Electrocardiogram (ECG or EKG)

To view the presentation, please click on the below link:

http://www.slideshare.net/minh65/electrocardiogram-ecg-or-ekg

To view the presentation, please click the below link:

http://www.slideshare.net/minh65/simulation-results-of-induction-heating-coil

matlab code to study upsampling(Sampling rate) of audio file

%% matlab code to study upsampling(Sampling rate) of audio file
% sounds like a problem of asynchronous sample rate conversion. 
% To convert from one sample rate to another: 
% use sinc interpolation to compute the continuous time representation 
% of the signal then resample at our new sample rate.
% resample the signal to have sample times that are fixed.
% Read in the sound
% returns the sample rate(FS) in Hertz
% N = number sample 
% the number of bits per sample (BITS) used to encode the data in the file
% Minh Anh Nguyen
% minhanhnguyen@q.com

% close
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables.
clc;% Clear the command window.
imtool close all; % Close all imtool figures.
workspace; % Make sure the workspace panel is showing.
%% read and plot .wav file
figure;

myvoice1 = audioread('good2.wav');
% Reads in the sound file, into a big array called y.
[y1, fs1] = audioread('good2.wav');
size(y1);
left1=y1(:,1);
right1=y1(:,2);
N = length(right1);
% Normalize y; that is, scale all values to its maximum. 
y = right1/max(abs(right1));
t1 = (0:1:N-1)/fs1;
plot(t1,right1 );
str1=sprintf('Sound with sampling rate = %d Hz and number sample = %d', fs1, N);
title(str1);
xlabel('time (sec)'); ylabel('relative signal strength'); grid on;
axis tight
grid on;

%% Compute the power spectral density, a measurement of the energy at various frequencies
% DFT to describe the signal in the frequency
NFFT = 2 ^ nextpow2(N);
Y = fft(y1, NFFT) / N;
f = (fs1 / 2 * linspace(0, 1, NFFT / 2+1))'; % Vector containing frequencies in Hz
amp = ( 2 * abs(Y(1: NFFT / 2+1))); % Vector containing corresponding amplitudes
figure;
plot (f, amp); xlim([0,1600]);  ylim([0,0.5e-4]);
title ('plot single-sided amplitude spectrume of signal')
xlabel ('frequency (Hz)')
ylabel ('|y(f)|')
grid on;

% display markers at specific data points on DFT graph 
indexmin1 = find(min(amp) == amp);
xmin1 = f(indexmin1);
ymin1 = amp(indexmin1);
indexmax1 = find(max(amp) == amp);
xmax1 = f(indexmax1);
ymax1 = amp(indexmax1);
strmax1 = [' Maximum = ',num2str(xmax1),' Hz','    ', num2str(ymax1),' dB'];
text(xmax1,ymax1,strmax1,'HorizontalAlignment','Left');

fsorg=44100;
fs = 8000;
%%  resample is your function. To downsample signal from 44100 Hz to 8000 Hz:
%(the "1" and "2" arguments define the resampling ratio: 8000/44100 = 1/2)
%To upsample back to 44100 Hz: x2 = resample(y,2,1);
figure;
y_1 = resample(y1,fs,fsorg);
N1_1 = length(y_1);

t1_1 = (0:1:length(y_1)-1)/fs;
plot(t1_1, y_1);
str1=sprintf('Sound with sampling rate = %d Hz and number sample = %d', fs, N1_1);
title(str1);
xlabel('time (sec)');
ylabel('signal strength')
axis tight
grid;

%% Compute the power spectral density, a measurement of the energy at various frequencies
% DFT to describe the signal in the frequency
NFFTd = 2 ^ nextpow2(N1_1);
Yd = fft(y_1, NFFTd) / N1_1;
fd = (fs / 2 * linspace(0, 1, NFFTd / 2+1))'; % Vector containing frequencies in Hz
amp_down = ( 2 * abs(Yd(1: NFFTd / 2+1))); % Vector containing corresponding amplitudes
figure;
plot (fd, amp_down); xlim([0,1600]);  ylim([0,0.5e-4]);
title ('\t plot single-sided amplitude spectrume of downsampling signal')
xlabel ('frequency (Hz)')
ylabel ('|y(f)|')
grid on;

% display markers at specific data points on DFT graph 
indexmin1 = find(min(amp_down) == amp_down);
xmin1 = fd(indexmin1);
ymin1 = amp_down(indexmin1);
indexmax1 = find(max(amp_down) == amp_down);
xmax1 = fd(indexmax1);
ymax1 = amp_down(indexmax1);
strmax1 = [' Maximum = ',num2str(xmax1),' Hz','    ', num2str(ymax1),' dB'];
text(xmax1,ymax1,strmax1,'HorizontalAlignment','Left');

Matlab code to compute the corresponding absorption coefficients

 %% oxyhemoglobin and deoxyhemoglobin extinction.m
 % Author:Minh Anh Nguyen
 % minhanhnguyen@q.com
 % Matlab code to compute the corresponding absorption coefficients and plot 
 % the three absorption spectra on the same graph. 
 % Identify the low-absorption near-IR window that provide deep
 % penetration.
 % data for molar extinction coefficients of oxy-and deoxyhemoglobin and 
 % absorption coefficient of pure water as a function of wavelength are
 % copied directly from this website: http://omlc.org/spectra/hemoglobin/summary.html
 % Use physiologically representative values for both oxygen saturation SO2
 % and total concentration of hemoglobin CHb.
 % These values for the molar extinction coefficient e in [cm-1/(moles/liter)] were compiled by Scott Prahl using data from

    %W. B. Gratzer, Med. Res. Council Labs, Holly Hill, London
    %N. Kollias, Wellman Laboratories, Harvard Medical School, Boston 

%To convert this data to absorbance A, multiply by the molar concentration and the pathlength. For example, if x is the number of grams per liter and a 1 cm cuvette is being used, then the absorbance is given by

        %(e) [(1/cm)/(moles/liter)] (x) [g/liter] (1) [cm]
  %A =  ---------------------------------------------------
                     %     64,500 [g/mole]

%using 64,500 as the gram molecular weight of hemoglobin.

%To convert this data to absorption coefficient in (cm-1), multiply by the molar concentration and 2.303,

   % µa = (2.303) e (x g/liter)/(64,500 g Hb/mole) 
%where x is the number of grams per liter. A typical value of x for whole blood is x=150 g Hb/liter. 


close all; clear; clc;
load ('oxy_deoxy.mat');
figure;
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,2),  'b', 'linewidth',1.5);
hold on
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,3),  'r', 'linewidth',1.5);
title('The molar oxyhemoglobin and deoxyhemoglobin extinction','FontSize',14);
set(gca,'FontSize',14);
ylabel('molar extinction coefficient (cm^{-1}(moles/l)^{-1})','fontsize',14);
xlabel('wavelength (nm)','fontsize',14);
axis([250 1000 0 10^6]);
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 5]);
grid on;
legend('y = HbO2 ','y = Hb')

%% purewater

load ('purewater.mat');
figure;
semilogy(water(:,1), water(:,2),  'b', 'linewidth',1.5);
title('The pure water specific absorption coefficient ','FontSize',14);
set(gca,'FontSize',14);
ylabel(' specific absorption coefficient (um^{-1})','fontsize',14);
xlabel('wavelength (nm)','fontsize',14);
axis([300 1000 0 1*10^6]);
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 5]);
grid on;
legend('y = pure water')

%% all three graph
figure;
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,3)*0.0054,  'r', 'linewidth',1.5);
hold on
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,2),  'b', 'linewidth',1.5);
hold on
semilogy(water(:,1), water(:,2),  'y', 'linewidth',1.5);
title('The molar hemoglobin and water extinction','FontSize',14);
set(gca,'FontSize',14);
ylabel('molar extinction coefficient (cm^{-1}(moles/l)^{-1})','fontsize',14);
xlabel('wavelength (nm)','fontsize',14);
%axis([250 1000 0 0.6*10^6]);
axis([250 1000 0 1*10^6]);
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 5]);
grid on;
legend('y = HbO2 ','y = Hb', 'y = pure water')

%% Absorption
figure;
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,2)*0.0054,  'b', 'linewidth',1.5);
hold on
semilogy(oxy_deoxy(:,1), oxy_deoxy(:,3)*0.0054,  'r', 'linewidth',1.5);
hold on
semilogy(water(:,1), water(:,2),  'y', 'linewidth',1.5);
title('The hemoglobin and water','FontSize',14);
set(gca,'FontSize',14);
ylabel('effective absorption coefficient (um^{-1})','fontsize',14);
xlabel('wavelength (nm)','fontsize',14);
axis([250 1000 0 1*10^6]);
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 5]);
grid on;
legend('y = HbO2 ','y = Hb', 'y = pure water')

Matlab code to calculate and plot pulses on a lossless transmission line at13.5Mhz

% this matlab code is calculate and plot pulses on a lossless transmission line
% Frequency is 13.5Mhz
%minhanhnguyen@q.com

% Clear the screen
clc;
clear;
% close all windows
close all;

% use these Parameters to calculate and plot Pulse Propagation on a Transline
Ro=50; %Ro = line impedance
Rl=100; %Rl = load resistance
Rg=25; %Rg = generator resistance
Vo=10; %Vo = voltage source
T=.08; %T = pulse width
v=1; %v = wave velocity
d=1; %d = line length
dt=.02; %dt = time step,
n=170; %n = number of time steps

% Voltage Divider at Input
vDivider = (Ro/(Ro+Rg));

% Reflection Coefficient at Load
gamLoad = (Rl-Ro)/(Rl+Ro);

% Reflection Coefficient at Generator
gamGenerator = (Rg-Ro)/(Rg+Ro);

% Transit Time
tTime = d/v;

% Position along the line
x=[0:d/500:d];

for j = 0:n;

% Time
t = j*dt;

% Leading edge of pulse
xl = v*t;

% Trailing edge of pulse
xt = v*(t-T);

% Voltage along the line at time t
V = Vo*(vDivider*(x<xl).*(x>xt));
V = V + Vo*(vDivider*gamLoad)*(x>(2*d-xl)).*(x<(2*d-xt));
V = V + Vo*(vDivider*gamLoad*gamGenerator)*(x<(xl-2*d)).*(x>(xt-2*d));
V = V + Vo*(vDivider*(gamLoad^2)*gamGenerator)*(x>(4*d-xl)).*(x<(4*d-xt));

% Plotting the result
plot(x,V);axis([0 d -Vo Vo]);grid;
title('Pulse voltage vs. distance');
xlabel('Distance Along The Line');
ylabel('Pulse Voltage');
pause(.5)
end

Matlab code to calculate the voltage on the transmission line

% This matlab code is setup for calculating the voltage on the 
% transmission line. The code will then plot the results. 
% frequency is 13.5Mhz


% Clear the screen
clc;
clear all;
% close all windows
close all;


%% input values 
RL = 20;        % resistive part of load
CL = 3.3e-9;    % capacitive part of load
len = 80;       % transmission line length
freq = 13.5e+6;  % frequency
omega = 2*pi*freq;
Z0 = 50;        % characteristic impedance of line
v = 2e+8;       % velocity in RG 58 cable
ZS = 50;        % source impedance

%% set up the node measurements with arbitrary values

z_node = [0:4:len];      % equivalent position of nodes on transmission line

V_node = [0 1 2 3.1 4 5 6 7 8.2 9 10 11.4 12 13 14 15 16 17];
V_node = [V_node 18.1 19 20.5];

%%set up phase measurements with arbitrary values
phase_node = [0 1 2 3.1 4 5 6 7 8.2 9 10 11.4 12 13 14 15 16 17];
phase_node = [phase_node  18.1 19 20.5];


%%calculating the transmission line voltage 

z = [0:1:len];                  % z position on line
ZL = RL - j./omega./CL;         % load impedance
V_line = ZL .* z .* exp(-j.*omega.*z./v) ./len;


%% Find the magnitude and angle of the voltage phasor
V_line_mag = abs(V_line);
V_line_deg = 180*angle(V_line)./pi;


%% Plot results
figure(1);
subplot(2,1,1), plot(z,V_line_mag, z_node, V_node, 'o');
title('Unmodified line vs. V magnitude');
ylabel('V magnitude');
legend('trans. line analysis','circuit analysis', 0);
subplot(2,1,2), plot(z,V_line_deg, z_node, phase_node, 'o');
title('Unmodified line vs. phase');
ylabel('phase(degrees)');
xlabel('z position on line (meters)');
legend('trans. line analysis','circuit analysis', 0);

MatLab function to plot Amplitude Envelopes of .wav file

% This MatLab function takes a "wav" sound file as an input
% perform the average and peak envelopes of an input signal,
% and then plot all three plots on a graph.
% usage: amplitude_envelopes ('*.wav')
% Author: Minh Anh Nguyen
% email: minhanhnguyen@q.com


function [amplitude_envelopes] = amplitude_envelopes ( file );
close all;% Close all figures (except those of imtool.)
 clf % Clears the graphic screen.


% Reads in the sound file, into a big array called y.
y1=audioread(file);
[y1, fs1]=audioread(file);
size(y1);
left1=y1(:,1);
right1=y1(:,2);

% Normalize y; that is, scale all values to its maximum. 
y = right1/max(abs(right1));

% If you want to hear the sound after you read it in 
% Sound just plays a file to the speaker.

sound(y, 44100);

% Initialize peak and average arrays to be the same as the signal. We’re 
% keeping three big arrays, all of the same length.

average_env = y;
max_env = y;

% Set the window lengths directly, in number of samples.
% the average should be smaller than the peak, since it will tend to 
% flatten out if it gets too big. 
% average and peak window size are two numbers, which can be played with 
% to vary what the pictures will look like. 
% Note: use two different window sizes so that we can have 
% different kinds of resolution for peak and average charts.

average_window_size = 512;
peak_window_size = 10000;

% from the input signal, taking an average of the previous, 
% average window size number of samples, and store that in the current 
% place in the average array.
% Use a loop that starts at the end of the first window and goes to the 
% end of the sound file, indicated by length(average_env). 
% use "sum" command to take some range of a vector.

for k = average_window_size:length(average_env)
running_sum = sum(abs(y(k-average_window_size+1:k)));
average_env(k) = running_sum /average_window_size ;
end

% from the input signal, taking the maximum value of the previous 
% peak_window_size number of samples.

for k = peak_window_size:length(max_env)
max_env(k)= max(abs(y(k-peak_window_size+1:k)));

end

% Plot the three "signals": the original in the color cyan, the 
% peak in magenta, and the average in blue. The colors are the 
% letters in single quotes.

plot(y, 'c')
hold on
plot (max_env, 'm')
hold on
plot(average_env, 'b')
title('Monochord: Signal, Average Signal Envelope, Peak Signal Envelope')
xlabel('sample number')
ylabel('amplitude (-1 to 1)')
legend('original signal', 'peak envelope', 'running average envelope', 0)

Matlab code to calculate the potential of line charges

Contents

• set up arrays of line charge locations
• strength of each line charge
• plot the Efield arrows and labels for the voltage contours

% Matlab code to calculate the potential due to a set of line charges.  The voltage
% reference is taken as the origin.  The code will have problems if any line
% charges are located at the origin.

% Clear the screen
clc;
clear all;
% close all windows
close all;

set up arrays of line charge locations
xcharge = [3.5 2 -2];  % x position of line charge in mm
ycharge = [-0.1 -1 3];  % y position of line charge in mm
xcharge = xcharge * .001; % convert to meters
ycharge = ycharge * .001;


strength of each line charge
rho_l_basic = 1e-7;   % units are C/m
rho_l = rho_l_basic * [1 3 -2];

% Set up grid for plotting
Ngrid = 33;
gridmax = .004;
% grid is the x and y values at which the calculation is done
grid = linspace(-gridmax, gridmax, Ngrid);

% Calculate voltage on grid due to each charge
% create 2 3D grids.  size of the arrays are Ngrid x Ngrid x ncharge
% The first array represents all combination of xgrid and ygrid
% locations with the xposition of the line charge.  The second
% represents all combinations with the y position of the line charges.
[xx1, yy1, xc1] = meshgrid(grid, grid, xcharge);
[xx2, yy2, yc2] = meshgrid(grid, grid, ycharge);
% Distance between the line charges and the grid points (3D array)
dist1 = sqrt( (xx1-xc1).^2 + (yy2 - yc2).^2);
% Grid points very close to a line charge will have a very high voltage that
%  will dominate contour plot.  Suppress this.
  dist1min =  .0002;
  dist1 = max(dist1, dist1min);
%  distance to reference voltage location (the origin).
dist2 = sqrt(xc1.^2 + yc2.^2);

% Calculate voltage at each grid point.  Vparts is the partial contribution to
% the voltage at each grid point (except for a charge strength factor).  It is
% an(Ngrid x Ngrid x ncharge) array.  The loop to calculate Vgrid then sums up
% the contributions of the various line charges.  Vgrid is an Ngrid x Ngrid
% array.
fac = 1./(2*pi*8.854e-12); % 1/(2*pi* epsilon0)
Vparts = fac.* log(dist2./dist1);
ncharge = length(xcharge); % get number of charges from length of array
Vgrid = zeros(Ngrid, Ngrid); % initialize Vgrid array
for ii = 1:ncharge
  Vgrid = Vgrid + Vparts(:,:,ii).*rho_l(ii);
end
[Ex, Ey] = gradient(-Vgrid);  % calculate electric field everywhere





plot the Efield arrows and labels for the voltage contours
% Plot results
% create position arrays in mm
grid_mm = grid*1000;
figure(1)
[cc, hh] = contour(grid_mm, grid_mm, Vgrid,15);

% adds contour value labels the voltage contours
clabel(cc,hh);

axis('equal');
axis([-4 4 -4 4]);
hold on;

% plot E field vectors
quiver(grid_mm, grid_mm, Ex, Ey);

title('Voltage contours and E field arrows');
ylabel('y (mm)');
xlabel('x (mm)');
hold off;

figure(2)
grid_cen = fix((Ngrid+1)/2);
plot(grid_mm, Vgrid(grid_cen,:));
title('Voltage on x axis');
ylabel('Voltage');
xlabel('x (mm)')

Matlab code to plot field for 2 point charges

Contents

• input info.
• Plot result of equipotential contours at high resolution and countours
• plot equipotential contours at lower resolution to see individual contours easier
• plots all four graph on the same page for comparison

% This matlab code is used to plot field for 2 point charges,
%minhanhnguyen@q.com
% Clear the screen
clc;
clear all;
% close all windows
close all;

input info.

Dimensions

dimension=1;
d=dimension;
% Charge Value
charge =1;
q=charge;

% Creates the array of points for plotting v
[x,y]=meshgrid([-d:d/33:d],[-d:d/33:d]);

% Evaluate v using Coulombs Law
v=-q./(4.*pi.*sqrt((x+d./2).^2+(y+d./2).^2))+q./(4.*pi.*sqrt((x-d./2).^2+(y-d./2).^2));

Plot result of equipotential contours at high resolution and countours

figure (1);
contour(v,[-1:.005:1]);
title('equipotential contours at high resolution');

%plot contours at an elevation proportional to voltage
figure;
contour3(v,[-1:.005:1]);
title('contours at elevation proportional to voltage for high resolution');

plot equipotential contours at lower resolution to see individual contours easier

figure (2);
contour(v,[-1:.05:1]);
title('equipotential contours at low resolution');

%%plot contours at an elevation proportional to voltage
figure;
contour3(v,[-1:.05:1]);
title('contours at elevation proportional to voltage');

plots all four graph on the same page for comparison

figure (3);
subplot(2,2,1);contour(v,[-1:.005:1]);
title('equipotential contours at high resolution');
subplot(2,2,2);contour3(v,[-1:.005:1]);
title('contours at elevation proportional to voltage for high resolution');
subplot(2,2,3);contour(v,[-1:.05:1]);
title('equipotential contours at low resolution');
subplot(2,2,4);contour3(v,[-1:.05:1]);
title('contours at elevation proportional to voltage');

Published with MATLAB® R2015a

Matlab code to calculate Magnetic Flux of solenoid

Contents

• Clear the screen
• information of coil
• test
• test

% Magnetic Flux distribution using Finite Element Method...
% of a Solenoid Vertically placed on XY plane..
% Field distribution is calculated on XZ plane @ origin (Y=0)..
% We will use Biot-Savart Law for this...
% Refer - http://en.wikipedia.org/wiki/Biot-Savart_law...
% minhanhnguyen@q.com

Contents


Clear the screen
information of coil
test
test


% Magnetic Flux distribution using Finite Element Method...
% of a Solenoid Vertically placed on XY plane..
% Field distribution is calculated on XZ plane @ origin (Y=0)..
% We will use Biot-Savart Law for this...
% Refer - http://en.wikipedia.org/wiki/Biot-Savart_law...
% minhanhnguyen@q.com


Clear the screen
clear all
clc
% close all windows
close all;


information of coil
global u0
u0=4*pi*1e-7;

d = 2;                  % Radius of the Loop.. (2cm = 20 mm)
m = -1;                 % Direction of current through the Loop... 1(ANTI-CLOCK), -1(CLOCK)
N = 30;                 % Number sections/elements in the conductor...
T = 10;                 % Number of Turns in the Solenoid..
g = 0.75;               % Gap between Turns.. (mm)
dl = 2*pi*d/N;          % Length of each element..



% XYZ Coordinates/Location of each element from the origin(0,0,0), Center of the Loop is taken as origin..
dtht = 360/N;                           % Loop elements divided w.r.to degrees..
tht = (0+dtht/2): dtht : (360-dtht/2);  % Angle of each element w.r.to origin..

xC =  d.*cosd(tht).*ones(1,N);      % X coordinate...
yC =  d.*sind(tht).*ones(1,N);      % Y coordinate...

% zC will change for each turn, -Z to +Z, and will be varied during iteration...
zC = ones(1,N);
h = -(g/2)*(T-1) : g : (g/2)*(T-1);

% Length(Projection) & Direction of each current element in Vector form..
Lx = dl.*cosd(90+tht);        % Length of each element on X axis..
Ly = dl.*sind(90+tht);        % Length of each element on Y axis..
Lz = zeros(1,N);              % Length of each element is zero on Z axis..

% Points/Locations in space (here XZ plane) where B is to be computed..
NP = 125;               % Detector points..
xPmax = 3*d;            % Dimensions of detector space.., arbitrary..
zPmax = 1.5*(T*g);

xP = linspace(-xPmax,xPmax,NP);        % Divide space with NP points..
zP = linspace(-zPmax,zPmax,NP);
[xxP zzP] = meshgrid(xP,zP);            % Creating the Mesh..

% Initialize B..
Bx = zeros(NP,NP);
By = zeros(NP,NP);
Bz = zeros(NP,NP);

% Computation of Magnetic Field (B) using Superposition principle..
% Compute B at each detector points due to each small cond elements & integrate them..
for p = 1:T
    for q = 1:N
        rx = xxP - xC(q);               % Displacement Vector along X direction from Conductor..
        ry = yC(q);                     % No detector points on Y direction..
        rz = zzP - h(p)*zC(q);          % zC Vertical location changes per Turn..

        r = sqrt(rx.^2+ry.^2+rz.^2);    % Displacement Magnitude for an element on the conductor..

        r3 = r.^3;


        Bx = Bx + m*Ly(q).*rz./r3;      % m - direction of current element..
        By = By - m*Lx(q).*rz./r3;
        Bz = Bz + m*Lx(q).*ry./r3 - m*Ly(q).*rx./r3;
    end
end
B = sqrt(Bx.^2 + By.^2 + Bz.^2);        % Magnitude of B..
B = B/max(max(B));                      % Normalizing...

% Plotting...


test
 figure(1);
 pcolor(xxP,zzP,B);
 colormap(jet);
 shading interp;
 axis equal;
 axis([-xPmax xPmax -zPmax zPmax]);
 xlabel('<-- x -->');ylabel('<-- z -->');
 title('Magnetic Field Distibution');
 colorbar;

figure(2);
surf(xxP,zzP,B,'FaceColor','interp',...
    'EdgeColor','none',...
    'FaceLighting','phong');
daspect([1 1 1]);
axis tight;
view(-10,30);
camlight right;
colormap(jet);
grid off;
axis off;
colorbar;
title('Magnetic Field Distibution');

 figure(3);
quiver(xxP,zzP,Bx,Bz);
colormap(lines);
 axis([-2*d 2*d -T*g T*g]);
 title('Magnetic Field Distibution');
 xlabel('<-- x -->');ylabel('<-- z -->');
 zoom on;


 % Computation of (H)Field  using Superposition principle..
% Compute H at each detector points due to each small cond elements & integrate them..
for p = 1:T
    for q = 1:N
        rx = xxP - xC(q);               % Displacement Vector along X direction from Conductor..
        ry = yC(q);                     % No detector points on Y direction..
        rz = zzP - h(p)*zC(q);          % zC Vertical location changes per Turn..

        r = sqrt(rx.^2+ry.^2+rz.^2);    % Displacement Magnitude for an element on the conductor..

        r3 = r.^3;


        Hx = (Bx + m*Ly(q).*rz./r3)*u0;      % m - direction of current element..
        Hy = (By - m*Lx(q).*rz./r3)*u0;
        Hz = (Bz + m*Lx(q).*ry./r3 - m*Ly(q).*rx./r3)*u0;
    end
end
 H= sqrt(Hx.^2 + Hy.^2 + Hz.^2);        % Magnitude of H..
H = H/max(max(H));                      % Normalizing...



























test
 figure(1);
 pcolor(xxP,zzP,H);
 colormap(jet);
 shading interp;
 axis equal;
 axis([-xPmax xPmax -zPmax zPmax]);
 xlabel('<-- x -->');ylabel('<-- z -->');
 title('H Field Distibution');
 colorbar;

figure(2);
surf(xxP,zzP,H,'FaceColor','interp',...
    'EdgeColor','none',...
    'FaceLighting','phong');
daspect([1 1 1]);
axis tight;
view(-10,30);
camlight right;
colormap(jet);
grid off;
axis off;
colorbar;
title('H Field Distibution');

 figure(3);
quiver(xxP,zzP,Hx,Hz);
colormap(lines);
 axis([-2*d 2*d -T*g T*g]);
 title('H Field Distibution');
 xlabel('<-- x -->');ylabel('<-- z -->');
 zoom on;














Published with MATLAB® R2015a

example of plot and find and mark maximum and minimum values on a plot using Matlab

Contents

• example of plot and find and mark maximum and minimum values on a plot
• close
• generate a simple plot
• find the mimimum value
• find the max value

example of plot and find and mark maximum and minimum values on a plot

Author: minhanhnguyen@q.com

close

close all; % Clear all windows
clear all; % Clear all variables
clc; % Clear console

generate a simple plot

x = linspace(-3,3);
y = (x/5-x.^3).*exp(-2*x.^2);
plot(x,y)

find the mimimum value

indexmin = find(min(y) == y);
xmin = x(indexmin);
ymin = y(indexmin);

strmin = ['Minimum = ',num2str(ymin)];
text(xmin,ymin,strmin,'HorizontalAlignment','left');

find the max value
indexmax = find(max(y) == y);
xmax = x(indexmax);
ymax = y(indexmax);
strmax = ['Maximum = ',num2str(ymax)];
text(xmax,ymax,strmax,'HorizontalAlignment','right');




Published with MATLAB® R2015a

example to display MRI image and data

• close
• display one of the MRI images
• 2-D Contour Slice
• Isocaps Show Cut-Away Surface
• Defining the View
• Slices 3-Dimensional MRI Data

close

close all; % Clear all windows
clear all; % Clear all variables
clc; % Clear console

% load the data and transform the data array from 4-D to 3-D
% The MRI data, D, is stored as a 128-by-128-by-1-by-27 array.
% Use the squeeze command to remove  4-D to 3-D.
% The result is a 128-by-128-by-27 array
load mri
D = squeeze(D);

display one of the MRI images

figure
colormap(map)
image_num = 10;
image(D(:,:,image_num))
axis image
x = xlim;
y = ylim;

2-D Contour Slice

contour plot uses the jet colormap

twodc = brighten(jet(length(map)),-.5);
figure;
colormap(twodc);
contourslice(D,[],[],image_num)
axis ij
xlim(x)
ylim(y)
daspect([1,1,1])

%%3-D Contour Slices
figure
colormap(twodc)
contourslice(D,[],[],[1,12,19,27],10);
view(3);
axis tight

%%Isosurface to the MRI Data
figure
colormap(map)
Ds = smooth3(D);
hiso = patch(isosurface(Ds,5),...
   'FaceColor',[1,.75,.65],...
   'EdgeColor','none');
   isonormals(Ds,hiso);

Isocaps Show Cut-Away Surface

 hcap = patch(isocaps(D,5),...
   'FaceColor','interp',...
   'EdgeColor','none');

Defining the View

%Define the view and set the aspect ratio (view, axis, daspect).


view(75,30)
axis tight
daspect([1,1,.4])
lightangle(75,30);

lighting gouraud
hcap.AmbientStrength = 0.5;
hiso.SpecularColorReflectance = 0;
hiso.SpecularExponent = 60;

figure;

close;

Slices 3-Dimensional MRI Data

load mri;%Load the MRI data
figure; montage(D,map) %view the 27 horizontal slices as a montage.
title('Horizontal Slices');

M1 = D(:,64,:,:); size(M1);
M2 = reshape(M1,[128 27]); size(M2)
figure; imshow(M2,map);
title('Sagittal - Raw Data');

T0 = maketform('affine',[0 -2.5; 1 0; 0 0]);

R2 = makeresampler({'cubic','nearest'},'fill');
M3 = imtransform(M2,T0,R2);
figure; imshow(M3,map);
title('Sagittal - IMTRANSFORM');

T1 = maketform('affine',[-2.5 0; 0 1; 68.5 0]);
inverseFcn = @(X,t) [X repmat(t.tdata,[size(X,1) 1])];
T2 = maketform('custom',3,2,[],inverseFcn,64);
Tc = maketform('composite',T1,T2);

R3 = makeresampler({'cubic','nearest','nearest'},'fill');

M4 = tformarray(D,Tc,R3,[4 1 2],[1 2],[66 128],[],0);
figure; imshow(M4,map);
title('Sagittal - TFORMARRAY');

T3 = maketform('affine',[-2.5 0 0; 0 1 0; 0 0 0.5; 68.5 0 -14]);
S = tformarray(D,T3,R3,[4 1 2],[1 2 4],[66 128 35],[],0);

S2 = padarray(S,[6 0 0 0],0,'both');
figure, montage(S2,map)
title('Sagittal Slices');




M1 = D(:,64,:,:); size(M1)


M2 = reshape(M1,[128 27]); size(M2)
figure, imshow(M2,map);
title('Sagittal - Raw Data');

R2 = makeresampler({'cubic','nearest'},'fill');
M3 = imtransform(M2,T0,R2);
figure, imshow(M3,map);
title('Sagittal - IMTRANSFORM')


T1 = maketform('affine',[-2.5 0; 0 1; 68.5 0]);
inverseFcn = @(X,t) [X repmat(t.tdata,[size(X,1) 1])];
T2 = maketform('custom',3,2,[],inverseFcn,64);
Tc = maketform('composite',T1,T2);


M4 = tformarray(D,Tc,R3,[4 1 2],[1 2],[66 128],[],0);


figure, imshow(M4,map);
title('Sagittal - TFORMARRAY');





T3 = maketform('affine',[-2.5 0 0; 0 1 0; 0 0 0.5; 68.5 0 -14]);


S = tformarray(D,T3,R3,[4 1 2],[1 2 4],[66 128 35],[],0);


S2 = padarray(S,[6 0 0 0],0,'both');
figure, montage(S2,map)
title('Sagittal Slices');


T4 = maketform('affine',[-2.5 0 0; 0 1 0; 0 0 -0.5; 68.5 0 61]);

C = tformarray(D,T4,R3,[4 2 1],[1 2 4],[66 128 45],[],0);
C2 = padarray(C,[6 0 0 0],0,'both');
figure, montage(C2,map)
title('Coronal Slices');

ans =

   128    27


ans =

   128     1     1    27


ans =

   128    27

Published with MATLAB® R2015a