Adding noise to a Gaussian

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Nicole Bonino 2015-8-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/232927-adding-noise-to-a-gaussian

评论： Image Analyst 2015-8-9

采纳的回答： Neo

在 MATLAB Online 中打开

My code keeps returning an error saying my signal-to-noise ratio must be a real scalar.

this is my code:

y=A.*exp((-(x-x_0).^2)./s);
% part a
A=100;
x=[-0.5:.01:.5-.01];
x_0=0;
s=1;
figure(2)
G=Gaussian(A,x,x_0,s);
plot(x,G)
% part b
n = rand(1,100);
Gnew1= y + 0*n;
Gnew2= y + 0.5*n;
Gnew3= y + 7.5*n;
Gnew4= y + 15*n;
figure(3)
w = awgn(x,n);
plot(x,G,x,w)
legend('Original Gaussian','Gaussian with Noise');
plot(x, Gnew1)
hold on
plot(x, Gnew2)
plot(x, Gnew3)
plot(x, Gnew4)
hold off

Here is the problem:

This problem deals with data fitting in the presence of noise.

a. Write a function Gaussian.m which will generate a 1D Gaussian function of the form y=A.*exp((-(x-x_0).^2)./s);, where s is the spread of the Gaussian, A is a constant factor and the mean x_0. The inputs to the function should be a vector of values (x), A, , and !. To test your function, plot the Gaussian corresponding to x= [-0.5:0.01:0.5-0.01], A = 100, s = 1, and x0= 0.

b. Add noise the Gaussian you generated above and plot the corresponding result. You may use the randn.m function in Matlab to generate a 100 random (noise) values between 0-1. Hence the new Gaussian function (Gnew = y + factor*noise) can be obtained. On the same graph, plot out Gnew for 4 different values of factor = {0.0, 0.5, 7.5, 15}.

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Walter Roberson 2015-8-8

Please show the traceback of the error message. Which line is reporting that error?

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采纳的回答

Neo 2015-8-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/232927-adding-noise-to-a-gaussian#answer_188752

Does anyone know how to do part C for this problem?

C. Use the polyval and polyfit functions to fit polynomials of different degrees to the Gnew functions generated in (b) above. Fit 4 polynomials corresponding to degrees of 1, 2, 10, and 15 to Gnew for each value of factor (i.e. 0.0, 0.5, 7.5, 15). You should use the subplot function to generate 4 subplots on a single figure, each subplot corresponding to a different noise level.

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Walter Roberson 2015-8-9

在 MATLAB Online 中打开

noise = randn(size(y));
for Kb = 1 : nb
  b = bvals(Kb);
  Gnew{Kb} = y + b .* noise;
end

Image Analyst 2015-8-9

Put that code into a function. Then just call the function for each of the 4 Gnew variables that you have.

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Walter Roberson 2015-8-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/232927-adding-noise-to-a-gaussian#answer_188716

在 MATLAB Online 中打开

http://www.mathworks.com/help/comm/ref/awgn.html

y = awgn(x,snr) adds white Gaussian noise to the vector signal x. The scalar snr specifies the signal-to-noise ratio per sample, in dB.

But your code has

n = rand(1,100);
w = awgn(x,n);

so the value you pass in for the second parameter is a vector 1 x 100, where the awgn routine needs a scalar.

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Image Analyst 2015-8-8

Not to mention the fact that it said to use randn() - it didn't mention awgn(). Why do you want to use both? I'd use only the one noise addition function that you were told to use, and that is randn().

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