-level 2d high golden section transform
ihgst2d.m % 2-level inverse 2d high golden section transform
hword.m % Type-H golden section decomposion of fibonacci number
d42d.m % 3-level 2d Daubechies-4 wavelet lifting scheme
id42d.m % 3-level inverse 2d D4 wavelet transform
keep.m % keep largest abs(values) in matrix
psnr.m % compute MSE and PSNR
all the codes can be downloaded here:
http://goldensectiontransform.org/
10. haar2d.m
function H = haar2d(X)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% function H = haar2d(X,nlevel)
% 3-level 2d haar wavelet transform of 8*8 image matrix
nlevel = 3; % 3-level transform for each 8*8 image block
[xx,yy] = size(X);
H=X;
for i=1:nlevel
for j=1:xx
[ss,dd] = haar1d(H(j,1:yy)); % row transform
H(j,1:yy) = [ss,dd];
end
for k=1:yy
[ss,dd] = haar1d(H(1:xx,k)'); % column transform
H(1:xx,k) = [ss,dd]';
end
xx = xx/2;
yy = yy/2;
end
%% 1d haar lifting scheme
function [ss,dd] = haar1d(S)
N = length(S);
s0 = S(1:2:N-1); % S(1),S(3),S(5),S(7)...
d0 = S(2:2:N); % S(2),S(4),S(6),S(8)...
s1 = s0 + d0;
d1 = s0 - 1/2*s1;
ss = s1/sqrt(2);
dd = sqrt(2)*d1;
11. d42d.m function H = d42d(X)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% function H = d42d(X,nlevel)
% 3-level 2d Daubechies-4 wavelet transform of 8*8 image matrix
nlevel = 3; % 3-level transform for each 8*8 image block
[xx,yy] = size(X);
H=X;
for i=1:nlevel
for j=1:xx
[ss,dd] = d41d(H(j,1:yy)); % row transform
H(j,1:yy) = [ss,dd];
end
for k=1:yy
[ss,dd] = d41d(H(1:xx,k)'); % column transform
H(1:xx,k) = [ss,dd]';
end
xx = xx/2;
yy = yy/2;
end
%% 1d D4 wavelet lifting scheme
function [ss,dd] = d41d(S)
N = length(S);
s0 = S(1:2:N-1); % S(1),S(3),S(5),S(7)...
d0 = S(2:2:N); % S(2),S(4),S(6),S(8)...
s1 = s0 + sqrt(3)*d0;
d1 = d0 - sqrt(3)/4*s1 - (sqrt(3)-2)/4*[s1(N/2) s1(1:N/2-1)]; % per_ext
s2 = s1 - [d1(2:N/2) d1(1)]; % per_ext
ss = (sqrt(3)-1)/sqrt(2)*s2;
dd = (sqrt(3)+1)/sqrt(2)*d1;
% ref: http://en.wikipedia.org/wiki/Daubechies_wavelet
12. lgst2d.m
function H = lgst2d(X)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% function H = lgst2d(X,nlevel)
% 4-level 2d low golden section transform of 8*8 image matrix
nlevel = 4; % 4-level transform for each 8*8 image block
global lj; % only used by function lgst1d(S) below.
global FBL; % only used by function lgst1d(S) below.
[xx,yy] = size(X);
ind = floor(log(xx*sqrt(5)+1/2)/log((sqrt(5)+1)/2)); % determine index
FBL = filter(1,[1 -1 -1],[1 zeros(1,ind-1)]);
% FBL = Fibonacci sequence -> [1 1 2 3 5 8...];
H=X;
for lj=1:nlevel
for j=1:xx
[ss,dd] = lgst1d(H(j,1:yy)); % row transform
H(j,1:yy) = [ss,dd];
end
for k=1:yy
[ss,dd] = lgst1d(H(1:xx,k)'); % column transform
H(1:xx,k) = [ss,dd]';
end
xx = FBL(end-lj); % round((sqrt(5)-1)/2*xx); 8*8 block: xx=8->5->3->2
yy = FBL(end-lj); % round((sqrt(5)-1)/2*yy); 8*8 block: yy=8->5->3->2
end
%% 1d low golden section transform
function [ss,dd] = lgst1d(S)
global lj;
global FBL;
index = 0;
h = 1;
lform = lword(length(S));
for i=1:length(lform)
index = index + lform(i);
if lform(i) == 1
ss(i) = S(index);
else % lform(i) == 2
ss(i) = (sqrt(FBL(lj))*S(index-1)+sqrt(FBL(lj+1))*S(index))/sqrt(FBL(lj+2));
dd(h) = (sqrt(FBL(lj+1))*S(index-1)-sqrt(FBL(lj))*S(index))/sqrt(FBL(lj+2));
h = h+1;
end
end
13. lword.m
function lform = lword(n)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% Type-L golden section decomposion of fibonacci number n,
% e.g. lword(8) = [1 2 2 1 2];
if n == 1
lform = [1];
elseif n == 2
lform = [2];
else
next = round((sqrt(5)-1)/2*n);
lform = [lword(n-next),lword(next)];
end
14. hgst2d.m
function H = hgst2d(X)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% function H = hgst2d(X,nlevel)
% 2-level 2d high golden section transform of 8*8 image matrix
nlevel = 2; % 2-level transform for each 8*8 image block
global hj; % only used by function hgst1d(S) below.
global FBH; % only used by function hgst1d(S) below.
[xx,yy] = size(X);
ind = floor(log(xx*sqrt(5)+1/2)/log((sqrt(5)+1)/2)); % determine index
FBH = filter(1,[1 -1 -1],[1 zeros(1,ind-1)]);
% FBH = Fibonacci sequence -> [1 1 2 3 5 8...];
H=X;
for hj=1:nlevel
for j=1:xx
[ss,dd] = hgst1d(H(j,1:yy)); % row transform
H(j,1:yy) = [ss,dd];
end
for k=1:yy
[ss,dd] = hgst1d(H(1:xx,k)'); % column transform
H(1:xx,k) = [ss,dd]';
end
xx = FBH(end-2*hj); % round((3-sqrt(5))/2*xx); 8*8 block: xx=8->3
yy = FBH(end-2*hj); % round((3-sqrt(5))/2*yy); 8*8 block: yy=8->3
end
%% 1d high golden section transform
function [ss,dd] = hgst1d(S)
global hj;
global FBH;
index = 0;
g = 1;
h = 1;
hform = hword(length(S));
for i=1:length(hform)
index = index + hform(i);
if hform(i) == 2
ss(i) = (sqrt(FBH(2*hj-1))*S(index-1)+sqrt(FBH(2*hj))*S(index))/sqrt(FBH(2*hj+1));
dd(2*i-g) = (sqrt(FBH(2*hj))*S(index-1)-sqrt(FBH(2*hj-1))*S(index))/sqrt(FBH(2*hj+1));
g = g+1;
else % hform(i) == 3
ss(i) = (sqrt(FBH(2*hj))*S(index-2)+sqrt(FBH(2*hj-1))*S(index-1)+sqrt(FBH(2*hj))*S(index))/sqrt(FBH(2*hj+2));
dd(i+h-1) = (sqrt(FBH(2*hj-1))*S(index-2)-2*sqrt(FBH(2*hj))*S(index-1)+sqrt(FBH(2*hj-1))*S(index))/sqrt(2*FBH(2*hj+2));
dd(i+h) = (S(index-2)-S(index))/sqrt(2);
h = h+1;
end
end
15. hword.m
function hform = hword(n)
% Author: Jun Li, more info@ http://goldensectiontransform.org/
% Type-H golden section decomposion of fibonacci number n,
% e.g. hword(8) = [3 2 3];
if n == 2
hform = [2];
elseif n == 3
hform = [3];
else
next = round((sqrt(5)-1)/2*n);
hform = [hword(n-next),hword(next)];
end
16. keep.m
function X = keep(X)
% keep the largest abs(elements) of X,
% global RATIO set in gstdemo.m is in [0,1].
global RATIO;
N = floor(prod(size(X))*RATIO);
[MM,i] = sort(abs(X(:)));
X(i(1:end-N)) = 0;
17. psnr.m
function [MSE,PSNR] = psnr(X,Y)
% Compute MSE and PSNR.
MSE = sum((X(:)-Y(:)).^2)/prod(size(X));
if MSE == 0
PSNR = Inf;
else
PSNR = 10*log10(255^2/MSE);
end
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27. Links
Jun Li's Golden Section Transform Home Page
http://goldensectiontransform.org/
http://www.maths.surrey.ac.uk/hosted-sites/
R.Knott/Fibonacci/fibrab.html
http://en.wikipedia.org/wiki/Fibonacci_word
http://mathworld.wolfram.com/RabbitSequence.html
The infinite Fibonacci word, https://oeis.org/A005614
Lower Wythoff sequence, http://oeis.org/A000201
Upper Wythoff sequence, http://oeis.org/A001950
https://oeis.org/A072042