How to get a signal without NaN values?

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Haya Ali on 12 Mar 2023

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Commented: Walter Roberson on 14 Mar 2023

I have a signal and I have applied the Shannon's Nyquist Theorem to get the rate and the reconstructed signal by following formulas.

But I am getting NaN values in the Rate Signal. Is there any way that to not get the NaN values? Below is my code.

close all; clear all; clc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Addnum=20;%Number of additional data points in each time interval.
N=Addnum*length(X); %Length of the reconstructed signal(the continuous signal);
Rec=zeros([1,N]);
Rate=zeros([1,N]);
nx=zeros([1,N]);
NX=zeros([1,length(X)]);
zeroline=zeros([1,N]);
index=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
    if mod(i,Addnum)==1
        index=index+1;
        NX(index)=i;
    end
  nx(i)=i;  
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
Rec(i)=0;
Rate(i)=0;
for j=1:length(X)
    Rec(i)=Rec(i)+X(j)*sinc((1/Addnum)*(i-Addnum*(j-1)));
    Rate(i)=Rate(i)+X(j)*(cos((pi/Addnum)*(i-Addnum*(j-1)))/(i-Addnum*(j-1))-sin((pi/Addnum)*(i-Addnum*(j-1)))/((pi/Addnum)*(i-Addnum*(j-1))^2));
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mean_X=mean(X);
X=X-mean_X;
mean_Rec=mean(Rec);
Rec=Rec-mean_Rec;
plot(nx,Rec,'sg');
hold on
plot(nx,zeroline,'k');
plot(nx,Rate,'*b');
plot(NX,X,'or')
axis([1000 10000 -400 600])
legend ('Reconstructed Signal','zeroline','Rate Signal','BOLD Signal X')

4 Comments
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Dyuman Joshi on 12 Mar 2023

What you are trying to do for the variable Rate? Do you have a reference formula?

What value it should be instead of NaN?

Haya Ali on 12 Mar 2023

I have attached a formula for rate signal in the image. The value can be anything other than NaN

Accepted Answer

Image Analyst on 12 Mar 2023

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Direct link to this answer

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Open in MATLAB Online

Try removing the nans or infs

badIndexes = isnan(Rate) | isinf(Rate);
nx2 = nx(~badIndexes);
Rate2 = Rate(~badIndexes);
plot(nx2, Rate2, '*b');

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Image Analyst on 14 Mar 2023

OK. Though it's probably more trouble to avoid/prevent the NaNs than to just fix them afterwards. But whatever you intuitively feel most comfortable with is fine.

Walter Roberson on 14 Mar 2023

The code involves loop summing terms, some of which might be Nan. If you detect the potential for NaN at the term level, then you can omit adding that term to the summation, so you end up with a sum of non-NaN values that might contain useful information. If you wait until afterwards to detect the NaN then you lose the information in the non-NaN terms.

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