Adding noise to a Gaussian

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}.

[Walter Roberson]

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

Answer 1

[Neo]

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.

[Walter Roberson]

degrees = [1 2 10 15];
for K = 1 : length(degrees)
   degree = degrees(K);
   pp = polyfit(x, Gnew, degree);
   fit_Gnew{K} = polyval(x, pp);
end

[Neo]

How do I graph it then?

[Nicole Bonino]

how did you write the code for part b for Gnew to keep it one variable. I have Gnew1, Gnew2, etc. for each noise factor. to use this code for part C I would need one Gnew variable.

[Nicole Bonino]

I figure I must use a loop, but I can't seem to get it to work.

[Neo]

I am unsure of how to use just one Gnew variable either. Also can't figure out how to use Gnew = y + factor*noise cause if you manually put the values in for factor it keeps giving a size error

[Nicole Bonino]

I used noise=rand(1,100) to get my noise values and then Gnew1=y+0*noise, Gnew2=y+.5*noise, etc. and it worked. But I don't know how to use that code I made with Gnew for part C. I also am unsure of how many figures it is asking for. I read it as 4 figures each with 4 subplots but I don't think that is right.

[Walter Roberson]

degrees = [1 2 10 15];
nd = length(degrees);

bvals = [0.0, 0.5, 7.5, 15];
nb = length(bvals);

for Kb = 1 : nb
  b = bvals(Kb);
  Gnew{Kb} = .....
end

for Kd = 1 : nd
   subplot(nd, 1, Kd)
   degree = degrees(Kd);
   for Kb = 1 : nb
     b = bvals(Kb)
     pp = polyfit(x, Gnew{Kb}, degree);
     fit_Gnew = polyval(x, pp);
     plot(x, fit_Gnew);
     hold on
   end
end

[Walter Roberson]

4 subplots per figure, one per noise level. all of the different fitting degrees combined in the same subplot.

The code I show above does it the other way around, but you can easily switch the order of the statements.

[Nicole Bonino]

how would you make the Gnew variable? right now I have 4 seperate Gnew variables for each noise factor so this code cant work for me unless I have a single Gnew factor. I've been trying to make a for loop but it keeps giving me an error saying my dimensions don't agree for the multiplication in the Gnew equation. this is what I have so far.

A=100;

x=[-0.5:.01:(.5-.01)];

x_0=0;

s=1;

y=A.*exp((-(x-x_0).^2)./s);

figure(2)

G = Gaussian(A, x, x_0, s);

plot(x,G)

title('Gaussian with Given Values')

xlabel('x-axis')

ylabel('y-axis')

% part b

noise = randn(10);

x=1;

n=[0, .5, 7.5, 15];

for x=1:1:length(n);

     Gnew(n(x))=y+n*noise;

     x=x+1;

end

[Walter Roberson]

noise = randn(size(y));

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

[Image Analyst]

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

Answer 2

[Walter Roberson]

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.

[Image Analyst]

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().