Matlab level 7
Matlab Part1 in electricity and electronics:
Fig-1
Fig-3
Electrical / electronics Signals :
I will show you my friends some examples using matlab in
signal analysis and responses.
1-
a+ Firstly you know that:
Here using cosine signals in our application (Fig-1), but
also if you want to calculate using sine signals you can write the fonctions as
this.
I(t) =
Im cos (w*t)
I(t) =
Im cos ((2*pi*f )*t)
V(t) = Vm
cos (w*t)
V(t) = Vm
cos ((2*pi*f )*t)
………………………………………..
I(t) =
Im sin (w*t)
I(t) =
Im sin ((2*pi*f )*t)
V(t) = Vm
sin (w*t)
V(t) = Vm
sin ((2*pi*f )*t)
1-
b+ Secondly appling this
equations in our example using matlab:
Now in this example i used and explaned the time domain
inbetween –pi until +pi
so
I defined x between –pi until +pi.
Defined y1 using the addition or the superpossition of 2
cosine signals.
Y2 is the fast forrier transform of y1 in the time domain.
Y3 sa,ple cosine
signal.
Also in y1 first signal is 2*pi*f + another signal of
cosine type using amplitude of
0.5 v, doubling the
same cosine with the same phase (theta ø).
X remember is varies between –pi until + pi.
Another thing figure(1) our figure will appear in this
window output.
In the function subplot I used to define first part in
the graph with colors to differentiate between function responses so y1 ---> red,
y2 ---> blue, y3 ---> green.
Fig-2
I show you the electrical functions in graph fig1,fig2,
fig3 which using adding or superposition of
2 cosine functions, also fast furrier transform (fft), a simple cosine signal.
Fig-3
++++++++++++++++
1- In
this example i will show you another 4 signals with another 4 responses with
changing the frequencies and the phase angel.
So we will see 2 superposition signals and 1 fft and 1 cosine signal.
I defined it as shown in the figure using matlab file.
And in this example I used the function plot to show
you the output.
Fig-4
Fig-5
These applications can be used in time analysis of continuous
systems or for describing a superposition in physics and electronics, or seeing the
output of signal responses over the entire time domain interval.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Matlab Part2 in electricity and electronics:
Deblurring Images Using a Regularized Filter
This example shows how to use regularized
deconvolution to deblur images.
Regularized deconvolution can be used effectively when
constraints are applied on the recovered image (e.g., smoothness) and limited
information is known about the additive noise.
The blurred and
noisy image is restored by a constrained least square restoration algorithm that
uses a regularized filter.
Step 1: Read Image
The example
reads in an RGB image and cropsit to be 256-by-256-by-3.
The
deconvreg function can handle arrays of any dimension.
I = imread('tissue.png');
I = I(125+(1:256),1:256,:);
f1 = figure;
imshow(I);
figure(f1);
title('Original Image');
text(size(I,2),size(I,1)+15, ...
'Image courtesy of Alan Partin, Johns Hopkins
University', ...
'FontSize',7,'HorizontalAlignment','right');
Step 2: Simulate a Blur and Noise
Simulate a
real-life image that could be blurred (e.g., due to camera motion or lack of
focus) and noisy (e.g., due to randomdisturbances).
The example
simulates the blur by convolving a Gaussian filter with the true image
(usingimfilter).
The
Gaussian filter represents a point-spread function, PSF.
PSF = fspecial('gaussian',11,5);
Blurred = imfilter(I,PSF,'conv');
f2 = figure;
imshow(Blurred);
figure(f2);
title('Blurred');
We simulate
the noise by adding a Gaussian noise of variance V to the blurred image (using imnoise).
V = .02;
BlurredNoisy = imnoise(Blurred,'gaussian',0,V);
f3 = figure;
imshow(BlurredNoisy);
figure(f3);
title('Blurred& Noisy');
Step 3: Restore the Blurred and Noisy Image
Restore the
blurred and noisy image supplying noise power, NP, as the third input parameter.
To
illustrate how sensitive the algorithm is to the value of noise power, NP, the
example performs three restorations.
The first
restoration, reg1, uses the true NP. Note that the example outputs two parameter
shere.
The first return value, reg1, is the restored
image.
The second return value, LAGRA, is a
scalar, Lagrange multiplier, on which the deconvreg has converged.
This value
is used later in the example.
NP = V*numel(I); % noise
power
[reg1, LAGRA] = deconvreg(BlurredNoisy,PSF,NP);
f4 = figure;
imshow(reg1);
figure(f4);
title('Restoredwith NP');
The second
restoration, reg2, uses a slightly over-estimated noise power, which leads to a
poor resolution.
reg2 = deconvreg(BlurredNoisy,PSF,NP*1.3);
f5 = figure;
imshow(reg2);
figure(f5);
title('Restoredwithlarger NP');
The third restoration,
reg3, is given an under-estimated NP value.
This leads
to an overwhelming noise amplification and "ringing" from the image
borders.
reg3 = deconvreg(BlurredNoisy,PSF,NP/1.3);
f6 = figure;
imshow(reg3);
figure(f6);
title('Restoredwithsmaller NP');
Step 4: Reduce Noise Amplification and Ringing
Reduce the
noise amplification and "ringing" along the boundary of the image by
calling the edge taper function prior to deconvolution.
Note how
the image restorationbecomesless sensitive to the noise power parameter.
Use the
noise power value NP from the previous example.
Edged = edgetaper(BlurredNoisy,PSF);
reg4 = deconvreg(Edged,PSF,NP/1.3);
f7 = figure;
imshow(reg4);
figure(f7);
title('Edgetapereffect');
Step 5: Use the Lagrange Multiplier
Restore the
blurred and noisy image, assuming that the optimal solution is already found
and the corresponding Lagrange multiplier, LAGRA, is given.
In this case, any value passed for noise
power, NP, is ignored.
To
illustrate how sensitive the algorithm is to the LAGRA value, the example performs
three restorations.
The first
restoration (reg5) uses the LAGRA output from the earlier solution (LAGRA
output from first solution in Step 3).
reg5 = deconvreg(Edged,PSF,[],LAGRA);
f8 = figure;
imshow(reg5);
figure(f8);
title('Restoredwith LAGRA');
The second
restoration (reg6) uses 100*LAGRA which increases the significance of the
constraint.
By default,
this leads to over-smoothing of the image.
reg6 = deconvreg(Edged,PSF,[],LAGRA*100);
f9 = figure;
imshow(reg6);
figure(f9);
title('Restoredwith large LAGRA');
The third restoration
uses LAGRA/100 which weakens the constraint (the smooth ness requirement set
for the image).
It
amplifies the noise and eventually leads to a pure inverse filtering for LAGRA
= 0.
reg7 = deconvreg(Edged,PSF,[],LAGRA/100);
f10 = figure;
imshow(reg7);
figure(f10);
title('Restoredwithsmall LAGRA');
Step 6: Use a DifferentConstraint
Restore the
blurred and noisy image using a different constraint (REGOP) in the search for
the optimal solution.
Instead of constraining the image smoothness
(REGOP is Laplacian by default), constrain the image smoothness only in one
dimension (1-D Laplacian).
REGOP = [1 -2 1];
reg8 =
deconvreg(BlurredNoisy,PSF,[],LAGRA,REGOP);
f11 = figure;
imshow(reg8);
figure(f11);
title('Constrained by 1D Laplacian');
In 2017-2018 and 2018-2019.
RépondreSupprimerTeaching electronics, digital ciruits, matlab arround 8 levels, teaching examples html programing, veysis epowertrain, sensors and image fabrications....
Hope building a day to day instead of any other thing.
I wish you can build for your communities and countries by this great knowledge.
Thank you dear friends.