Remidies for changed values in a vector as a result of fftshift?

Question

Robert 2017-2-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/325398-remidies-for-changed-values-in-a-vector-as-a-result-of-fftshift

评论： Star Strider 2017-2-16

Hi,

While rewriting a script, I noticed that the sum of a vector changes if ifftshift/fftshift has been carried out. Take the following example:

t=-10:.1:10-.1; y=exp(-t.^2/2); s1=sum(y); s2=sum(ifftshift(y)); s3=sum(fftshift(y)); d1=vpa(s1-s2); d2=vpa(s1-s3);

I get the following: d1=d2=0.0000000000000035527136788005009293556213378906

I also found that I get the same difference if I carry out the shift manually like:

y2=[y(101:200),y(1:100)]; s4=sum(y2); s4-s2=0

So my question is, why does the sum of the vector change if the vector is shifted in this manner and are there any ways to make sure that the sum stays the same without having to evaluate both of the sums and then re-scaling the shifted vector?

Thanks in advance, Robert

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2017-2-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/325398-remidies-for-changed-values-in-a-vector-as-a-result-of-fftshift#answer_255078

在 MATLAB Online 中打开

I believe you intend ‘d1-d2’ here:

d1=d2=0.0000000000000035527136788005009293556213378906

In any event, that value, 3.6E-15, is on the order of floating point approximation error. See: Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? for a thorough discussion.

2 个评论
显示无隐藏无

Robert 2017-2-16

Hi,

I meant that d1 and d2 gives the same result, but thank you for your answer, do you know if there are any ways of adjusting the floating point approximation? Like using more significant digits or something like that?

Star Strider 2017-2-16

My pleasure.

You can use single precision instead of the default double, but I would not recommend that. You’ve already discovered the Symbolic Math Toolbox and its extended-precision capabilities.

Another option is John D’Errico’s HPF - a big decimal class. I’ve no experience with it, since I rarely need precision beyond the MATLAB default. If you want extended-precision computations, it would definitely be worth exploring.

请先登录，再进行评论。