Matlab level 7

Matlab  Part1 in electricity and electronics:

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) = I_m cos (w*t)

I(t) = I_m cos ((2*pi*f )*t)

V(t) = V_m cos (w*t)

V(t) = V_m cos ((2*pi*f )*t)

………………………………………..

I(t) = I_m sin (w*t)

I(t) = I_m sin ((2*pi*f )*t)

V(t) = V_m sin (w*t)

V(t) = V_m 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.

                                    Fig-1

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

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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.

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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');